Predictive model for the growth kinetics of Staphylococcus aureus in raw pork developed using Integrated Pathogen Modeling Program (IPMP) 2013.

PubMed

Lee, Yong Ju; Jung, Byeong Su; Kim, Kee-Tae; Paik, Hyun-Dong

2015-09-01

A predictive model was performed to describe the growth of Staphylococcus aureus in raw pork by using Integrated Pathogen Modeling Program 2013 and a polynomial model as a secondary predictive model. S. aureus requires approximately 180 h to reach 5-6 log CFU/g at 10 °C. At 15 °C and 25 °C, approximately 48 and 20 h, respectively, are required to cause food poisoning. Predicted data using the Gompertz model was the most accurate in this study. For lag time (LT) model, bias factor (Bf) and accuracy factor (Af) values were both 1.014, showing that the predictions were within a reliable range. For specific growth rate (SGR) model, Bf and Af were 1.188 and 1.190, respectively. Additionally, both Bf and Af values of the LT and SGR models were close to 1, indicating that IPMP Gompertz model is more adequate for predicting the growth of S. aureus on raw pork than other models. Copyright © 2015 Elsevier Ltd. All rights reserved.

A model for predicting Xanthomonas arboricola pv. pruni growth as a function of temperature

PubMed Central

Llorente, Isidre; Montesinos, Emilio; Moragrega, Concepció

2017-01-01

A two-step modeling approach was used for predicting the effect of temperature on the growth of Xanthomonas arboricola pv. pruni, causal agent of bacterial spot disease of stone fruit. The in vitro growth of seven strains was monitored at temperatures from 5 to 35°C with a Bioscreen C system, and a calibrating equation was generated for converting optical densities to viable counts. In primary modeling, Baranyi, Buchanan, and modified Gompertz equations were fitted to viable count growth curves over the entire temperature range. The modified Gompertz model showed the best fit to the data, and it was selected to estimate the bacterial growth parameters at each temperature. Secondary modeling of maximum specific growth rate as a function of temperature was performed by using the Ratkowsky model and its variations. The modified Ratkowsky model showed the best goodness of fit to maximum specific growth rate estimates, and it was validated successfully for the seven strains at four additional temperatures. The model generated in this work will be used for predicting temperature-based Xanthomonas arboricola pv. pruni growth rate and derived potential daily doublings, and included as the inoculum potential component of a bacterial spot of stone fruit disease forecaster. PMID:28493954

Non-linear Growth Models in Mplus and SAS

PubMed Central

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Modeling the growth of Listeria monocytogenes in mold-ripened cheeses.

PubMed

Lobacz, Adriana; Kowalik, Jaroslaw; Tarczynska, Anna

2013-06-01

This study presents possible applications of predictive microbiology to model the safety of mold-ripened cheeses with respect to bacteria of the species Listeria monocytogenes during (1) the ripening of Camembert cheese, (2) cold storage of Camembert cheese at temperatures ranging from 3 to 15°C, and (3) cold storage of blue cheese at temperatures ranging from 3 to 15°C. The primary models used in this study, such as the Baranyi model and modified Gompertz function, were fitted to growth curves. The Baranyi model yielded the most accurate goodness of fit and the growth rates generated by this model were used for secondary modeling (Ratkowsky simple square root and polynomial models). The polynomial model more accurately predicted the influence of temperature on the growth rate, reaching the adjusted coefficients of multiple determination 0.97 and 0.92 for Camembert and blue cheese, respectively. The observed growth rates of L. monocytogenes in mold-ripened cheeses were compared with simulations run with the Pathogen Modeling Program (PMP 7.0, USDA, Wyndmoor, PA) and ComBase Predictor (Institute of Food Research, Norwich, UK). However, the latter predictions proved to be consistently overestimated and contained a significant error level. In addition, a validation process using independent data generated in dairy products from the ComBase database (www.combase.cc) was performed. In conclusion, it was found that L. monocytogenes grows much faster in Camembert than in blue cheese. Both the Baranyi and Gompertz models described this phenomenon accurately, although the Baranyi model contained a smaller error. Secondary modeling and further validation of the generated models highlighted the issue of usability and applicability of predictive models in the food processing industry by elaborating models targeted at a specific product or a group of similar products. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Hyperbolastic growth models: theory and application

PubMed Central

Tabatabai, Mohammad; Williams, David Keith; Bursac, Zoran

2005-01-01

Background Mathematical models describing growth kinetics are very important for predicting many biological phenomena such as tumor volume, speed of disease progression, and determination of an optimal radiation and/or chemotherapy schedule. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied to a wide range of medical and biological studies. We introduce a class of three and four parameter models called "hyperbolastic models" for accurately predicting and analyzing self-limited growth behavior that occurs e.g. in tumors. To illustrate the application and utility of these models and to gain a more complete understanding of them, we apply them to two sets of data considered in previously published literature. Results The results indicate that volumetric tumor growth follows the principle of hyperbolastic growth model type III, and in both applications at least one of the newly proposed models provides a better fit to the data than the classical models used for comparison. Conclusion We have developed a new family of growth models that predict the volumetric growth behavior of multicellular tumor spheroids with a high degree of accuracy. We strongly believe that the family of hyperbolastic models can be a valuable predictive tool in many areas of biomedical and epidemiological research such as cancer or stem cell growth and infectious disease outbreaks. PMID:15799781

Model comparison for Escherichia coli growth in pouched food.

PubMed

Fujikawa, Hiroshi; Yano, Kazuyoshi; Morozumi, Satoshi

2006-06-01

We recently studied the growth characteristics of Escherichia coli cells in pouched mashed potatoes (Fujikawa et al., J. Food Hyg. Soc. Japan, 47, 95-98 (2006)). Using those experimental data, in the present study, we compared a logistic model newly developed by us with the modified Gompertz and the Baranyi models, which are used as growth models worldwide. Bacterial growth curves at constant temperatures in the range of 12 to 34 degrees C were successfully described with the new logistic model, as well as with the other models. The Baranyi gave the least error in cell number and our model gave the least error in the rate constant and the lag period. For dynamic temperature, our model successfully predicted the bacterial growth, whereas the Baranyi model considerably overestimated it. Also, there was a discrepancy between the growth curves described with the differential equations of the Baranyi model and those obtained with DMfit, a software program for Baranyi model fitting. These results indicate that the new logistic model can be used to predict bacterial growth in pouched food.

Effects of Temperature, Water Activity, and Syrup Film Composition on the Growth of Wallemia sebi: Development and Assessment of a Model Predicting Growth Lags in Syrup Agar and Crystalline Sugar

PubMed Central

Vindeløv, Jannik; Arneborg, Nils

2002-01-01

We investigated the effects of temperature, water activity (aw), and syrup film composition on the CFU growth of Wallemia sebi in crystalline sugar. At a high aw (0.82) at both high (20°C) and low (10°C) temperatures, the CFU growth of W. sebi in both white and extrawhite sugar could be described using a modified Gompertz model. At a low aw (0.76), however, the modified Gompertz model could not be fitted to the CFU data obtained with the two sugars due to long CFU growth lags and low maximum specific CFU growth rates of W. sebi at 20°C and due to the fact that growth did not occur at 10°C. At an aw of 0.82, regardless of the temperature, the carrying capacity (i.e., the cell concentration at t = ∞) of extrawhite sugar was lower than that of white sugar. Together with the fact that the syrup film of extrawhite sugar contained less amino-nitrogen relative to other macronutrients than the syrup film of white sugar, these results suggest that CFU growth of W. sebi in extrawhite sugar may be nitrogen limited. We developed a secondary growth model which is able to predict colony growth lags of W. sebi on syrup agar as a function of temperature and aw. The ability of this model to predict CFU growth lags of W. sebi in crystalline sugar was assessed. PMID:11916681

Dynamic Predictive Model for Growth of Bacillus cereus from Spores in Cooked Beans.

PubMed

Juneja, Vijay K; Mishra, Abhinav; Pradhan, Abani K

2018-02-01

Kinetic growth data for Bacillus cereus grown from spores were collected in cooked beans under several isothermal conditions (10 to 49°C). Samples were inoculated with approximately 2 log CFU/g heat-shocked (80°C for 10 min) spores and stored at isothermal temperatures. B. cereus populations were determined at appropriate intervals by plating on mannitol-egg yolk-polymyxin agar and incubating at 30°C for 24 h. Data were fitted into Baranyi, Huang, modified Gompertz, and three-phase linear primary growth models. All four models were fitted to the experimental growth data collected at 13 to 46°C. Performances of these models were evaluated based on accuracy and bias factors, the coefficient of determination ( R 2 ), and the root mean square error. Based on these criteria, the Baranyi model best described the growth data, followed by the Huang, modified Gompertz, and three-phase linear models. The maximum growth rates of each primary model were fitted as a function of temperature using the modified Ratkowsky model. The high R 2 values (0.95 to 0.98) indicate that the modified Ratkowsky model can be used to describe the effect of temperature on the growth rates for all four primary models. The acceptable prediction zone (APZ) approach also was used for validation of the model with observed data collected during single and two-step dynamic cooling temperature protocols. When the predictions using the Baranyi model were compared with the observed data using the APZ analysis, all 24 observations for the exponential single rate cooling were within the APZ, which was set between -0.5 and 1 log CFU/g; 26 of 28 predictions for the two-step cooling profiles also were within the APZ limits. The developed dynamic model can be used to predict potential B. cereus growth from spores in beans under various temperature conditions or during extended chilling of cooked beans.

Growth curves for ostriches (Struthio camelus) in a Brazilian population.

PubMed

Ramos, S B; Caetano, S L; Savegnago, R P; Nunes, B N; Ramos, A A; Munari, D P

2013-01-01

The objective of this study was to fit growth curves using nonlinear and linear functions to describe the growth of ostriches in a Brazilian population. The data set consisted of 112 animals with BW measurements from hatching to 383 d of age. Two nonlinear growth functions (Gompertz and logistic) and a third-order polynomial function were applied. The parameters for the models were estimated using the least-squares method and Gauss-Newton algorithm. The goodness-of-fit of the models was assessed using R(2) and the Akaike information criterion. The R(2) calculated for the logistic growth model was 0.945 for hens and 0.928 for cockerels and for the Gompertz growth model, 0.938 for hens and 0.924 for cockerels. The third-order polynomial fit gave R(2) of 0.938 for hens and 0.924 for cockerels. Among the Akaike information criterion calculations, the logistic growth model presented the lowest values in this study, both for hens and for cockerels. Nonlinear models are more appropriate for describing the sigmoid nature of ostrich growth.

Skew-t fits to mortality data--can a Gaussian-related distribution replace the Gompertz-Makeham as the basis for mortality studies?

PubMed

Clark, Jeremy S C; Kaczmarczyk, Mariusz; Mongiało, Zbigniew; Ignaczak, Paweł; Czajkowski, Andrzej A; Klęsk, Przemysław; Ciechanowicz, Andrzej

2013-08-01

Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.

Compound equation developed for postnatal growth of birds and mammals

NASA Technical Reports Server (NTRS)

Laird, A. K.

1968-01-01

Compound growth equation was developed in which the rate of this linear growth process is regarded as proportional to the mass already attained at any instant by an underlying Gompertz process. This compound growth model was fitted to the growth data of a variety of birds and mammals of both sexes.

Modeling Surface Growth of Escherichia coli on Agar Plates

PubMed Central

Fujikawa, Hiroshi; Morozumi, Satoshi

2005-01-01

Surface growth of Escherichia coli cells on a membrane filter placed on a nutrient agar plate under various conditions was studied with a mathematical model. The surface growth of bacterial cells showed a sigmoidal curve with time on a semilogarithmic plot. To describe it, a new logistic model that we presented earlier (H. Fujikawa et al., Food Microbiol. 21:501-509, 2004) was modified. Growth curves at various constant temperatures (10 to 34°C) were successfully described with the modified model (model III). Model III gave better predictions of the rate constant of growth and the lag period than a modified Gompertz model and the Baranyi model. Using the parameter values of model III at the constant temperatures, surface growth at various temperatures was successfully predicted. Surface growth curves at various initial cell numbers were also sigmoidal and converged to the same maximum cell numbers at the stationary phase. Surface growth curves at various nutrient levels were also sigmoidal. The maximum cell number and the rate of growth were lower as the nutrient level decreased. The surface growth curve was the same as that in a liquid, except for the large curvature at the deceleration period. These curves were also well described with model III. The pattern of increase in the ATP content of cells grown on a surface was sigmoidal, similar to that for cell growth. We discovered several characteristics of the surface growth of bacterial cells under various growth conditions and examined the applicability of our model to describe these growth curves. PMID:16332768

Growth and mortality of larval Myctophum affine (Myctophidae, Teleostei).

PubMed

Namiki, C; Katsuragawa, M; Zani-Teixeira, M L

2015-04-01

The growth and mortality rates of Myctophum affine larvae were analysed based on samples collected during the austral summer and winter of 2002 from south-eastern Brazilian waters. The larvae ranged in size from 2·75 to 14·00 mm standard length (L(S)). Daily increment counts from 82 sagittal otoliths showed that the age of M. affine ranged from 2 to 28 days. Three models were applied to estimate the growth rate: linear regression, exponential model and Laird-Gompertz model. The exponential model best fitted the data, and L(0) values from exponential and Laird-Gompertz models were close to the smallest larva reported in the literature (c. 2·5 mm L(S)). The average growth rate (0·33 mm day(-1)) was intermediate among lanternfishes. The mortality rate (12%) during the larval period was below average compared with other marine fish species but similar to some epipelagic fishes that occur in the area. © 2015 The Fisheries Society of the British Isles.

Use of the modified Gompertz equation to assess the Stevia rebaudiana Bertoni antilisterial kinetics.

PubMed

Belda-Galbis, Clara Miracle; Pina-Pérez, María Consuelo; Espinosa, Josepa; Marco-Celdrán, Aurora; Martínez, Antonio; Rodrigo, Dolores

2014-04-01

In order to assess the antibacterial activity of Stevia rebaudiana Bertoni (Stevia), Listeria innocua growth was characterized at 37 °C, in reference medium supplemented with a leaf infusion, a crude extract, and a steviol glycosides purified extract. Experimental data were fitted to the modified Gompertz model and the antibacterial activity of Stevia was determined based on the lag time (λ) and the maximum growth rate (μmax) reached, depending on the incubation conditions. As the leaf infusion showed the most marked elongation of λ and the most marked μmax reduction, its antimicrobial effect was evaluated at different concentrations, at 37, 22 and 10 °C. According to the results obtained, in general, the lower the temperature or the higher the Stevia concentration, the longer the λ and the lower the μmax, statistically significant being the effect of reducing temperature from 37 or 22 to 10 °C, the effect of increasing Stevia concentration from 0 or 0.5 to 1.5 or 2.5% (w/v), at 37 °C, and the elongation of λ observed in presence of 1.5 and 2.5% (w/v) of Stevia, at 22 °C. These results show that Stevia could be a bacterial growth control measure if a cold chain failure occurs. Copyright © 2013 Elsevier Ltd. All rights reserved.

Deciphering death: a commentary on Gompertz (1825) 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies'.

PubMed

Kirkwood, Thomas B L

2015-04-19

In 1825, the actuary Benjamin Gompertz read a paper, 'On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies', to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental 'law of mortality' has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

Deciphering death: a commentary on Gompertz (1825) ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’

PubMed Central

Kirkwood, Thomas B. L.

2015-01-01

In 1825, the actuary Benjamin Gompertz read a paper, ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’, to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz's work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz's way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750242

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

Description of Aspergillus flavus growth under the influence of different factors (water activity, incubation temperature, protein and fat concentration, pH, and cinnamon essential oil concentration) by kinetic, probability of growth, and time-to-detection models.

PubMed

Kosegarten, Carlos E; Ramírez-Corona, Nelly; Mani-López, Emma; Palou, Enrique; López-Malo, Aurelio

2017-01-02

A Box-Behnken design was used to determine the effect of protein concentration (0, 5, or 10g of casein/100g), fat (0, 3, or 6g of corn oil/100g), a w (0.900, 0.945, or 0.990), pH (3.5, 5.0, or 6.5), concentration of cinnamon essential oil (CEO, 0, 200, or 400μL/kg) and incubation temperature (15, 25, or 35°C) on the growth of Aspergillus flavus during 50days of incubation. Mold response under the evaluated conditions was modeled by the modified Gompertz equation, logistic regression, and time-to-detection model. The obtained polynomial regression models allow the significant coefficients (p<0.05) for linear, quadratic and interaction effects for the Gompertz equation's parameters to be identified, which adequately described (R 2 >0.967) the studied mold responses. After 50days of incubation, every tested model system was classified according to the observed response as 1 (growth) or 0 (no growth), then a binary logistic regression was utilized to model A. flavus growth interface, allowing to predict the probability of mold growth under selected combinations of tested factors. The time-to-detection model was utilized to estimate the time at which A. flavus visible growth begins. Water activity, temperature, and CEO concentration were the most important factors affecting fungal growth. It was observed that there is a range of possible combinations that may induce growth, such that incubation conditions and the amount of essential oil necessary for fungal growth inhibition strongly depend on protein and fat concentrations as well as on the pH of studied model systems. The probabilistic model and the time-to-detection models constitute another option to determine appropriate storage/processing conditions and accurately predict the probability and/or the time at which A. flavus growth occurs. Copyright © 2016 Elsevier B.V. All rights reserved.

Phase transition in tumor growth: I avascular development

NASA Astrophysics Data System (ADS)

Izquierdo-Kulich, E.; Rebelo, I.; Tejera, E.; Nieto-Villar, J. M.

2013-12-01

We propose a mechanism for avascular tumor growth based on a simple chemical network. This model presents a logistic behavior and shows a “second order” phase transition. We prove the fractal origin of the empirical logistics and Gompertz constant and its relation to mitosis and apoptosis rate. Finally, the thermodynamics framework developed demonstrates the entropy production rate as a Lyapunov function during avascular tumor growth.

Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

PubMed

González, Maraelys Morales; Joa, Javier Antonio González; Cabrales, Luis Enrique Bergues; Pupo, Ana Elisa Bergues; Schneider, Baruch; Kondakci, Suleyman; Ciria, Héctor Manuel Camué; Reyes, Juan Bory; Jarque, Manuel Verdecia; Mateus, Miguel Angel O'Farril; González, Tamara Rubio; Brooks, Soraida Candida Acosta; Cáceres, José Luis Hernández; González, Gustavo Victoriano Sierra

2017-03-07

Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×10 5 ) are inoculated to 28 BALB/c male mice. Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

Modelling the growth of the brown frog (Rana dybowskii)

PubMed Central

Du, Xiao-peng; Hu, Zong-fu; Cui, Li-yong

2018-01-01

Well-controlled development leads to uniform body size and a better growth rate; therefore, the ability to determine the growth rate of frogs and their period of sexual maturity is essential for producing healthy, high-quality descendant frogs. To establish a working model that can best predict the growth performance of frogs, the present study examined the growth of one-year-old and two-year-old brown frogs (Rana dybowskii) from metamorphosis to hibernation (18 weeks) and out-hibernation to hibernation (20 weeks) under the same environmental conditions. Brown frog growth was studied and mathematically modelled using various nonlinear, linear, and polynomial functions. The model input values were statistically evaluated using parameters such as the Akaike’s information criterion. The body weight/size ratio (Kwl) and Fulton’s condition factor (K) were used to compare the weight and size of groups of frogs during the growth period. The results showed that the third- and fourth-order polynomial models provided the most consistent predictions of body weight for age 1 and age 2 brown frogs, respectively. Both the Gompertz and third-order polynomial models yielded similarly adequate results for the body size of age 1 brown frogs, while the Janoschek model produced a similarly adequate result for the body size of age 2 brown frogs. The Brody and Janoschek models yielded the highest and lowest estimates of asymptotic weight, respectively, for the body weights of all frogs. The Kwl value of all frogs increased from 0.40 to 3.18. The K value of age 1 frogs decreased from 23.81 to 9.45 in the first four weeks. The K value of age 2 frogs remained close to 10. Graphically, a sigmoidal trend was observed for body weight and body size with increasing age. The results of this study will be useful not only for amphibian research but also for frog farming management strategies and decisions.

Age, growth and fall diet of channel catfish in Cheat Lake, West Virginia

USGS Publications Warehouse

Hilling, Corbin D.; Welsh, Stuart A.; Smith, Dustin M.

2016-01-01

Acidification has historically impaired Cheat Lake's fish community, but recent mitigation efforts within the Cheat River watershed have improved water quality and species richness. Presently, channel catfish Ictalurus punctatus are abundant and attain desirable sizes for anglers. We evaluated the age, growth, and fall diet of the population. We collected a sample of 155 channel catfish from Cheat Lake from 5 August to 4 December 2014, a subset of which we aged (n = 148) using lapillus otoliths. We fit four growth models (von Bertalanffy, logistic, Gompertz, and power) to length-at-age data and compared models using an information theoretic approach. We collected fall diets from 55 fish sampled from 13 October to 4 December 2014. Total lengths of individuals in the sample ranged from 154 to 721 mm and ages ranged from 2 to 19 y. We AICc-selected the von Bertalanffy growth model as the best approximating model, and the power and Gompertz models also had considerable support. Diets were numerically dominated by Diptera larvae, specifically Chironomidae and Chaoboridae, while 39% of stomachs contained terrestrial food items. This study provides baseline data for management of Cheat Lake's channel catfish population. Further, this study fills a knowledge gap in the scientific literature on channel catfish, because few previously published studies have examined the population ecology of channel catfish in the Central Appalachian region.

Inhibitory effect of chlorine and ultraviolet radiation on growth of Listeria monocytogenes in chicken breast and development of predictive growth models.

PubMed

Oh, S R; Kang, I; Oh, M H; Ha, S D

2014-01-01

The inhibitory effect of chlorine (50, 100, and 200 mg/kg) was investigated with and without UV radiation (300 mW·s/cm(2)) for the growth of Listeria monocytogenes in chicken breast meat. Using a polynomial model, predictive growth models were also developed as a function of chlorine concentration, UV exposure, and storage temperature (4, 10, and 15°C). A maximum L. monocytogenes reduction (0.8 log cfu, cfu/g) was obtained when combining chlorine at 200 mg/kg and UV at 300 mW·s/cm(2), and a maximum synergistic effect (0.4 log cfu/g) was observed when using chlorine at 100 mg/kg and UV at 300 mW·s/cm(2). Primary models developed for specific growth rate and lag time showed a good fitness (R(2) > 0.91), as determined by the reparameterized Gompertz equation. Secondary polynomial models were obtained using nonlinear regression analysis. The developed models were validated with mean square error, bias factor, and accuracy factor, which were 0.0003, 0.96, and 1.11, respectively, for specific growth rate and 7.69, 0.99, and 1.04, respectively, for lag time. The treatment of chlorine and UV did not change the color and texture of chicken breast after 7 d of storage at 4°C. As a result, the combination of chlorine at 100 mg/kg and UV at 300 mW·s/cm(2) appears to an effective method into inhibit L. monocytogenes growth in broiler carcasses with no negative effects on color and textural quality. Based on the validation results, the predictive models can be used to accurately predict L. monocytogenes growth in chicken breast.

Modeling the growth of Listeria monocytogenes on the surface of smear- or mold-ripened cheese.

PubMed

Schvartzman, M Sol; Gonzalez-Barron, Ursula; Butler, Francis; Jordan, Kieran

2014-01-01

Surface-ripened cheeses are matured by means of manual or mechanical technologies posing a risk of cross-contamination, if any cheeses are contaminated with Listeria monocytogenes. In predictive microbiology, primary models are used to describe microbial responses, such as growth rate over time and secondary models explain how those responses change with environmental factors. In this way, primary models were used to assess the growth rate of L. monocytogenes during ripening of the cheeses and the secondary models to test how much the growth rate was affected by either the pH and/or the water activity (aw) of the cheeses. The two models combined can be used to predict outcomes. The purpose of these experiments was to test three primary (the modified Gompertz equation, the Baranyi and Roberts model, and the Logistic model) and three secondary (the Cardinal model, the Ratowski model, and the Presser model) mathematical models in order to define which combination of models would best predict the growth of L. monocytogenes on the surface of artificially contaminated surface-ripened cheeses. Growth on the surface of the cheese was assessed and modeled. The primary models were firstly fitted to the data and the effects of pH and aw on the growth rate (μmax) were incorporated and assessed one by one with the secondary models. The Logistic primary model by itself did not show a better fit of the data among the other primary models tested, but the inclusion of the Cardinal secondary model improved the final fit. The aw was not related to the growth of Listeria. This study suggests that surface-ripened cheese should be separately regulated within EU microbiological food legislation and results expressed as counts per surface area rather than per gram.

Classification scheme for phenomenological universalities in growth problems in physics and other sciences.

PubMed

Castorina, P; Delsanto, P P; Guiot, C

2006-05-12

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.

Consistency Properties for Growth Model Parameters Under an Infill Asymptotics Domain

DTIC Science & Technology

2010-09-01

Gompertz in 1825 [15], was initially used for actuarial projections. Winsor’s 1932 reparameterization of the Gompertz curve in [38] is given by f(t;K, a, b...these assumptions it is possible to construct a pathological example which, while mathematically interesting, is of no practical use to a practitioner...Abramowitz, Milton and Irene A. Stegun. Handbook of Mathematical Functions . Washington D.C.: National Bureau of Standards, 1972. [2] Allgower, E. L

Evolutionary model of an anonymous consumer durable market

NASA Astrophysics Data System (ADS)

Kaldasch, Joachim

2011-07-01

An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation. The theory suggests that products play the role of species in biological evolutionary models. It implies that the evolution of man-made products can be arranged into an evolutionary tree. The model suggests that each product can be characterized by its product fitness. The fitness space contains elements of both sites of the market, supply and demand. The unit sales of products with a higher product fitness compared to the mean fitness increase. Durables with a constant fitness advantage replace other goods according to a logistic law. The model predicts in particular that the mean price exhibits an exponential decrease over a long time period for durable goods. The evolutionary diffusion process is directly related to this price decline and is governed by Gompertz equation. Therefore it is denoted as Gompertz diffusion. Describing the aggregate sales as the sum of first, multiple and replacement purchase the product life cycle can be derived. Replacement purchase causes periodic variations of the sales determined by the finite lifetime of the good (Juglar cycles). The model suggests that both, Bass- and Gompertz diffusion may contribute to the product life cycle of a consumer durable. The theory contains the standard equilibrium view of a market as a special case. It depends on the time scale, whether an equilibrium or evolutionary description is more appropriate. The evolutionary framework is used to derive also the size, growth rate and price distribution of manufacturing business units. It predicts that the size distribution of the business units (products) is lognormal

Gompertz type dechanneling functions for protons in <1 0 0>, <1 1 0> and <1 1 1> Si crystal channels

NASA Astrophysics Data System (ADS)

Petrović, S.; Erić, M.; Kokkoris, M.; Nešković, N.

2007-03-01

In this work the energy dependences of the Gompertz type sigmoidal dechanneling function parameters for protons in <1 0 0>, <1 1 0> and <1 1 1> Si crystal channels is investigated theoretically. The proton energy range considered is between 1 and 10 MeV. The original dechanneling functions are generated using a realistic Monte Carlo computer simulation code. We show that the Gompertz type dechanneling function, having two parameters, lc and k, representing the dechanneling range and rate, respectively, approximate accurately the original dechanneling function. It is also shown that the energy dependences of parameters lc and k can be approximated by a linear function and a sum of two exponential functions, respectively. The results obtained can be used for accurate reproduction of experimental proton channeling spectra recorded in the backscattering geometry.

Growth process and model simulation of three different classes of Schima superba in a natural subtropical forest in China

NASA Astrophysics Data System (ADS)

Wei, Hui; Deng, Xiangwen; Ouyang, Shuai; Chen, Lijun; Chu, Yonghe

2017-01-01

Schima superba is an important fire-resistant, high-quality timber species in southern China. Growth in height, diameter at breast height (DBH), and volume of the three different classes (overtopped, average and dominant) of S. superba were examined in a natural subtropical forest. Four growth models (Richards, edited Weibull, Logistic and Gompertz) were selected to fit the growth of the three different classes of trees. The results showed that there was a fluctuation phenomenon in height and DBH current annual growth process of all three classes. Multiple intersections were found between current annual increment (CAI) and mean annual increment (MAI) curves of both height and DBH, but there was no intersection between volume CAI and MAI curves. All selected models could be used to fit the growth of the three classes of S. superba, with determinant coefficients above 0.9637. However, the edited Weibull model performed best with the highest R2 and the lowest root of mean square error (RMSE). S. superba is a fast-growing tree with a higher growth rate during youth. The height and DBH CAIs of overtopped, average and dominant trees reached growth peaks at ages 5-10, 10-15 and 15-20 years, respectively. According to model simulation, the volume CAIs of overtopped, average and dominant trees reached growth peaks at ages 17, 55 and 76 years, respectively. The biological rotation ages of the overtopped, average and dominant trees of S. superba were 29, 85 and 128 years, respectively.

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

Numerical solution of a logistic growth model for a population with Allee effect considering fuzzy initial values and fuzzy parameters

NASA Astrophysics Data System (ADS)

Amarti, Z.; Nurkholipah, N. S.; Anggriani, N.; Supriatna, A. K.

2018-03-01

Predicting the future of population number is among the important factors that affect the consideration in preparing a good management for the population. This has been done by various known method, one among them is by developing a mathematical model describing the growth of the population. The model usually takes form in a differential equation or a system of differential equations, depending on the complexity of the underlying properties of the population. The most widely used growth models currently are those having a sigmoid solution of time series, including the Verhulst logistic equation and the Gompertz equation. In this paper we consider the Allee effect of the Verhulst’s logistic population model. The Allee effect is a phenomenon in biology showing a high correlation between population size or density and the mean individual fitness of the population. The method used to derive the solution is the Runge-Kutta numerical scheme, since it is in general regarded as one among the good numerical scheme which is relatively easy to implement. Further exploration is done via the fuzzy theoretical approach to accommodate the impreciseness of the initial values and parameters in the model.

Mathematical modelling of temperature effect on growth kinetics of Pseudomonas spp. on sliced mushroom (Agaricus bisporus).

PubMed

Tarlak, Fatih; Ozdemir, Murat; Melikoglu, Mehmet

2018-02-02

The growth data of Pseudomonas spp. on sliced mushrooms (Agaricus bisporus) stored between 4 and 28°C were obtained and fitted to three different primary models, known as the modified Gompertz, logistic and Baranyi models. The goodness of fit of these models was compared by considering the mean squared error (MSE) and the coefficient of determination for nonlinear regression (pseudo-R 2 ). The Baranyi model yielded the lowest MSE and highest pseudo-R 2 values. Therefore, the Baranyi model was selected as the best primary model. Maximum specific growth rate (r max ) and lag phase duration (λ) obtained from the Baranyi model were fitted to secondary models namely, the Ratkowsky and Arrhenius models. High pseudo-R 2 and low MSE values indicated that the Arrhenius model has a high goodness of fit to determine the effect of temperature on r max . Observed number of Pseudomonas spp. on sliced mushrooms from independent experiments was compared with the predicted number of Pseudomonas spp. with the models used by considering the B f and A f values. The B f and A f values were found to be 0.974 and 1.036, respectively. The correlation between the observed and predicted number of Pseudomonas spp. was high. Mushroom spoilage was simulated as a function of temperature with the models used. The models used for Pseudomonas spp. growth can provide a fast and cost-effective alternative to traditional microbiological techniques to determine the effect of storage temperature on product shelf-life. The models can be used to evaluate the growth behaviour of Pseudomonas spp. on sliced mushroom, set limits for the quantitative detection of the microbial spoilage and assess product shelf-life. Copyright © 2017 Elsevier B.V. All rights reserved.

On Selective Harvesting of an Inshore-Offshore Fishery: A Bioeconomic Model

ERIC Educational Resources Information Center

Purohit, D.; Chaudhuri, K. S.

2004-01-01

A bioeconomic model is developed for the selective harvesting of a single species, inshore-offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic…

Age and growth parameters of shark-like batoids.

PubMed

White, J; Simpfendorfer, C A; Tobin, A J; Heupel, M R

2014-05-01

Estimates of life-history parameters were made for shark-like batoids of conservation concern Rhynchobatus spp. (Rhynchobatus australiae, Rhynchobatus laevis and Rhynchobatus palpebratus) and Glaucostegus typus using vertebral ageing. The sigmoid growth functions, Gompertz and logistic, best described the growth of Rhynchobatus spp. and G. typus, providing the best statistical fit and most biologically appropriate parameters. The two-parameter logistic was the preferred model for Rhynchobatus spp. with growth parameter estimates (both sexes combined) L(∞) = 2045 mm stretch total length, LST and k = 0·41 year⁻¹. The same model was also preferred for G. typus with growth parameter estimates (both sexes combined) L∞  = 2770 mm LST and k = 0·30 year⁻¹. Annual growth-band deposition could not be excluded in Rhynchobatus spp. using mark-recaptured individuals. Although morphologically similar G. typus and Rhynchobatus spp. have differing life histories, with G. typus longer lived, slower growing and attaining a larger maximum size. © 2014 The Fisheries Society of the British Isles.

Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil

NASA Astrophysics Data System (ADS)

Moura, N. J.; Ribeiro, Marcelo B.

2013-05-01

This paper discusses the empirical validity of Goodwin’s (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz-Pareto distribution (GPD). This is formed by the combination of the Gompertz curve, representing the overwhelming majority of the population (˜99%), with the Pareto power law, representing the tiny richest part (˜1%). In line with Goodwin’s original model, we identify the Gompertzian part with the workers and the Paretian component with the class of capitalists. Since the GPD parameters are obtained for each year and the Goodwin macroeconomics is a time evolving model, we use previously determined, and further extended here, Brazilian GPD parameters, as well as unemployment data, to study the time evolution of these quantities in Brazil from 1981 to 2009 by means of the Goodwin dynamics. This is done in the original Goodwin model and an extension advanced by Desai et al. (2006). As far as Brazilian data is concerned, our results show partial qualitative and quantitative agreement with both models in the studied time period, although the original one provides better data fit. Nevertheless, both models fall short of a good empirical agreement as they predict single center cycles which were not found in the data. We discuss the specific points where the Goodwin dynamics must be improved in order to provide a more realistic representation of the dynamics of economic systems.

Variation in growth form and precocity at birth in eutherian mammals.

PubMed Central

Gaillard, J M; Pontier, D; Allaine, D; Loison, A; Herve, J C; Heizmann, A

1997-01-01

Using the flexible Chapman-Richards model for describing the growth curves from birth to adulthood of 69 species of eutherian mammals, we demonstrate that growth form differs among eutherian mammals. Thereby the commonly used Gompertz model can no longer be considered as the general model for describing mammalian growth. Precocial mammals have their peak growth rate earlier in the growth process than altricial mammals. However, the position on the altricial-precocial continuum accounts for most growth-form differences only between mammalian lineages. Within mammalian genera differences in growth form are not related to precocity at birth. This indicates that growth form may have been associated with precocity at birth early in mammalian evolution, when broad patterns of body development radiated. We discuss four non-exclusive interpretations to account for the role of precocity at birth on the observed variation in growth form among mammals. Precocial and altricial mammals could differ according to (i) the distribution of energy output by the mother, (ii) the ability of the young to assimilate the milk yield, (iii) the allocation of energy by the young between competing functions and (iv) the position of birth between conception and attainment of physical maturity. PMID:9225478

Modeling the Effect of Storage Temperatures on the Growth of Listeria monocytogenes on Ready-to-Eat Ham and Sausage.

PubMed

Luo, Ke; Hong, Sung-Sam; Oh, Deog-Hwan

2015-09-01

The aim of this study was to model the growth kinetics of Listeria monocytogenes on ready-to-eat ham and sausage at different temperatures (4 to 35°C). The observed data fitted well with four primary models (Baranyi, modified Gompertz, logistic, and Huang) with high coefficients of determination (R(2) > 0.98) at all measured temperatures. After the mean square error (0.009 to 0.051), bias factors (0.99 to1.06), and accuracy factors (1.01 to 1.09) were obtained in all models, the square root and the natural logarithm model were employed to describe the relation between temperature and specific growth rate (SGR) and lag time (LT) derived from the primary models. These models were validated against the independent data observed from additional experiments using the acceptable prediction zone method and the proportion of the standard error of prediction. All secondary models based on each of the four primary models were acceptable to describe the growth of the pathogen in the two samples. The validation results indicate that the optimal primary model for estimating the SGR was the Baranyi model, and the optimal primary model for estimating LT was the logistic model in ready-to-eat (RTE) ham. The Baranyi model was also the optimal model to estimate the SGR and LT in RTE sausage. These results could be used to standardize predictive models, which are commonly used to identify critical control points in hazard analysis and critical control point systems or for the quantitative microbial risk assessment to improve the food safety of RTE meat products.

Growth curves and age-related changes in carcass characteristics, organs, serum parameters, and intestinal transporter gene expression in domestic pigeon (Columba livia).

PubMed

Gao, C Q; Yang, J X; Chen, M X; Yan, H C; Wang, X Q

2016-04-01

Two experiments were conducted to fit growth curves, and determine age-related changes in carcass characteristics, organs, serum biochemical parameters, and gene expression of intestinal nutrient transporters in domestic pigeon (Columba livia). In experiment 1, body weight (BW) of 30 pigeons was respectively determined at 1, 3, 7, 14, 21, 28, and 35 days old to fit growth curves and to describe the growth of pigeons. In experiment 2, eighty-four 1-day-old squabs were grouped by weight into 7 groups. On d 1, 3, 7, 14, 21, 28, and 35, twelve birds from each group were randomly selected for slaughter and post-slaughter analysis. The results showed that BW of pigeons increased rapidly from d 1 to d 28 (a 25.7-fold increase), and then had little change until d 35. The Logistic, Gompertz, and Von Bertalanffy functions can all be well fitted with the growth curve of domestic pigeons (R2>0.90) and the Gompertz model showed the highest R2value among the models (R2=0.9997). The equation of Gompertz model was Y=507.72×e-(3.76exp(-0.17t))(Y=BW of pigeon (g); t=time (day)). In addition, breast meat yield (%) increased with age throughout the experiment, whereas the leg meat yield (%) reached to the peak on d 14. Serum total protein, albumin, globulin, and glucose concentration were increased with age, whereas serum uric acid concentration was decreased (P<0.05). Furthermore, the gene expressions of nutrient transporters (y+LAT2, LAT1, B0AT1, PepT1, and NHE2) in jejunum of pigeon were increased with age. The results of correlation analysis showed the gene expressions of B0AT1, PepT1, and NHE2 had positive correlations with BW (0.73

Model-based characterisation of growth performance and l-lactic acid production with high optical purity by thermophilic Bacillus coagulans in a lignin-supplemented mixed substrate medium.

PubMed

Glaser, Robert; Venus, Joachim

2017-07-25

Three Bacillus coagulans strains were characterised in terms of their ability to grow in lignin-containing fermentation media and to consume the lignocellulose-related sugars glucose, xylose, and arabinose. An optical-density high-throughput screening was used for precharacterisation by means of different mathematical models for comparison (Logistic, Gompertz, Baranyi, Richards & Stannard, and Schnute). The growth response was characterised by the maximum growth rate and lag time. For a comparison of the screening and fermentation results, an unstructured mathematical model was proposed to characterise the lactate production, bacterial growth and substrate consumption. The growth model was then applied to fermentation procedures using wheat straw hydrolysates. The results indicated that the unstructured growth model can be used to evaluate lactate producing fermentation. Under the experimental fermentation conditions, one strain showed the ability to tolerate a high lignin concentration (2.5g/L) but lacked the capacity for sufficient pentose uptake. The lactate yield of the strains that were able to consume all sugar fractions of glucose, xylose and arabinose was ∼83.4%. A photometric measurement at 280nm revealed a dynamic change in alkali-lignin concentrations during lactate producing fermentation. A test of decolourisation of vanillin, ferulic acid, and alkali-lignin samples also showed the decolourisation performance of the B. coagulans strains under study. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

Measuring aging rates of mice subjected to caloric restriction and genetic disruption of growth hormone signaling

PubMed Central

Koopman, Jacob J.E.; van Heemst, Diana; van Bodegom, David; Bonkowski, Michael S.; Sun, Liou Y.; Bartke, Andrzej

2016-01-01

Caloric restriction and genetic disruption of growth hormone signaling have been shown to counteract aging in mice. The effects of these interventions on aging are examined through age-dependent survival or through the increase in age-dependent mortality rates on a logarithmic scale fitted to the Gompertz model. However, these methods have limitations that impede a fully comprehensive disclosure of these effects. Here we examine the effects of these interventions on murine aging through the increase in age-dependent mortality rates on a linear scale without fitting them to a model like the Gompertz model. Whereas these interventions negligibly and non-consistently affected the aging rates when examined through the age-dependent mortality rates on a logarithmic scale, they caused the aging rates to increase at higher ages and to higher levels when examined through the age-dependent mortality rates on a linear scale. These results add to the debate whether these interventions postpone or slow aging and to the understanding of the mechanisms by which they affect aging. Since different methods yield different results, it is worthwhile to compare their results in future research to obtain further insights into the effects of dietary, genetic, and other interventions on the aging of mice and other species. PMID:26959761

Measuring aging rates of mice subjected to caloric restriction and genetic disruption of growth hormone signaling.

PubMed

Koopman, Jacob J E; van Heemst, Diana; van Bodegom, David; Bonkowski, Michael S; Sun, Liou Y; Bartke, Andrzej

2016-03-01

Caloric restriction and genetic disruption of growth hormone signaling have been shown to counteract aging in mice. The effects of these interventions on aging are examined through age-dependent survival or through the increase in age-dependent mortality rates on a logarithmic scale fitted to the Gompertz model. However, these methods have limitations that impede a fully comprehensive disclosure of these effects. Here we examine the effects of these interventions on murine aging through the increase in age-dependent mortality rates on a linear scale without fitting them to a model like the Gompertz model. Whereas these interventions negligibly and non-consistently affected the aging rates when examined through the age-dependent mortality rates on a logarithmic scale, they caused the aging rates to increase at higher ages and to higher levels when examined through the age-dependent mortality rates on a linear scale. These results add to the debate whether these interventions postpone or slow aging and to the understanding of the mechanisms by which they affect aging. Since different methods yield different results, it is worthwhile to compare their results in future research to obtain further insights into the effects of dietary, genetic, and other interventions on the aging of mice and other species.

Use of nonlinear models for describing scrotal circumference growth in Guzerat bulls raised under grazing conditions.

PubMed

Loaiza-Echeverri, A M; Bergmann, J A G; Toral, F L B; Osorio, J P; Carmo, A S; Mendonça, L F; Moustacas, V S; Henry, M

2013-03-15

The objective was to use various nonlinear models to describe scrotal circumference (SC) growth in Guzerat bulls on three farms in the state of Minas Gerais, Brazil. The nonlinear models were: Brody, Logistic, Gompertz, Richards, Von Bertalanffy, and Tanaka, where parameter A is the estimated testis size at maturity, B is the integration constant, k is a maturating index and, for the Richards and Tanaka models, m determines the inflection point. In Tanaka, A is an indefinite size of the testis, and B and k adjust the shape and inclination of the curve. A total of 7410 SC records were obtained every 3 months from 1034 bulls with ages varying between 2 and 69 months (<240 days of age = 159; 241-365 days = 451; 366-550 days = 1443; 551-730 days = 1705; and >731 days = 3652 SC measurements). Goodness of fit was evaluated by coefficients of determination (R(2)), error sum of squares, average prediction error (APE), and mean absolute deviation. The Richards model did not reach the convergence criterion. The R(2) were similar for all models (0.68-0.69). The error sum of squares was lowest for the Tanaka model. All models fit the SC data poorly in the early and late periods. Logistic was the model which best estimated SC in the early phase (based on APE and mean absolute deviation). The Tanaka and Logistic models had the lowest APE between 300 and 1600 days of age. The Logistic model was chosen for analysis of the environmental influence on parameters A and k. Based on absolute growth rate, SC increased from 0.019 cm/d, peaking at 0.025 cm/d between 318 and 435 days of age. Farm, year, and season of birth significantly affected size of adult SC and SC growth rate. An increase in SC adult size (parameter A) was accompanied by decreased SC growth rate (parameter k). In conclusion, SC growth in Guzerat bulls was characterized by an accelerated growth phase, followed by decreased growth; this was best represented by the Logistic model. The inflection point occurred at

Differential segmental growth of the vertebral column of the rat (Rattus norvegicus).

PubMed

Bergmann, Philip J; Melin, Amanda D; Russell, Anthony P

2006-01-01

Despite the pervasive occurrence of segmental morphologies in the animal kingdom, the study of segmental growth is almost entirely lacking, but may have significant implications for understanding the development of these organisms. We investigate the segmental and regional growth of the entire vertebral column of the rat (Rattus norvegicus) by fitting a Gompertz curve to length and age data for each vertebra and each vertebral region. Regional lengths are calculated by summing constituent vertebral lengths and intervertebral space lengths for cervical, thoracic, lumbar, sacral, and caudal regions. Gompertz curves allow for the estimation of parameters representing neonatal and adult vertebral and regional lengths, as well as initial growth rate and the rate of exponential growth decay. Findings demonstrate differences between neonatal and adult rats in terms of relative vertebral lengths, and differential growth rates between sequential vertebrae and vertebral regions. Specifically, relative differences in the length of vertebrae indicate increasing differences caudad. Vertebral length in neonates increases from the atlas to the middle of the thoracic series and decreases in length caudad, while adult vertebral lengths tend to increase caudad. There is also a general trend of increasing vertebral and regional initial growth and rate of growth decay caudad. Anteroposterior patterns of growth are sexually dimorphic, with males having longer vertebrae than females at any given age. Differences are more pronounced (a) increasingly caudad along the body axis, and (b) in adulthood than in neonates. Elucidated patterns of growth are influenced by a combination of developmental, functional, and genetic factors.

Prediction of microbial growth in fresh-cut vegetables treated with acidic electrolyzed water during storage under various temperature conditions.

PubMed

Koseki, S; Itoh, K

2001-12-01

Effects of storage temperature (1, 5, and 10 degrees C) on growth of microbial populations (total aerobic bacteria, coliform bacteria, Bacillus cereus, and psychrotrophic bacteria) on acidic electrolyzed water (AcEW)-treated fresh-cut lettuce and cabbage were determined. A modified Gompertz function was used to describe the kinetics of microbial growth. Growth data were analyzed using regression analysis to generate "best-fit" modified Gompertz equations, which were subsequently used to calculate lag time, exponential growth rate, and generation time. The data indicated that the growth kinetics of each bacterium were dependent on storage temperature, except at 1 degrees C storage. At 1 degrees C storage, no increases were observed in bacterial populations. Treatment of vegetables with AcEW produced a decrease in initial microbial populations. However, subsequent growth rates were higher than on nontreated vegetables. The recovery time required by the reduced microbial population to reach the initial (treated with tap water [TW]) population was also determined in this study, with the recovery time of the microbial population at 10 degrees C being <3 days. The benefits of reducing the initial microbial populations on fresh-cut vegetables were greatly affected by storage temperature. Results from this study could be used to predict microbial quality of fresh-cut lettuce and cabbage throughout their distribution.

2D motility tracking of Pseudomonas putida KT2440 in growth phases using video microscopy

PubMed Central

Davis, Michael L.; Mounteer, Leslie C.; Stevens, Lindsey K.; Miller, Charles D.; Zhou, Anhong

2011-01-01

Pseudomonas putida KT2440 is a gram negative motile soil bacterium important in bioremediation and biotechnology. Thus, it is important to understand its motility characteristics as individuals and in populations. Population characteristics were determined using a modified Gompertz model. Video microscopy and imaging software were utilized to analyze two dimensional (2D) bacteria movement tracks to quantify individual bacteria behavior. It was determined that inoculum density increased the lag time as seeding densities decreased, and that the maximum specific growth rate decreased as seeding densities increased. Average bacterial velocity remained relatively similar throughout exponential growth phase (~20.9 µm/sec), while maximum velocities peak early in exponential growth phase at a velocity of 51.2 µm/sec. Pseudomonas putida KT2440 also favor smaller turn angles indicating they often continue in the same direction after a change in flagella rotation throughout the exponential growth phase. PMID:21334971

A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing.

PubMed

Doona, Christopher J; Feeherry, Florence E; Ross, Edward W

2005-04-15

Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a(w), pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207-345 MPa (30,000-50,000 psi) and the temperature (T) range of 30-50 degrees C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial

Aging, Maturation and Growth of Sauropodomorph Dinosaurs as Deduced from Growth Curves Using Long Bone Histological Data: An Assessment of Methodological Constraints and Solutions

PubMed Central

Griebeler, Eva Maria; Klein, Nicole; Sander, P. Martin

2013-01-01

Information on aging, maturation, and growth is important for understanding life histories of organisms. In extinct dinosaurs, such information can be derived from the histological growth record preserved in the mid-shaft cortex of long bones. Here, we construct growth models to estimate ages at death, ages at sexual maturity, ages at which individuals were fully-grown, and maximum growth rates from the growth record preserved in long bones of six sauropod dinosaur individuals (one indeterminate mamenchisaurid, two Apatosaurus sp., two indeterminate diplodocids, and one Camarasaurus sp.) and one basal sauropodomorph dinosaur individual (Plateosaurus engelhardti). Using these estimates, we establish allometries between body mass and each of these traits and compare these to extant taxa. Growth models considered for each dinosaur individual were the von Bertalanffy model, the Gompertz model, and the logistic model (LGM), all of which have inherently fixed inflection points, and the Chapman-Richards model in which the point is not fixed. We use the arithmetic mean of the age at the inflection point and of the age at which 90% of asymptotic mass is reached to assess respectively the age at sexual maturity or the age at onset of reproduction, because unambiguous indicators of maturity in Sauropodomorpha are lacking. According to an AIC-based model selection process, the LGM was the best model for our sauropodomorph sample. Allometries established are consistent with literature data on other Sauropodomorpha. All Sauropodomorpha reached full size within a time span similar to scaled-up modern mammalian megaherbivores and had similar maximum growth rates to scaled-up modern megaherbivores and ratites, but growth rates of Sauropodomorpha were lower than of an average mammal. Sauropodomorph ages at death probably were lower than that of average scaled-up ratites and megaherbivores. Sauropodomorpha were older at maturation than scaled-up ratites and average mammals, but

Aging, Maturation and Growth of Sauropodomorph Dinosaurs as Deduced from Growth Curves Using Long Bone Histological Data: An Assessment of Methodological Constraints and Solutions.

PubMed

Griebeler, Eva Maria; Klein, Nicole; Sander, P Martin

2013-01-01

Information on aging, maturation, and growth is important for understanding life histories of organisms. In extinct dinosaurs, such information can be derived from the histological growth record preserved in the mid-shaft cortex of long bones. Here, we construct growth models to estimate ages at death, ages at sexual maturity, ages at which individuals were fully-grown, and maximum growth rates from the growth record preserved in long bones of six sauropod dinosaur individuals (one indeterminate mamenchisaurid, two Apatosaurus sp., two indeterminate diplodocids, and one Camarasaurus sp.) and one basal sauropodomorph dinosaur individual (Plateosaurus engelhardti). Using these estimates, we establish allometries between body mass and each of these traits and compare these to extant taxa. Growth models considered for each dinosaur individual were the von Bertalanffy model, the Gompertz model, and the logistic model (LGM), all of which have inherently fixed inflection points, and the Chapman-Richards model in which the point is not fixed. We use the arithmetic mean of the age at the inflection point and of the age at which 90% of asymptotic mass is reached to assess respectively the age at sexual maturity or the age at onset of reproduction, because unambiguous indicators of maturity in Sauropodomorpha are lacking. According to an AIC-based model selection process, the LGM was the best model for our sauropodomorph sample. Allometries established are consistent with literature data on other Sauropodomorpha. All Sauropodomorpha reached full size within a time span similar to scaled-up modern mammalian megaherbivores and had similar maximum growth rates to scaled-up modern megaherbivores and ratites, but growth rates of Sauropodomorpha were lower than of an average mammal. Sauropodomorph ages at death probably were lower than that of average scaled-up ratites and megaherbivores. Sauropodomorpha were older at maturation than scaled-up ratites and average mammals, but

2D motility tracking of Pseudomonas putida KT2440 in growth phases using video microscopy.

PubMed

Davis, Michael L; Mounteer, Leslie C; Stevens, Lindsey K; Miller, Charles D; Zhou, Anhong

2011-05-01

Pseudomonas putida KT2440 is a gram negative motile soil bacterium important in bioremediation and biotechnology. Thus, it is important to understand its motility characteristics as individuals and in populations. Population characteristics were determined using a modified Gompertz model. Video microscopy and imaging software were utilized to analyze two dimensional (2D) bacteria movement tracks to quantify individual bacteria behavior. It was determined that inoculum density increased the lag time as seeding densities decreased, and that the maximum specific growth rate decreased as seeding densities increased. Average bacterial velocity remained relatively similar throughout the exponential growth phase (~20.9 μm/s), while maximum velocities peak early in the exponential growth phase at a velocity of 51.2 μm/s. P. putida KT2440 also favors smaller turn angles indicating that they often continue in the same direction after a change in flagella rotation throughout the exponential growth phase. Copyright © 2011 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

Slow growth of the overexploited milk shark Rhizoprionodon acutus affects its sustainability in West Africa.

PubMed

Ba, A; Diouf, K; Guilhaumon, F; Panfili, J

2015-10-01

Age and growth of Rhizoprionodon acutus were estimated from vertebrae age bands. From December 2009 to November 2010, 423 R. acutus between 37 and 112 cm total length (LT ) were sampled along the Senegalese coast. Marginal increment ratio was used to check annual band deposition. Three growth models were adjusted to the length at age and compared using Akaike's information criterion. The Gompertz growth model with estimated size at birth appeared to be the best and resulted in growth parameters of L∞ = 139.55 (LT ) and K = 0.17 year(-1) for females and L∞ = 126.52 (LT ) and K = 0.18 year(-1) for males. The largest female and male examined were 8 and 9 years old, but the majority was between 1 and 3 years old. Ages at maturity estimated were 5.8 and 4.8 years for females and males, respectively. These results suggest that R. acutus is a slow-growing species, which render the species particularly vulnerable to heavy fishery exploitation. The growth parameters estimated in this study are crucial for stock assessments and for demographic analyses to evaluate the sustainability of commercial harvests. © 2015 The Fisheries Society of the British Isles.

A Decentralized Wireless Solution to Monitor and Diagnose PV Solar Module Performance Based on Symmetrized-Shifted Gompertz Functions

PubMed Central

Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C.

2015-01-01

This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper. PMID:26230694

A Decentralized Wireless Solution to Monitor and Diagnose PV Solar Module Performance Based on Symmetrized-Shifted Gompertz Functions.

PubMed

Molina-García, Angel; Campelo, José Carlos; Blanc, Sara; Serrano, Juan José; García-Sánchez, Tania; Bueso, María C

2015-07-29

This paper proposes and assesses an integrated solution to monitor and diagnose photovoltaic (PV) solar modules based on a decentralized wireless sensor acquisition system. Both DC electrical variables and environmental data are collected at PV module level using low-cost and high-energy efficiency node sensors. Data is real-time processed locally and compared with expected PV module performances obtained by a PV module model based on symmetrized-shifted Gompertz functions (as previously developed and assessed by the authors). Sensor nodes send data to a centralized sink-computing module using a multi-hop wireless sensor network architecture. Such integration thus provides extensive analysis of PV installations, and avoids off-line tests or post-processing processes. In comparison with previous approaches, this solution is enhanced with a low-cost system and non-critical performance constraints, and it is suitable for extensive deployment in PV power plants. Moreover, it is easily implemented in existing PV installations, since no additional wiring is required. The system has been implemented and assessed in a Spanish PV power plant connected to the grid. Results and estimations of PV module performances are also included in the paper.

On the Gompertzian growth in the fractal space-time.

PubMed

Molski, Marcin; Konarski, Jerzy

2008-06-01

An analytical approach to determination of time-dependent temporal fractal dimension b(t)(t) and scaling factor a(t)(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values b(t)(t) and a(t)(t) at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=a(t)tb(t) and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.

Microbial modeling of Alicyclobacillus acidoterrestris CRA 7152 growth in orange juice with nisin added.

PubMed

Peña, Wilmer Edgard Luera; de Massaguer, Pilar Rodriguez

2006-08-01

The adaptation time of Alicyclobacillus acidoterrestris CRA 7152 in orange juice was determined as a response to pH (3 to 5.8), temperature (20 to 54 degrees C), soluble solids concentration ((o)Brix; 11 to 19 (o)Brix), and nisin concentration (0 to 70 IU/ ml) effects. A four-factor central composite rotational design was used. Viable microorganisms were enumerated by plating on K medium (pH 3.7). Two primary models were used to represent growth and adaptation time. A second-order polynomial model was applied to analyze the effects of factors. Results showed that the Baranyi and Roberts model was better than the modified Gompertz model, considering the determination coefficient (R2) for experimental data description. Inhibition of bacteria can be obtained through several studied combinations for at least 47 days of storage. The shortest period of adaptation was observed between 37 to 45 degrees C, with pHs between 4 and 5, yet the longest periods of adaptation could be obtained around 20 degrees C with pHs close to 3.0. Statistical analysis of the quadratic model showed that the adaptation time increased as temperature or pH decreased, and as nisin concentration or soluble solids increased. The model showed that adaptation time has a minimum value for juice without nisin added, with 13.5% soluble solids, pH 5.0, and incubated at 43.8 degrees C. The statistical parameters that validated this model were an R2 of 0.816, a bias factor of 0.96, and an accuracy factor of 1.14. Manipulation of more than one factor, as well as the use of an antimicrobial agent, can be an alternative to preventing the development of A. acidoterrestris in orange juice, thus contributing to increased orange juice shelf life.

Observing and modeling dynamics in terrestrial gross primary productivity and phenology from remote sensing: An assessment using in-situ measurements

NASA Astrophysics Data System (ADS)

Verma, Manish K.

Terrestrial gross primary productivity (GPP) is the largest and most variable component of the carbon cycle and is strongly influenced by phenology. Realistic characterization of spatio-temporal variation in GPP and phenology is therefore crucial for understanding dynamics in the global carbon cycle. In the last two decades, remote sensing has become a widely-used tool for this purpose. However, no study has comprehensively examined how well remote sensing models capture spatiotemporal patterns in GPP, and validation of remote sensing-based phenology models is limited. Using in-situ data from 144 eddy covariance towers located in all major biomes, I assessed the ability of 10 remote sensing-based methods to capture spatio-temporal variation in GPP at annual and seasonal scales. The models are based on different hypotheses regarding ecophysiological controls on GPP and span a range of structural and computational complexity. The results lead to four main conclusions: (i) at annual time scale, models were more successful capturing spatial variability than temporal variability; (ii) at seasonal scale, models were more successful in capturing average seasonal variability than interannual variability; (iii) simpler models performed as well or better than complex models; and (iv) models that were best at explaining seasonal variability in GPP were different from those that were best able to explain variability in annual scale GPP. Seasonal phenology of vegetation follows bounded growth and decay, and is widely modeled using growth functions. However, the specific form of the growth function affects how phenological dynamics are represented in ecosystem and remote sensing-base models. To examine this, four different growth functions (the logistic, Gompertz, Mirror-Gompertz and Richards function) were assessed using remotely sensed and in-situ data collected at several deciduous forest sites. All of the growth functions provided good statistical representation of in

Conifers in cold environments synchronize maximum growth rate of tree-ring formation with day length.

PubMed

Rossi, Sergio; Deslauriers, Annie; Anfodillo, Tommaso; Morin, Hubert; Saracino, Antonio; Motta, Renzo; Borghetti, Marco

2006-01-01

Intra-annual radial growth rates and durations in trees are reported to differ greatly in relation to species, site and environmental conditions. However, very similar dynamics of cambial activity and wood formation are observed in temperate and boreal zones. Here, we compared weekly xylem cell production and variation in stem circumference in the main northern hemisphere conifer species (genera Picea, Pinus, Abies and Larix) from 1996 to 2003. Dynamics of radial growth were modeled with a Gompertz function, defining the upper asymptote (A), x-axis placement (beta) and rate of change (kappa). A strong linear relationship was found between the constants beta and kappa for both types of analysis. The slope of the linear regression, which corresponds to the time at which maximum growth rate occurred, appeared to converge towards the summer solstice. The maximum growth rate occurred around the time of maximum day length, and not during the warmest period of the year as previously suggested. The achievements of photoperiod could act as a growth constraint or a limit after which the rate of tree-ring formation tends to decrease, thus allowing plants to safely complete secondary cell wall lignification before winter.

Uneven futures of human lifespans: reckonings from Gompertz mortality rates, climate change, and air pollution.

PubMed

Finch, Caleb E; Beltrán-Sánchez, Hiram; Crimmins, Eileen M

2014-01-01

The past 200 years have enabled remarkable increases in human lifespans through improvements in the living environment that have nearly eliminated infections as a cause of death through improved hygiene, public health, medicine, and nutrition. We argue that the limit to lifespan may be approaching. Since 1997, no one has exceeded Jeanne Calment's record of 122.5 years, despite an exponential increase of centenarians. Moreover, the background mortality may be approaching a lower limit. We calculate from Gompertz coefficients that further increases in longevity to approach a life expectancy of 100 years in 21st century cohorts would require 50% slower mortality rate accelerations, which would be a fundamental change in the rate of human aging. Looking into the 21st century, we see further challenges to health and longevity from the continued burning of fossil fuels that contribute to air pollution as well as global warming. Besides increased heat waves to which elderly are vulnerable, global warming is anticipated to increase ozone levels and facilitate the spread of pathogens. We anticipate continuing socioeconomic disparities in life expectancy.

Modeling Math Growth Trajectory--An Application of Conventional Growth Curve Model and Growth Mixture Model to ECLS K-5 Data

ERIC Educational Resources Information Center

Lu, Yi

2016-01-01

To model students' math growth trajectory, three conventional growth curve models and three growth mixture models are applied to the Early Childhood Longitudinal Study Kindergarten-Fifth grade (ECLS K-5) dataset in this study. The results of conventional growth curve model show gender differences on math IRT scores. When holding socio-economic…

Nonlinear Gompertz Curve Models of Achievement Gaps in Mathematics and Reading

ERIC Educational Resources Information Center

Cameron, Claire E.; Grimm, Kevin J.; Steele, Joel S.; Castro-Schilo, Laura; Grissmer, David W.

2015-01-01

This study examined achievement trajectories in mathematics and reading from school entry through the end of middle school with linear and nonlinear growth curves in 2 large longitudinal data sets (National Longitudinal Study of Youth--Children and Young Adults and Early Childhood Longitudinal Study--Kindergarten Cohort [ECLS-K]). The S-shaped…

Anaerobic digestion characteristics of pig manures depending on various growth stages and initial substrate concentrations in a scaled pig farm in Southern China.

PubMed

Zhang, Wanqin; Lang, Qianqian; Wu, Shubiao; Li, Wei; Bah, Hamidou; Dong, Renjie

2014-03-01

The characteristics of anaerobic digestion of pig manure from different growth stages were investigated. According to growth stage, batch experiments were performed using gestating sow manure (GSM), swine nursery with post-weaned piglet manure (SNM), growing fattening manure (GFM) and mixed manure (MM) as substrates at four substrate concentrations (40, 50, 65 and 80gVS/L) under mesophilic conditions. The maximum methane yields of MM, SNM, GSM and GFM were 354.7, 328.7, 282.4 and 263.5mLCH4/gVSadded, respectively. Volatile fatty acids/total inorganic carbon (VFA/TIC) ratio increased from 0.10 to 0.89 when loading increased from 40 to 80gVS/L for GFM. The modified Gompertz model shows a better fit to the experimental results than the first order model with a lower difference between measured and predicted methane yields. The kinetic parameters indicated that the methane production curve on the basis of differences in biodegradability of the pig manure at different growth stages. Copyright © 2014 Elsevier Ltd. All rights reserved.

BGFit: management and automated fitting of biological growth curves.

PubMed

Veríssimo, André; Paixão, Laura; Neves, Ana Rute; Vinga, Susana

2013-09-25

Existing tools to model cell growth curves do not offer a flexible integrative approach to manage large datasets and automatically estimate parameters. Due to the increase of experimental time-series from microbiology and oncology, the need for a software that allows researchers to easily organize experimental data and simultaneously extract relevant parameters in an efficient way is crucial. BGFit provides a web-based unified platform, where a rich set of dynamic models can be fitted to experimental time-series data, further allowing to efficiently manage the results in a structured and hierarchical way. The data managing system allows to organize projects, experiments and measurements data and also to define teams with different editing and viewing permission. Several dynamic and algebraic models are already implemented, such as polynomial regression, Gompertz, Baranyi, Logistic and Live Cell Fraction models and the user can add easily new models thus expanding current ones. BGFit allows users to easily manage their data and models in an integrated way, even if they are not familiar with databases or existing computational tools for parameter estimation. BGFit is designed with a flexible architecture that focus on extensibility and leverages free software with existing tools and methods, allowing to compare and evaluate different data modeling techniques. The application is described in the context of bacterial and tumor cells growth data fitting, but it is also applicable to any type of two-dimensional data, e.g. physical chemistry and macroeconomic time series, being fully scalable to high number of projects, data and model complexity.

Tumour model with intrusive morphology, progressive phenotypical heterogeneity and memory

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Alqahtani, Rubayyi T.

2018-03-01

The model of a tumour, taking into account invasive morphology, progressive phenotypical heterogeneity and also memory, is developed and analyzed in this paper. Three models are investigated: first we consider the model describing the proliferation concentrates in proximity of tumour boundaries, in which the oxygen levels are pronounced. Then we consider the model where the oxygen around the tumour is considered to be unchanged by the vascular system. Finally, we investigate the model of growth of tumours using the concept of non-local operators with the Mittag-Leffler kernel. We provide the numerical solution using the extended 3/8 Simpson method for the new trends of fractional integration for the proliferation concentrates in the proximity of the tumour model. Then we provide the exact solutions of the Gompertz model with three different fractional differentiations involving power law, exponential decay law and the Mittag-Leffler law.

Predicting bacterial growth in raw, salted, and cooked chicken breast fillets during storage.

PubMed

Galarz, Liane Aldrighi; Fonseca, Gustavo Graciano; Prentice, Carlos

2016-09-01

Growth curves were evaluated for aerobic mesophilic and psychrotrophic bacteria, Pseudomonas spp. and Staphylococcus spp., grown in raw, salted, and cooked chicken breast at 2, 4, 7, 10, 15, and 20 ℃, respectively, using the modified Gompertz and modified logistic models. Shelf life was determined based on microbiological counts and sensory analysis. Temperature increase reduced the shelf life, which varied from 10 to 26 days at 2 ℃, from nine to 21 days at 4 ℃, from six to 12 days at 7 ℃, from four to eight days at 10 ℃, from two to four days at 15 ℃, and from one to two days at 20 ℃. In most cases, cooked chicken breast showed the highest microbial count, followed by raw breast and lastly salted breast. The data obtained here were useful for the generation of mathematical models and parameters. The models presented high correlation and can be used for predictive purposes in the poultry meat supply chain. © The Author(s) 2015.

Life-long protein malnutrition in the rat (Rattus norvegicus) results in altered patterns of craniofacial growth and smaller individuals

PubMed Central

Lobe, Shannon L; Bernstein, Marica C; German, Rebecca Z

2006-01-01

Dietary protein is a limiting factor in mammalian growth, significantly affecting the non-linear trajectories of skeletal growth. Young females may be particularly vulnerable to protein malnutrition if the restriction is not lifted before they become reproductive. With such early malnutrition, limited amino acids would be partitioned between two physiological objectives, successful reproduction vs. continued growth. Thus, the consequences of protein malnutrition could affect more than one generation. However, few studies have quantified these cross-generational effects. Our objective was to test for differences in skeletal growth in a second generation of malnourished rats compared with rats malnourished only post-weaning, the first generation and with controls. In this longitudinal study we modelled the growth of 22 craniofacial measurements with the logistic Gompertz equation, and tested for differences in the equation's parameters among the diet groups. The female offspring of post-weaning malnourished dams did not catch up in size to the first generation or to controls, although certain aspects of their craniofacial skeleton were less affected than others. The second generation's growth trajectories resembled the longer and slower growth of the first malnourished generation. There was a complex interaction between developmental processes and early nutritional environment, which affected variation of adult size. PMID:16761979

Incidence of the Bertillon and Gompertz effects on the outcome of clinical trials

NASA Astrophysics Data System (ADS)

Roehner, Bertrand M.

2014-11-01

The accounts of medical trials provide very detailed information about the patients’ health conditions. On the contrary, almost no vital data such as marital status or age distribution are usually given. Yet, some of these factors can have a notable impact on the overall death rate, thereby changing the outcome and conclusions of the trial. This paper focuses on two of these variables. The first is marital status; its effect on life expectancy (which will be referred to as the Bertillon effect) may double death rates in all age intervals. The second variable is the age distribution of the oldest patients. Because of the exponential nature of Gompertz’s law changes in the distribution of ages in the oldest age group can have dramatic consequences on the overall number of deaths. One should recall that the death rate at the age of 82 is 40 times higher than at the age of 37. It will be seen that randomization alone can hardly take care of these problems. Appropriate remedies are easy to formulate however. First, the marital status of patients as well as the age distribution of those over 65 should be documented for both study groups. Then, thanks to these data and based on the Bertillon and Gompertz laws, it will become possible to perform appropriate corrections. Such corrections will notably improve the reliability and accuracy of the conclusions, especially in trials which include a large proportion of elderly subjects.

Predicting the growth situation of Pseudomonas aeruginosa on agar plates and meat stuffs using gas sensors

PubMed Central

Gu, Xinzhe; Sun, Ye; Tu, Kang; Dong, Qingli; Pan, Leiqing

2016-01-01

A rapid method of predicting the growing situation of Pseudomonas aeruginosa is presented. Gas sensors were used to acquire volatile compounds generated by P. aeruginosa on agar plates and meat stuffs. Then, optimal sensors were selected to simulate P. aeruginosa growth using modified Logistic and Gompertz equations by odor changes. The results showed that the responses of S8 or S10 yielded high coefficients of determination (R2) of 0.89–0.99 and low root mean square errors (RMSE) of 0.06–0.17 for P. aeruginosa growth, fitting the models on the agar plate. The responses of S9, S4 and the first principal component of 10 sensors fit well with the growth of P. aeruginosa inoculated in meat stored at 4 °C and 20 °C, with R2 of 0.73–0.96 and RMSE of 0.25–1.38. The correlation coefficients between the fitting models, as measured by electronic nose responses, and the colony counts of P. aeruginosa were high, ranging from 0.882 to 0.996 for both plate and meat samples. Also, gas chromatography–mass spectrometry results indicated the presence of specific volatiles of P. aeruginosa on agar plates. This work demonstrated an acceptable feasibility of using gas sensors—a rapid, easy and nondestructive method for predicting P. aeruginosa growth. PMID:27941841

Actual measurement, hygrothermal response experiment and growth prediction analysis of microbial contamination of central air conditioning system in Dalian, China

PubMed Central

Lv, Yang; Hu, Guangyao; Wang, Chunyang; Yuan, Wenjie; Wei, Shanshan; Gao, Jiaoqi; Wang, Boyuan; Song, Fangchao

2017-01-01

The microbial contamination of central air conditioning system is one of the important factors that affect the indoor air quality. Actual measurement and analysis were carried out on microbial contamination in central air conditioning system at a venue in Dalian, China. Illumina miseq method was used and three fungal samples of two units were analysed by high throughput sequencing. Results showed that the predominant fungus in air conditioning unit A and B were Candida spp. and Cladosporium spp., and two fungus were further used in the hygrothermal response experiment. Based on the data of Cladosporium in hygrothermal response experiment, this paper used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladosporium genera in different temperature and relative humidity conditions, and the square root model was fitted based on the two environmental factors. In addition, the models were carried on the analysis to verify the accuracy and feasibility of the established model equation. PMID:28367963

Actual measurement, hygrothermal response experiment and growth prediction analysis of microbial contamination of central air conditioning system in Dalian, China.

PubMed

Lv, Yang; Hu, Guangyao; Wang, Chunyang; Yuan, Wenjie; Wei, Shanshan; Gao, Jiaoqi; Wang, Boyuan; Song, Fangchao

2017-04-03

The microbial contamination of central air conditioning system is one of the important factors that affect the indoor air quality. Actual measurement and analysis were carried out on microbial contamination in central air conditioning system at a venue in Dalian, China. Illumina miseq method was used and three fungal samples of two units were analysed by high throughput sequencing. Results showed that the predominant fungus in air conditioning unit A and B were Candida spp. and Cladosporium spp., and two fungus were further used in the hygrothermal response experiment. Based on the data of Cladosporium in hygrothermal response experiment, this paper used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladosporium genera in different temperature and relative humidity conditions, and the square root model was fitted based on the two environmental factors. In addition, the models were carried on the analysis to verify the accuracy and feasibility of the established model equation.

Urban tree growth modeling

Treesearch

E. Gregory McPherson; Paula J. Peper

2012-01-01

This paper describes three long-term tree growth studies conducted to evaluate tree performance because repeated measurements of the same trees produce critical data for growth model calibration and validation. Several empirical and process-based approaches to modeling tree growth are reviewed. Modeling is more advanced in the fields of forestry and...

Plant growth modelling and applications: the increasing importance of plant architecture in growth models.

PubMed

Fourcaud, Thierry; Zhang, Xiaopeng; Stokes, Alexia; Lambers, Hans; Körner, Christian

2008-05-01

Modelling plant growth allows us to test hypotheses and carry out virtual experiments concerning plant growth processes that could otherwise take years in field conditions. The visualization of growth simulations allows us to see directly and vividly the outcome of a given model and provides us with an instructive tool useful for agronomists and foresters, as well as for teaching. Functional-structural (FS) plant growth models are nowadays particularly important for integrating biological processes with environmental conditions in 3-D virtual plants, and provide the basis for more advanced research in plant sciences. In this viewpoint paper, we ask the following questions. Are we modelling the correct processes that drive plant growth, and is growth driven mostly by sink or source activity? In current models, is the importance of soil resources (nutrients, water, temperature and their interaction with meristematic activity) considered adequately? Do classic models account for architectural adjustment as well as integrating the fundamental principles of development? Whilst answering these questions with the available data in the literature, we put forward the opinion that plant architecture and sink activity must be pushed to the centre of plant growth models. In natural conditions, sinks will more often drive growth than source activity, because sink activity is often controlled by finite soil resources or developmental constraints. PMA06: This viewpoint paper also serves as an introduction to this Special Issue devoted to plant growth modelling, which includes new research covering areas stretching from cell growth to biomechanics. All papers were presented at the Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), held in Beijing, China, from 13-17 November, 2006. Although a large number of papers are devoted to FS models of agricultural and forest crop species, physiological and genetic processes have

Effects of substrate concentrations on the growth of heterotrophic bacteria and algae in secondary facultative ponds.

PubMed

Kayombo, S; Mbwette, T S A; Katima, J H Y; Jorgensen, S E

2003-07-01

This paper presents the effect of substrate concentration on the growth of a mixed culture of algae and heterotrophic bacteria in secondary facultative ponds (SFPs) utilizing settled domestic sewage as a sole source of organic carbon. The growth of the mixed culture was studied at the concentrations ranging between 200 and 800 mg COD/l in a series of batch chemostat reactors. From the laboratory data, the specific growth rate (micro) was determined using the modified Gompertz model. The maximum specific growth rate ( micro(max)) and half saturation coefficients (K(s)) were calculated using the Monod kinetic equation. The maximum observed growth rate ( micro(max)) for heterotrophic bacteria was 3.8 day(-1) with K(s) of 200 mg COD/l. The micro(max) for algal biomass based on suspended volatile solids was 2.7 day(-1) with K(s) of 110 mg COD/l. The micro(max) of algae based on the chlorophyll-a was 3.5 day(-1) at K(s) of 50mg COD/l. The observed specific substrate removal by heterotrophic bacteria varied between the concentrations of substrate used and the average value was 0.82 (mg COD/mg biomass). The specific substrate utilization rate in the bioreactors was direct proportional to the specific growth rate. Hence, the determined Monod kinetic parameters are useful for the definition of the operation of SFPs.

Mathematical modeling of the aging processes and the mechanisms of mortality: paramount role of heterogeneity.

PubMed

Rossolini, G; Piantanelli, L

2001-08-01

Main problems of modeling the link between aging processes and mechanisms of mortality are addressed. Various applications of Gompertz's law, which allowed to formulate some fruitful hypotheses on the field, are reviewed. Some pitfalls occurring in its applications are also discussed using a model built on purpose to overcome these difficulties. The role played by heterogeneity emerges as the common cause of some relevant failure in using Gompertz's law and the necessary key ingredient of any model aimed to interpret the link between aging and mortality correctly. Though a number of problems are related to inter-individual variability, the search for their solution can lead to an intriguing approach to the study of aging and mortality. Living beings can be considered as complex systems and their age-related changes can be described at the light of complex system theory.

A new approach to the study of Romanization in Britain: a regional perspective of cultural change in late Iron Age and Roman Dorset using the Siler and Gompertz-Makeham models of mortality

PubMed Central

Redfern, Rebecca C.; DeWitte, Sharon N.

2011-01-01

This is the first study of Romanization to use the Siler and Gompertz-Makeham models of mortality in order to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N=518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose 2002) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern 2007; Redfern 2008b; Roberts and Cox 2003). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality were present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for males. The latter finding challenges received wisdom concerning the benefits of Romanization and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of males did not out-weigh underlying sex differences in biology that advantage females. PMID:20925081

A study of the effect of dietary fiber fractions obtained from artichoke (Cynara cardunculus L. var. scolymus) on the growth of intestinal bacteria associated with health.

PubMed

Fissore, Eliana N; Santo Domingo, Cinthia; Gerschenson, Lía N; Giannuzzi, Leda

2015-05-01

The effect of different fractions enriched in soluble fiber obtained from artichoke using citric acid or citric acid/hemicellulase on the selective growth of Lactobacillus plantarum 8114 and Bifidobacterium bifidum ATCC 11863 was evaluated. Gompertz modeling of Lactobacillus plantarum 8114 growth showed a higher specific growth rate (μ: 0.16 h(-1)) in the presence of fractions isolated from stems using hemicellulase (fraction A) than in the presence of glucose (μ: 0.09 h(-1)). In the case of Bifidobacterium bifidum 11863, the highest μ was obtained for the microorganism grown in the presence of fraction A and for the fraction isolated from stems without hemicellulase, their rate being twice that observed for glucose (0.04 h(-1)). The positive prebiotic activity scores observed with respect to Escherichia coli 25922 indicated that fibers assayed are metabolized as well as glucose by Lactobacillus plantarum 8114 and Bifidobacterium bifidum ATCC 11863 and that they are selectively metabolized by these microorganisms. The potential capacity to selectively stimulate the growth of intestinal bacteria associated with health shown by fraction A can be ascribed to its high inulin and low methylation degree pectin contents.

Determination of longevities, chamber building rates and growth functions for Operculina complanata from long term cultivation experiments

NASA Astrophysics Data System (ADS)

Woeger, Julia; Kinoshita, Shunichi; Wolfgang, Eder; Briguglio, Antonino; Hohenegger, Johann

2016-04-01

Operculina complanata was collected in 20 and 50 m depth around the Island of Sesoko belonging to Japans southernmost prefecture Okinawa in a series of monthly sampling over a period of 16 months (Apr.2014-July2015). A minimum of 8 specimens (4 among the smallest and 4 among the largest) per sampling were cultured in a long term experiment that was set up to approximate conditions in the field as closely as possible. A set up allowing recognition of individual specimens enabled consistent documentation of chamber formation, which in combination with μ-CT-scanning after the investigation period permitted the assignment of growth steps to specific time periods. These data were used to fit various mathematical models to describe growth (exponential-, logistic-, generalized logistic-, Gompertz-function) and chamber building rate (Michaelis-Menten-, Bertalanffy- function) of Operculina complanata. The mathematically retrieved maximum lifespan and mean chamber building rate found in cultured Operculina complanata were further compared to first results obtained by the simultaneously conducted "natural laboratory approach". Even though these comparisons hint at a somewhat stunted growth and truncated life spans of Operculina complanata in culture, they represent a possibility to assess and improve the quality of further cultivation set ups, opening new prospects to a better understanding of the their theoretical niches.

Modelling the growth of plants with a uniform growth logistics.

PubMed

Kilian, H G; Bartkowiak, D; Kazda, M; Kaufmann, D

2014-05-21

The increment model has previously been used to describe the growth of plants in general. Here, we examine how the same logistics enables the development of different superstructures. Data from the literature are analyzed with the increment model. Increments are growth-invariant molecular clusters, treated as heuristic particles. This approach formulates the law of mass action for multi-component systems, describing the general properties of superstructures which are optimized via relaxation processes. The daily growth patterns of hypocotyls can be reproduced implying predetermined growth invariant model parameters. In various species, the coordinated formation and death of fine roots are modeled successfully. Their biphasic annual growth follows distinct morphological programs but both use the same logistics. In tropical forests, distributions of the diameter in breast height of trees of different species adhere to the same pattern. Beyond structural fluctuations, competition and cooperation within and between the species may drive optimization. All superstructures of plants examined so far could be reproduced with our approach. With genetically encoded growth-invariant model parameters (interaction with the environment included) perfect morphological development runs embedded in the uniform logistics of the increment model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Modeling the kinetics of survival of Staphylococcus aureus in regional yogurt from goat's milk.

PubMed

Bednarko-Młynarczyk, E; Szteyn, J; Białobrzewski, I; Wiszniewska-Łaszczych, A; Liedtke, K

2015-01-01

The aim of this study was to determine the kinetics of the survival of the test strain of Staphylococcus aureus in the product investigated. Yogurt samples were contaminated with S. aure to an initial level of 10(3)-10(4) cfu/g. The samples were then stored at four temperatures: 4, 6, 20, 22°C. During storage, the number of S. aureus forming colonies in a gram of yogurt was determined every two hours. Based on the results of the analysis culture the curves of survival were plotted. Three primary models were selected to describe the kinetics of changes in the count of bacteria: Cole's model, a modified model of Gompertz and the model of Baranyi and Roberts. Analysis of the model fit carried out based on the average values of Pearson's correlation coefficient, between the modeled and measured values, showed that the Cole's model had the worst fit. The modified Gompertz model showed the count of S. aureus as a negative value. These drawbacks were not observed in the model of Baranyi and Roberts. For this reason, this model best reflects the kinetics of changes in the number of staphylococci in yogurt.

Biodegradability and methane production from secondary paper and pulp sludge: effect of fly ash and modeling.

PubMed

Huiliñir, César; Montalvo, Silvio; Guerrero, Lorna

2015-01-01

The effect of fly ash on biodegradability and methane production from secondary paper and pulp sludge, including its modeling, was evaluated. Three tests with fly ash concentrations of 0, 10 and 20 mg/L were evaluated at 32 °C. Methane production was modeled using the modified Gompertz equation. The results show that the doses used produce a statistically significant increase of accumulated methane, giving values greater than 225 mL of CH4 per gram of volatile solids (VS) added, and 135% greater than that obtained in the control assay. Biodegradability of VS increased 143% with respect to the control assays, giving values around 43%. The modified Gompertz model can describe well methane generation from residual sludge of the paper industry water treatment, with parameter values between those reported in the literature. Thus, the addition of fly ash to the process causes a significant increase of accumulated methane and VS removal, improving the biodegradability of paper and pulp sludge.

Mortality profiles of Rhodnius prolixus (Heteroptera: Reduviidae), vector of Chagas disease.

PubMed

Chaves, Luis Fernando; Hernandez, Maria-Josefina; Revilla, Tomás A; Rodríguez, Diego J; Rabinovich, Jorge E

2004-10-01

Life table data of Rhodnius prolixus (Heteroptera: Reduviidae) kept at laboratory conditions were analysed in search for mortality patterns. Gompertz and Weibull mortality models seem adequate to explain the sigmoid shape of the survivorship curve. A significant fit was obtained with both models for females (R(2) = 0.70, P < 0.0005 for the Gompertz model; R(2) = 0.78, P < 0.0005 for the Weibull model) and for males (R(2) = 0.39, P < 0.0005 for the Gompertz model; R(2) = 0.48, P < 0.0005 for the Weibull model). The mortality parameter (b) is higher for females in Gompertz and Weibull models, using smoothed and non-smoothed data (P < 0.05), revealing a significant sex mortality differential. Given the particular life history of this insect, the non-linear relationship between the force of mortality and age may have an important impact in the vectorial capacity of R. prolixus as Chagas disease vector, and its consideration should be included as an important factor in the transmission of Trypanosoma cruzi by triatomines.

Kinetic model of continuous ethanol fermentation in closed-circulating process with pervaporation membrane bioreactor by Saccharomyces cerevisiae.

PubMed

Fan, Senqing; Chen, Shiping; Tang, Xiaoyu; Xiao, Zeyi; Deng, Qing; Yao, Peina; Sun, Zhaopeng; Zhang, Yan; Chen, Chunyan

2015-02-01

Unstructured kinetic models were proposed to describe the principal kinetics involved in ethanol fermentation in a continuous and closed-circulating fermentation (CCCF) process with a pervaporation membrane bioreactor. After ethanol was removed in situ from the broth by the membrane pervaporation, the secondary metabolites accumulated in the broth became the inhibitors to cell growth. The cell death rate related to the deterioration of the culture environment was described as a function of the cell concentration and fermentation time. In CCCF process, 609.8 g L(-1) and 750.1 g L(-1) of ethanol production were obtained in the first run and second run, respectively. The modified Gompertz model, correlating the ethanol production with the fermentation period, could be used to describe the ethanol production during CCCF process. The fitting results by the models showed good agreement with the experimental data. These models could be employed for the CCCF process technology development for ethanol fermentation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic models for tumoral growth

NASA Astrophysics Data System (ADS)

Escudero, Carlos

2006-02-01

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border and the surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are reported in this paper in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantage of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. An analysis of these models allows us to quantitatively estimate the response of the tumor to an unfavorable perturbation during growth.

Latent Growth and Dynamic Structural Equation Models.

PubMed

Grimm, Kevin J; Ram, Nilam

2018-05-07

Latent growth models make up a class of methods to study within-person change-how it progresses, how it differs across individuals, what are its determinants, and what are its consequences. Latent growth methods have been applied in many domains to examine average and differential responses to interventions and treatments. In this review, we introduce the growth modeling approach to studying change by presenting different models of change and interpretations of their model parameters. We then apply these methods to examining sex differences in the development of binge drinking behavior through adolescence and into adulthood. Advances in growth modeling methods are then discussed and include inherently nonlinear growth models, derivative specification of growth models, and latent change score models to study stochastic change processes. We conclude with relevant design issues of longitudinal studies and considerations for the analysis of longitudinal data.

Capital Growth Paths of the Neoclassical Growth Model

PubMed Central

Takahashi, Taro

2012-01-01

This paper derives the first-order approximated paths of both types of capital in the two-capital neoclassical growth model. The derived capital growth paths reveal that the short-run growth effect of capital injection differs considerably depending on which type of capital is enhanced. This result demonstrates the importance of well-targeted capital enhancement programs such as public sector projects and foreign aid. PMID:23185344

Testing mechanistic models of growth in insects.

PubMed

Maino, James L; Kearney, Michael R

2015-11-22

Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. © 2015 The Author(s).

Growth rates of young-of-year shovelnose sturgeon in the Upper Missouri River

USGS Publications Warehouse

Braaten, P. J.; Fuller, D.B.

2007-01-01

Information on growth during the larval and young-of-year life stages in natural river environments is generally lacking for most sturgeon species. In this study, methods for estimating ages and quantifying growth were developed for field-sampled larval and young-of-year shovelnose sturgeon Scaphirhynchus platorynchus in the upper Missouri River. First, growth was assessed by partitioning samples of young-of-year shovelnose sturgeon into cohorts, and regressing weekly increases in cohort mean length on sampling date. This method quantified relative growth because ages of the cohorts were unknown. Cohort increases in mean length among sampling dates were positively related (P < 0.05, r2 > 0.59 for all cohorts) to sampling date, and yielded growth rate estimates of 0.80–2.95 mm day−1 (2003) and 0.44–2.28 mm day−1 (2004). Highest growth rates occurred in the largest (and earliest spawned) cohorts. Second, a method was developed to estimate cohort hatch dates, thus age on date of sampling could be determined. This method included quantification of post-hatch length increases as a function of water temperature (growth capacity; mm per thermal unit, mm TU−1), and summation of mean daily water temperatures to achieve the required number of thermal units that corresponded to post-hatch lengths of shovelnose sturgeon on sampling dates. For six of seven cohorts of shovelnose sturgeon analyzed, linear growth models (r2 ≥ 0.65, P < 0.0001) or Gompertz growth models (r2 ≥ 0.83, P < 0.0001) quantified length-at-age from hatch through 55 days post-hatch (98–100 mm). Comparisons of length-at-age derived from the growth models indicated that length-at-age was greater for the earlier-hatched cohorts than later-hatched cohorts. Estimated hatch dates for different cohorts were corroborated based on the dates that newly-hatched larval shovelnose sturgeon were sampled in the drift. These results provide the first quantification of growth dynamics

Comparison of argon-based and nitrogen-based modified atmosphere packaging on bacterial growth and product quality of chicken breast fillets.

PubMed

Herbert, Ulrike; Rossaint, Sonja; Khanna, Meik-Ankush; Kreyenschmidt, Judith

2013-05-01

Poultry fillets were packaged under 6 different gas atmospheres (A: 15% Ar, 60% O2, 25% CO2; B: 15% N2, 60% O2, 25% CO2; C: 25% Ar, 45% O2, 30% CO2; D: 25% N2, 45% O2, 30% CO2; E: 82% Ar; 18% CO2; F: 82% N2, 18% CO2) and stored at 4°C. During storage, the growth of typical spoilage organisms (Brochothrix thermosphacta, Pseudomonas spp., Enterobacteriaceae, and Lactobacilli spp.) and total viable count were analyzed and modeled using the Gompertz function. Sensory analyses of the poultry samples were carried out by trained sensory panelists for color, odor, texture, drip loss, and general appearance. No significant difference in microbiological growth parameters was observed for fresh poultry stored under an argon-enriched atmosphere in comparison with nitrogen, except the B. thermosphacta stored under 82% argon. The sensory evaluation showed a significant effect of an argon-enriched atmosphere, particularly on color of meat stored under 15% argon (P < 0.05). In contrast, 25 and 82% argon concentrations in place of nitrogen showed no beneficial effect on sensory parameters.

Stochastic ontogenetic growth model

NASA Astrophysics Data System (ADS)

West, B. J.; West, D.

2012-02-01

An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

Modelling the growth of feather crystals

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

Wood, H.J.; Hunt, J.D.; Evans, P.V.

1997-02-01

An existing numerical model of dendritic growth has been adapted to model the growth of twinned columnar dendrites (feather crystals) in a binary aluminium alloy, Examination of the effect of dendrite tip angle on growth has led to an hypothesis regarding the stability of a pointed tip morphology in these crystals.

A new approach to the study of Romanization in Britain: a regional perspective of cultural change in late iron age and roman dorset using the siler and gompertz-makeham models of mortality.

PubMed

Redfern, Rebecca C; Dewitte, Sharon N

2011-02-01

This is the first study of health in the Roman Empire to use the Siler and Gompertz-Makeham models of mortality to investigate the health consequences of the 43 AD conquest of Britain. The study examined late Iron Age and Romano-British populations (N = 518) from Dorset, England, which is the only region of Britain to display continuity in inhumation burial practice and cemetery use throughout the two periods. Skeletal evidence for frailty was assessed using cribra orbitalia, porotic hyperostosis, periosteal lesions, enamel hypoplasia, dental caries, tuberculosis, and rickets. These health variables were chosen for analysis because they are reliable indicators of general health for diachronic comparison (Steckel and Rose: The backbone of history: health and nutrition in the western hemisphere (2002)) and are associated with the introduction of urbanism in Britain during the Roman period (Redfern: J Rom Archaeol Supp Series 64 (2007) 171-194; Redfern: Britannia 39 (2008a) 161-191; Roberts and Cox: Health and disease in Britain: from prehistory to the present day (2003)). The results show that levels of frailty and mortality were lower in the late Iron Age period, and no sex differences in mortality was present. However, post-conquest, mortality risk increased for children and the elderly, and particularly for men. The latter finding challenges received wisdom concerning the benefits of incorporation into the Empire and the higher status of the male body in the Roman world. Therefore, we conclude that the consequences of urbanism, changes in diet, and increased population heterogeneity negatively impacted health, to the extent that the enhanced cultural buffering of men did not outweigh underlying sex differences in biology that advantage women. 2010 Wiley-Liss, Inc.

Modeling Reliability Growth in Accelerated Stress Testing

DTIC Science & Technology

2013-12-01

MODELING RELIABILITY GROWTH IN ACCELERATED STRESS TESTING DISSERTATION Jason K. Freels Major...Defense, or the United States Government. AFIT-ENS-DS-13-D-02 MODELING RELIABILITY GROWTH IN ACCELERATED STRESS TESTING ...DISTRIBUTION UNLIMITED AFIT-ENS-DS-13-D-02 MODELING RELIABILITY GROWTH IN ACCELERATED STRESS TESTING Jason K. Freels

Growth, efficiency, and yield of commercial broilers from 1957, 1978, and 20051

PubMed Central

Zuidhof, M. J.; Schneider, B. L.; Carney, V. L.; Korver, D. R.; Robinson, F. E.

2014-01-01

The effect of commercial selection on the growth, efficiency, and yield of broilers was studied using 2 University of Alberta Meat Control strains unselected since 1957 and 1978, and a commercial Ross 308 strain (2005). Mixed-sex chicks (n = 180 per strain) were placed into 4 replicate pens per strain, and grown on a current nutritional program to 56 d of age. Weekly front and side profile photographs of 8 birds per strain were collected. Growth rate, feed intake, and measures of feed efficiency including feed conversion ratio, residual feed intake, and residual maintenance energy requirements were characterized. A nonlinear mixed Gompertz growth model was used to predict BW and BW variation, useful for subsequent stochastic growth simulation. Dissections were conducted on 8 birds per strain semiweekly from 21 to 56 d of age to characterize allometric growth of pectoralis muscles, leg meat, abdominal fat pad, liver, gut, and heart. A novel nonlinear analysis of covariance was used to test the hypothesis that allometric growth patterns have changed as a result of commercial selection pressure. From 1957 to 2005, broiler growth increased by over 400%, with a concurrent 50% reduction in feed conversion ratio, corresponding to a compound annual rate of increase in 42 d live BW of 3.30%. Forty-two-day FCR decreased by 2.55% each year over the same 48-yr period. Pectoralis major growth potential increased, whereas abdominal fat decreased due to genetic selection pressure over the same time period. From 1957 to 2005, pectoralis minor yield at 42 d of age was 30% higher in males and 37% higher in females; pectoralis major yield increased by 79% in males and 85% in females. Over almost 50 yr of commercial quantitative genetic selection pressure, intended beneficial changes have been achieved. Unintended changes such as enhanced sexual dimorphism are likely inconsequential, though musculoskeletal, immune function, and parent stock management challenges may require additional

Modeling Heterogeneity of Latent Growth Depending on Initial Status

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2006-01-01

In this article, a heterogeneous latent growth curve model for modeling heterogeneity of growth rates is proposed. The suggested model is an extension of a conventional growth curve model and a complementary tool to mixed growth modeling. It allows the modeling of heterogeneity of growth rates as a continuous function of latent initial status and…

A Vernacular for Linear Latent Growth Models

ERIC Educational Resources Information Center

Hancock, Gregory R.; Choi, Jaehwa

2006-01-01

In its most basic form, latent growth modeling (latent curve analysis) allows an assessment of individuals' change in a measured variable X over time. For simple linear models, as with other growth models, parameter estimates associated with the a construct (amount of X at a chosen temporal reference point) and b construct (growth in X per unit…

A novel approach for calculating shelf life of minimally processed vegetables.

PubMed

Corbo, Maria Rosaria; Del Nobile, Matteo Alessandro; Sinigaglia, Milena

2006-01-15

Shelf life of minimally processed vegetables is often calculated by using the kinetic parameters of Gompertz equation as modified by Zwietering et al. [Zwietering, M.H., Jongenburger, F.M., Roumbouts, M., van't Riet, K., 1990. Modelling of the bacterial growth curve. Applied and Environmental Microbiology 56, 1875-1881.] taking 5x10(7) CFU/g as the maximum acceptable contamination value consistent with acceptable quality of these products. As this method does not allow estimation of the standard errors of the shelf life, in this paper the modified Gompertz equation was re-parameterized to directly include the shelf life as a fitting parameter among the Gompertz parameters. Being the shelf life a fitting parameter is possible to determine its confidence interval by fitting the proposed equation to the experimental data. The goodness-of-fit of this new equation was tested by using mesophilic bacteria cell loads from different minimally processed vegetables (packaged fresh-cut lettuce, fennel and shredded carrots) that differed for some process operations or for package atmosphere. The new equation was able to describe the data well and to estimate the shelf life. The results obtained emphasize the importance of using the standard errors for the shelf life value to show significant differences among the samples.

The Potential of Growth Mixture Modelling

ERIC Educational Resources Information Center

Muthen, Bengt

2006-01-01

The authors of the paper on growth mixture modelling (GMM) give a description of GMM and related techniques as applied to antisocial behaviour. They bring up the important issue of choice of model within the general framework of mixture modelling, especially the choice between latent class growth analysis (LCGA) techniques developed by Nagin and…

Island growth as a growth mode in atomic layer deposition: A phenomenological model

NASA Astrophysics Data System (ADS)

Puurunen, Riikka L.; Vandervorst, Wilfried

2004-12-01

Atomic layer deposition (ALD) has recently gained world-wide attention because of its suitability for the fabrication of conformal material layers with thickness in the nanometer range. Although the principles of ALD were realized about 40 years ago, the description of many physicochemical processes that occur during ALD growth is still under development. A constant amount of material deposited in an ALD reaction cycle, that is, growth-per-cycle (GPC), has been a paradigm in ALD through decades. The GPC may vary, however, especially in the beginning of the ALD growth. In this work, a division of ALD processes to four classes is proposed, on the basis of how the GPC varies with the number of ALD reaction cycles: linear growth, substrate-enhanced growth, and substrate-inhibited growth of type 1 and type 2. Island growth is identified as a likely origin for type 2 substrate-inhibited growth, where the GPC increases and goes through a maximum before it settles to a constant value characteristic of a steady growth. A simple phenomenological model is developed to describe island growth in ALD. The model assumes that the substrate is unreactive with the ALD reactants, except for reactive defects. ALD growth is assumed to proceed symmetrically from the defects, resulting islands of a conical shape. Random deposition is the growth mode on the islands. The model allows the simulation of GPC curves, surface fraction curves, and surface roughness, with physically significant parameters. When the model is applied to the zirconium tetrachloride/water and the trimethylaluminum/water ALD processes on hydrogen-terminated silicon, the calculated GPC curves and surface fractions agree with the experiments. The island growth model can be used to assess the occurrence of island growth, the size of islands formed, and point of formation of a continuous ALD-grown film. The benefits and limitations of the model and the general characteristics of type 2 substrate-inhibited ALD are

Effect of poultry decontaminants concentration on growth kinetics for pathogenic and spoilage bacteria.

PubMed

del Río, Elena; González de Caso, Beatriz; Prieto, Miguel; Alonso-Calleja, Carlos; Capita, Rosa

2008-10-01

Various chemical compounds are currently under review for final approval as poultry decontaminants in the European Union (EU). Concentration is among the factors considered by the EU authorities in the evaluation of these treatments. The aim of this research was to compare the growth parameters for pathogenic and spoilage bacteria in presence of high and low concentrations of poultry decontaminants to assess whether such treatments could involve a potential sanitary risk for consumers. Growth curves for Salmonella enterica serotype Enteritidis, Listeria monocytogenes, Pseudomonas fluorescens and Brochothrix thermosphacta were obtained at different levels of trisodium phosphate (TSP; 1.74%; 0.58%), acidified sodium chlorite (ASC; 210 ppm; 70 ppm) and citric acid (CA; 0.27%; 0.09%). The modified Gompertz equation was used as primary model to fit observed data. ASC and TSP were the most effective compounds in increasing lag phase (L) and reducing maximum growth rate (mu) in Gram-negative bacteria. Gram-positive bacteria were more influenced by CA. At high TSP levels, mu for Salmonella decreased. Low TSP levels increased mu for Salmonella and Listeria relative to control samples. In presence of 0.27% CA, Brochothrix showed the highest L and the lowest mu among strains tested. These results suggest that low TSP and high CA concentrations could favour the outgrowth of pathogenic bacteria (e.g. Salmonella) relative to spoilage bacteria, rending these treatments potentially dangerous for consumers. The findings of this study may be useful to the EU authorities and meat processors in their efforts to select adequate treatments for control of bacteria on poultry.

Nonconvex Model of Material Growth: Mathematical Theory

NASA Astrophysics Data System (ADS)

Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

2018-06-01

The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

Comparison of growth curve parameters of organs and body components in meat- (Coturnix coturnix coturnix) and laying-type (Coturnix coturnix japonica) quail show interactions between gender and genotype.

PubMed

Grieser, D O; Marcato, S M; Furlan, A C; Zancanela, V; Ton, A P S; Batista, E; Perine, T P; Pozza, P C; Sakomura, N K

2015-01-01

1. The objective of this study was to estimate growth parameters of carcass components (wing, thighs and drumsticks, back and breast) and organs (heart, liver, gizzard and gut) in males and females of one meat-type quail strain (Coturnix coturnix coturnix) and two laying strains (Coturnix coturnix japonica) designated either yellow or red. 2. A total of 1350 quail from 1 to 42 d old were distributed in a completely randomised design, with 5 replicates of each strain. The carcass component weights and body organs were analysed weekly and evaluated using the Gompertz function; growth rates were evaluated through derivative equations. 3. The meat-type strain presented the highest growth rates in carcass components and organs. Across strains, females showed the highest weight of internal organs at maturity compared to males. 4. Females had greater growth potential in breast, wings and back than males for both yellow and red laying quail.

Development of simple-to-apply biogas kinetic models for the co-digestion of food waste and maize husk.

PubMed

Owamah, H I; Izinyon, O C

2015-10-01

Biogas kinetic models are often used to characterize substrate degradation and prediction of biogas production potential. Most of these existing models are however difficult to apply to substrates they were not developed for since their applications are usually substrate specific. Biodegradability kinetic (BIK) model and maximum biogas production potential and stability assessment (MBPPSA) model were therefore developed in this study for better understanding of the anaerobic co-digestion of food waste and maize husk for biogas production. Biodegradability constant (k) was estimated as 0.11 d(-1) using the BIK model. The results of maximum biogas production potential (A) obtained using the MBPPSA model were found to be in good correspondence, both in value and trend with the results obtained using the popular but complex modified Gompertz model for digesters B-1, B-2, B-3, B-4, and B-5. The (If) value of MBPPSA model also showed that digesters B-3, B-4, and B-5 were stable, while B-1 and B-2 were inhibited/unstable. Similar stability observation was also obtained using the modified Gompertz model. The MBPPSA model can therefore be used as an alternative model for anaerobic digestion feasibility studies and plant design. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling elasticity in crystal growth.

PubMed

Elder, K R; Katakowski, Mark; Haataja, Mikko; Grant, Martin

2002-06-17

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

Kinetic Model of Growth of Arthropoda Populations

NASA Astrophysics Data System (ADS)

Ershov, Yu. A.; Kuznetsov, M. A.

2018-05-01

Kinetic equations were derived for calculating the growth of crustacean populations ( Crustacea) based on the biological growth model suggested earlier using shrimp ( Caridea) populations as an example. The development cycle of successive stages for populations can be represented in the form of quasi-chemical equations. The kinetic equations that describe the development cycle of crustaceans allow quantitative prediction of the development of populations depending on conditions. In contrast to extrapolation-simulation models, in the developed kinetic model of biological growth the kinetic parameters are the experimental characteristics of population growth. Verification and parametric identification of the developed model on the basis of the experimental data showed agreement with experiment within the error of the measurement technique.

Growth/reflectance model interface for wheat and corresponding model

NASA Technical Reports Server (NTRS)

Suits, G. H.; Sieron, R.; Odenweller, J.

1984-01-01

The use of modeling to explore the possibility of discovering new and useful crop condition indicators which might be available from the Thematic Mapper and to connect these symptoms to the biological causes in the crop is discussed. A crop growth model was used to predict the day to day growth features of the crop as it responds biologically to the various environmental factors. A reflectance model was used to predict the character of the interaction of daylight with the predicted growth features. An atmospheric path radiance was added to the reflected daylight to simulate the radiance appearing at the sensor. Finally, the digitized data sent to a ground station were calculated. The crop under investigation is wheat.

A new computational growth model for sea urchin skeletons.

PubMed

Zachos, Louis G

2009-08-07

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.

Assessment of MARMOT Grain Growth Model

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

Fromm, B.; Zhang, Y.; Schwen, D.

2015-12-01

This report assesses the MARMOT grain growth model by comparing modeling predictions with experimental results from thermal annealing. The purpose here is threefold: (1) to demonstrate the validation approach of using thermal annealing experiments with non-destructive characterization, (2) to test the reconstruction capability and computation efficiency in MOOSE, and (3) to validate the grain growth model and the associated parameters that are implemented in MARMOT for UO 2. To assure a rigorous comparison, the 2D and 3D initial experimental microstructures of UO 2 samples were characterized using non-destructive Synchrotron x-ray. The same samples were then annealed at 2273K for grainmore » growth, and their initial microstructures were used as initial conditions for simulated annealing at the same temperature using MARMOT. After annealing, the final experimental microstructures were characterized again to compare with the results from simulations. So far, comparison between modeling and experiments has been done for 2D microstructures, and 3D comparison is underway. The preliminary results demonstrated the usefulness of the non-destructive characterization method for MARMOT grain growth model validation. A detailed analysis of the 3D microstructures is in progress to fully validate the current model in MARMOT.« less

Graphene growth process modeling: a physical-statistical approach

NASA Astrophysics Data System (ADS)

Wu, Jian; Huang, Qiang

2014-09-01

As a zero-band semiconductor, graphene is an attractive material for a wide variety of applications such as optoelectronics. Among various techniques developed for graphene synthesis, chemical vapor deposition on copper foils shows high potential for producing few-layer and large-area graphene. Since fabrication of high-quality graphene sheets requires the understanding of growth mechanisms, and methods of characterization and control of grain size of graphene flakes, analytical modeling of graphene growth process is therefore essential for controlled fabrication. The graphene growth process starts with randomly nucleated islands that gradually develop into complex shapes, grow in size, and eventually connect together to cover the copper foil. To model this complex process, we develop a physical-statistical approach under the assumption of self-similarity during graphene growth. The growth kinetics is uncovered by separating island shapes from area growth rate. We propose to characterize the area growth velocity using a confined exponential model, which not only has clear physical explanation, but also fits the real data well. For the shape modeling, we develop a parametric shape model which can be well explained by the angular-dependent growth rate. This work can provide useful information for the control and optimization of graphene growth process on Cu foil.

Screening of Bacillus coagulans strains in lignin supplemented minimal medium with high throughput turbidity measurements.

PubMed

Glaser, Robert; Venus, Joachim

2014-12-01

The aim of this study was to extend the options for screening and characterization of microorganism through kinetic growth parameters. In order to obtain data, automated turbidimetric measurements were accomplished to observe the response of strains of Bacillus coagulans . For the characterization, it was decided to examine the influence of varying concentrations of lignin with respect to bacterial growth. Different mathematical models are used for comparison: logistic, Gompertz, Baranyi and Richards and Stannard. The growth response was characterized by parameters like maximum growth rate, maximum population, and the lag time. In this short analysis we present a mathematical approach towards a comparison of different microorganisms. Furthermore, it can be demonstrated that lignin in low concentrations can have a positive influence on the growth of B. coagulans .

Dissipative-particle-dynamics model of biofilm growth

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

Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.

2011-06-13

A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm.

Dendritic growth shapes in kinetic Monte Carlo models

NASA Astrophysics Data System (ADS)

Krumwiede, Tim R.; Schulze, Tim P.

2017-02-01

For the most part, the study of dendritic crystal growth has focused on continuum models featuring surface energies that yield six pointed dendrites. In such models, the growth shape is a function of the surface energy anisotropy, and recent work has shown that considering a broader class of anisotropies yields a correspondingly richer set of growth morphologies. Motivated by this work, we generalize nanoscale models of dendritic growth based on kinetic Monte Carlo simulation. In particular, we examine the effects of extending the truncation radius for atomic interactions in a bond-counting model. This is done by calculating the model’s corresponding surface energy and equilibrium shape, as well as by running KMC simulations to obtain nanodendritic growth shapes. Additionally, we compare the effects of extending the interaction radius in bond-counting models to that of extending the number of terms retained in the cubic harmonic expansion of surface energy anisotropy in the context of continuum models.

Modeling Population Growth and Extinction

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2009-01-01

The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…

Detecting Appropriate Trajectories of Growth in Latent Growth Models: The Performance of Information-Based Criteria

ERIC Educational Resources Information Center

Whittaker, Tiffany A.; Khojasteh, Jam

2017-01-01

Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact…

A Simulation To Model Exponential Growth.

ERIC Educational Resources Information Center

Appelbaum, Elizabeth Berman

2000-01-01

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Modeling to predict growth/no growth boundaries and kinetic behavior of Salmonella on cutting board surfaces.

PubMed

Yoon, Hyunjoo; Lee, Joo-Yeon; Suk, Hee-Jin; Lee, Sunah; Lee, Heeyoung; Lee, Soomin; Yoon, Yohan

2012-12-01

This study developed models to predict the growth probabilities and kinetic behavior of Salmonella enterica strains on cutting boards. Polyethylene coupons (3 by 5 cm) were rubbed with pork belly, and pork purge was then sprayed on the coupon surface, followed by inoculation of a five-strain Salmonella mixture onto the surface of the coupons. These coupons were stored at 13 to 35°C for 12 h, and total bacterial and Salmonella cell counts were enumerated on tryptic soy agar and xylose lysine deoxycholate (XLD) agar, respectively, every 2 h, which produced 56 combinations. The combinations that had growth of ≥0.5 log CFU/cm(2) of Salmonella bacteria recovered on XLD agar were given the value 1 (growth), and the combinations that had growth of <0.5 log CFU/cm(2) were assigned the value 0 (no growth). These growth response data from XLD agar were analyzed by logistic regression for producing growth/no growth interfaces of Salmonella bacteria. In addition, a linear model was fitted to the Salmonella cell counts to calculate the growth rate (log CFU per square centimeter per hour) and initial cell count (log CFU per square centimeter), following secondary modeling with the square root model. All of the models developed were validated with observed data, which were not used for model development. Growth of total bacteria and Salmonella cells was observed at 28, 30, 33, and 35°C, but there was no growth detected below 20°C within the time frame investigated. Moreover, various indices indicated that the performance of the developed models was acceptable. The results suggest that the models developed in this study may be useful in predicting the growth/no growth interface and kinetic behavior of Salmonella bacteria on polyethylene cutting boards.

State Growth Models for School Accountability: Progress on Development and Reporting Measures of Student Growth

ERIC Educational Resources Information Center

Blank, Rolf K.

2010-01-01

The Council of Chief State School Officers (CCSSO) is working to respond to increased interest in the use of growth models for school accountability. Growth models are based on tracking change in individual student achievement scores over multiple years. While growth models have been used for decades in academic research and program evaluation, a…

Modeling Tetragonal Lysozyme Crystal Growth Rates

NASA Technical Reports Server (NTRS)

Gorti, Sridhar; Forsythe, Elizabeth L.; Pusey, Marc L.

2003-01-01

Tetragonal lysozyme 110 face crystal growth rates, measured over 5 orders of magnitude in range, can be described using a model where growth occurs by 2D nucleation on the crystal surface for solution supersaturations of c/c(sub eq) less than or equal to 7 +/- 2. Based upon the model, the step energy per unit length, beta was estimated to be approx. 5.3 +/- 0.4 x 10(exp -7) erg/mol-cm, which for a step height of 56 A corresponds to barrier of approx. 7 +/- 1 k(sub B)T at 300 K. For supersaturations of c/c(sub eq) > 8, the model emphasizing crystal growth by 2D nucleation not only could not predict, but also consistently overestimated, the highest observable crystal growth rates. Kinetic roughening is hypothesized to occur at a cross-over supersaturation of c/c(sub eq) > 8, where crystal growth is postulated to occur by a different process such as adsorption. Under this assumption, all growth rate data indicated that a kinetic roughening transition and subsequent crystal growth by adsorption for all solution conditions, varying in buffer pH, temperature and precipitant concentration, occurs for c/c(sub eq)(T, pH, NaCl) in the range between 5 and 10, with an energy barrier for adsorption estimated to be approx. 20 k(sub B)T at 300 K. Based upon these and other estimates, we determined the size of the critical surface nucleate, at the crossover supersaturation and higher concentrations, to range from 4 to 10 molecules.

Comparing models for growth and management of forest tracts

Treesearch

J.J. Colbert; Michael Schuckers; Desta Fekedulegn

2003-01-01

The Stand Damage Model (SDM) is a PC-based model that is easily installed, calibrated and initialized for use in exploring the future growth and management of forest stands or small wood lots. We compare the basic individual tree growth model incorporated in this model with alternative models that predict the basal area growth of trees. The SDM is a gap-type simulator...

Value function in economic growth model

NASA Astrophysics Data System (ADS)

Bagno, Alexander; Tarasyev, Alexandr A.; Tarasyev, Alexander M.

2017-11-01

Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models.

Analytical properties of a three-compartmental dynamical demographic model

NASA Astrophysics Data System (ADS)

Postnikov, E. B.

2015-07-01

The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.

A Model of Controlled Growth

NASA Astrophysics Data System (ADS)

Bressan, Alberto; Lewicka, Marta

2018-03-01

We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric shape of the growing tissue is determined by the instantaneous minimization of an elastic deformation energy, subject to a constraint on the volumetric growth. For an initial domain with C}^{2,α boundary, our main result establishes the local existence and uniqueness of a classical solution, up to a rigid motion.

Modeling Thin Film Oxide Growth

NASA Astrophysics Data System (ADS)

Sherman, Quentin

Thin film oxidation is investigated using two modeling techniques in the interest of better understanding the roles of space charge and non-equilibrium effects. An electrochemical phase-field model of an oxide-metal interface is formulated in one dimension and studied at equilibrium and during growth. An analogous sharp interface model is developed to validate the phase-field model in the thick film limit. Electrochemical profiles across the oxide are shown to deviate from the sharp interface prediction when the oxide film is thin compared to the Debye length, however no effect on the oxidation kinetics is found. This is attributed to the simple thermodynamic and kinetic models used therein. The phase-field model provides a framework onto to which additional physics can be added to better model thin film oxidation. A model for solute trapping during the oxidation of binary alloys is developed to study non-equilibrium effects during the early stages of oxide growth. The model is applied to NiCr alloys, and steady-state interfacial composition maps are presented for the growth of an oxide with the rock salt structure. No detailed experimental data is available to verify the predictions of the solute trapping model, however it is shown to be consistent with the trends observed during the early stages of NiCr oxidation. Lastly, experimental studies of the wet infiltration technique for decorating solid oxide fuel cell anodes with nickel nanoparticles are presented. The effect of nickel nitrate calcination parameters on the resulting nickel oxide microstructures are studied on both porous and planar substrates. Decreasing the calcination temperature and dwell time, as well as a dehydration step after nickel nitrate infiltration, are all shown to decrease the initial nickel oxide particle size, but other factors such as geometry and nickel loading per unit area also affected the final nickel particle size and morphology upon reduction.

Mathematical models for Isoptera (Insecta) mound growth.

PubMed

Buschini, M L T; Abuabara, M A P; Petrere, Miguel

2008-08-01

In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

Activist model of political party growth

NASA Astrophysics Data System (ADS)

Jeffs, Rebecca A.; Hayward, John; Roach, Paul A.; Wyburn, John

2016-01-01

The membership of British political parties has a direct influence on their political effectiveness. This paper applies the mathematics of epidemiology to the analysis of the growth and decline of such memberships. The party members are divided into activists and inactive members, where all activists influence the quality of party recruitment, but only a subset of activists recruit and thus govern numerical growth. The activists recruit for only a limited period, which acts as a restriction on further party growth. This Limited Activist model is applied to post-war and recent memberships of the Labour, Scottish National and Conservative parties. The model reproduces data trends, and relates realistically to historical narratives. It is concluded that the political parties analysed are not in danger of extinction but experience repeated periods of growth and decline in membership, albeit at lower numbers than in the past.

Modeling error distributions of growth curve models through Bayesian methods.

PubMed

Zhang, Zhiyong

2016-06-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

On Latent Growth Models for Composites and Their Constituents.

PubMed

Hancock, Gregory R; Mao, Xiulin; Kher, Hemant

2013-09-01

Over the last decade and a half, latent growth modeling has become an extremely popular and versatile technique for evaluating longitudinal change and its determinants. Most common among the models applied are those for a single measured variable over time. This model has been extended in a variety of ways, most relevant for the current work being the multidomain and the second-order latent growth models. Whereas the former allows for growth function characteristics to be modeled for multiple outcomes simultaneously, with the degree of growth characteristics' relations assessed within the model (e.g., cross-domain slope factor correlations), the latter models growth in latent outcomes, each of which has effect indicators repeated over time. But what if one has an outcome that is believed to be formative relative to its indicator variables rather than latent? In this case, where the outcome is a composite of multiple constituents, modeling change over time is less straightforward. This article provides analytical and applied details for simultaneously modeling growth in composites and their constituent elements, including a real data example using a general computer self-efficacy questionnaire.

New theories of root growth modelling

NASA Astrophysics Data System (ADS)

Landl, Magdalena; Schnepf, Andrea; Vanderborght, Jan; Huber, Katrin; Javaux, Mathieu; Bengough, A. Glyn; Vereecken, Harry

2016-04-01

In dynamic root architecture models, root growth is represented by moving root tips whose line trajectory results in the creation of new root segments. Typically, the direction of root growth is calculated as the vector sum of various direction-affecting components. However, in our simulations this did not reproduce experimental observations of root growth in structured soil. We therefore developed a new approach to predict the root growth direction. In this approach we distinguish between, firstly, driving forces for root growth, i.e. the force exerted by the root which points in the direction of the previous root segment and gravitropism, and, secondly, the soil mechanical resistance to root growth or penetration resistance. The latter can be anisotropic, i.e. depending on the direction of growth, which leads to a difference between the direction of the driving force and the direction of the root tip movement. Anisotropy of penetration resistance can be caused either by microscale differences in soil structure or by macroscale features, including macropores. Anisotropy at the microscale is neglected in our model. To allow for this, we include a normally distributed random deflection angle α to the force which points in the direction of the previous root segment with zero mean and a standard deviation σ. The standard deviation σ is scaled, so that the deflection from the original root tip location does not depend on the spatial resolution of the root system model. Similarly to the water flow equation, the direction of the root tip movement corresponds to the water flux vector while the driving forces are related to the water potential gradient. The analogue of the hydraulic conductivity tensor is the root penetrability tensor. It is determined by the inverse of soil penetration resistance and describes the ease with which a root can penetrate the soil. By adapting the three dimensional soil and root water uptake model R-SWMS (Javaux et al., 2008) in this way

Growth response of Escherichia coli ATCC 35218 adapted to several concentrations of sodium benzoate and potassium sorbate.

PubMed

Santiesteban-López, N Angélica; Rosales, Mónica; Palou, Enrique; López-Malo, Aurelio

2009-11-01

Escherichia coli ATCC 35218 growth response was evaluated after repetitive cultivation in stepwise increasing antimicrobial agent concentrations (potassium sorbate or sodium benzoate) to observe its adaptation process to high weak-acid concentrations. The effect of antimicrobial (potassium sorbate or sodium benzoate) concentration (0 to 7,000 ppm) was tested using laboratory media. Cells adapted at 1,000 ppm were inoculated in media containing the same concentration of the antimicrobial; after that, cells were transferred to media containing a higher concentration, followed by repetitive cultivations. In every case, viable cells were determined by surface plating every hour up to 48 h. Logarithmic representations of survival or growing fraction were modeled using the Gompertz equation. Adapted and nonadapted cells were analyzed for plasmid presence as well as phosphofructokinase and succinate dehydrogenase activity. Bacterial growth was observed after adaptation processes in media formulated up to 7,000 ppm of potassium sorbate or sodium benzoate. Analyses of variance demonstrated that no significant difference (P > 0.05) in lag time or growth rate was observed among adapted cells cultured in media containing the studied concentrations for each of the antimicrobials tested. These results suggest that E. coli can be adapted to high weak-acid concentrations if the exposure is performed under sublethal conditions. Furthermore, there was demonstrated inhibition of the enzymes phosphofructokinase and succinate dehydrogenase by action of sodium benzoate and potassium sorbate, respectively. E. coli adaptation to antimicrobial agents was not related to plasmid presence but appears to be due to other action mechanisms.

Czochralski crystal growth: Modeling study

NASA Technical Reports Server (NTRS)

Dudukovic, M. P.; Ramachandran, P. A.; Srivastava, R. K.; Dorsey, D.

1986-01-01

The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.

Mycoflora assessment, growth and toxigenic features of patulin-producers in kiwifruit in China.

PubMed

Wang, Yuan; Feng, Kewei; Liu, Bin; Zhang, Zhiwei; Wei, Jianping; Yuan, Yahong; Yue, Tianli

2018-05-01

Fungal development in agricultural products may cause mycotoxin contamination, which is a significant threat to food safety. Patulin (PAT) and PAT-producer contamination has been established as a worldwide problem. The present study aimed to investigate the mycoflora and PAT-producers present in kiwifruits and environmental samples collected from orchards and processing plants in Shaanxi Province, China. Variations in mycoflora were observed in different samples, with penicillia and aspergilli as the predominant genera. Approximately 42.86% of dropped fruits were contaminated with PAT-producers, which harbored the 6-methylsalicylic acid synthase and the isoepoxydon dehydrogenase genes that are involved in PAT biosynthesis. The growth of Penicillium expansum, Penicillium griseofulvum and Penicillium paneum in kiwi puree agar (KPA) medium and kiwi juice well fitted the modified Gompertz and Baranyi and Roberts models (R 2 ≥ 0.95). A significant positive correlation between colony diameter and PAT content in KPA medium of P. expansum and P. griseofulvum was observed (P < 0.05). The present study analyzed the mycofloral composition and the potential risk for PAT and PAT-producer contamination in kiwifruit, which may be utilized in the establishment of proper management practices in the kiwifruit industry. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

Brain tumor modeling: glioma growth and interaction with chemotherapy

NASA Astrophysics Data System (ADS)

Banaem, Hossein Y.; Ahmadian, Alireza; Saberi, Hooshangh; Daneshmehr, Alireza; Khodadad, Davood

2011-10-01

In last decade increasingly mathematical models of tumor growths have been studied, particularly on solid tumors which growth mainly caused by cellular proliferation. In this paper we propose a modified model to simulate the growth of gliomas in different stages. Glioma growth is modeled by a reaction-advection-diffusion. We begin with a model of untreated gliomas and continue with models of polyclonal glioma following chemotherapy. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter. Tumor growth is characterized by a dangerous change in the control mechanisms, which normally maintain a balance between the rate of proliferation and the rate of apoptosis (controlled cell death). Result shows that this model closes to clinical finding and can simulate brain tumor behavior properly.

A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new Belehdradek-type model for evaluating the effect of temperature on growth rate

USDA-ARS?s Scientific Manuscript database

A new mechanistic growth model was developed to describe microbial growth under isothermal conditions. The new mathematical model was derived from the basic observation of bacterial growth that may include lag, exponential, and stationary phases. With this model, the lag phase duration and exponen...

Operculina from the northwestern Pacific (Sesoko Island, Japan) Species Differentiation, Population Dynamics, Growth and Development

NASA Astrophysics Data System (ADS)

Woeger, Julia; Eder, Wolfgang; Kinoshita, Shunichi; Briguglio, Antonino; Hohenegger, Johann

2017-04-01

During the last decades larger benthic foraminifera have gained importance as indicator species and are used in a variety of applications, from ecological monitoring, studying the effects of ocean acidification, or reconstructing paleoenvironments. They significantly contribute to the carbonate budget of costal areas and are invaluable tools in biostratigraphy. Even before their advancement as bioindicators, laboratory experiments have been conducted to investigate the effects of various ecological parameters on community composition, biology of single species, or investigating the effects of salinity and temperature on stable isotope composition of the foraminiferal test, to name only a few. The natural laboratory approach (continuous sampling over a period of more than one year) was conducted at the island of Sesoko (Okinawa, Japan). in combination with µ-CT scanning was used to reveal population dynamics of 3 different morphotypes of Operculina. The clarification of reproductive cycles as well as generation and size abundances were used to calculate natural growth models. Best fit was achieved using Bertalanffy and Michaelis-Menten functions. Exponential-, logistic-, generalized logistic-, Gompertz-function yielded weaker fits, when compared by coefficient of determination as well as Akaike Information criterion. The resulting growth curves and inferred growth rates were in turn used to evaluate the quality of a laboratory cultivation experiment carried out simultaneously over a period of 15 months. Culturing parameters such as temperature, light intensities, salinity and pH and light-dark duration were continuously adapted to measurements in the field. The average investigation time in culture was 77days. 13 Individuals lived more than 200 days, 3 reproduced asexually and one sexually. 14% of 186 Individuals were lost, while 22% could not be kept alive for more than one month. Growth curves also represent an instrumental source of information for the various

Time-course of germination, initiation of mycelium proliferation and probability of visible growth and detectable AFB1 production of an isolate of Aspergillus flavus on pistachio extract agar.

PubMed

Aldars-García, Laila; Sanchis, Vicente; Ramos, Antonio J; Marín, Sonia

2017-06-01

The aim of this work was to assess the temporal relationship among quantified germination, mycelial growth and aflatoxin B 1 (AFB1) production from colonies coming from single spores, in order to find the best way to predict as accurately as possible the presence of AFB1 at the early stages of contamination. Germination, mycelial growth, probability of growth and probability of AFB1 production of an isolate of Aspergillus flavus were determined at 25 °C and two water activities (0.85 and 0.87) on 3% Pistachio Extract Agar (PEA). The percentage of germinated spores versus time was fitted to the modified Gompertz equation for the estimation of the germination parameters (geometrical germination time and germination rate). The radial growth curve for each colony was fitted to a linear model for the estimation of the apparent lag time for growth and the growth rate, and besides the time to visible growth was estimated. Binary data obtained from growth and AFB1 studies were modeled using logistic regression analysis. Both water activities led to a similar fungal growth and AFB1 production. In this study, given the suboptimal set conditions, it has been observed that germination is a stage far from the AFB1 production process. Once the probability of growth started to increase it took 6 days to produce AFB1, and when probability of growth was 100%, only a 40-57% probability of detection of AFB1 production was predicted. Moreover, colony sizes with a radius of 1-2 mm could be a helpful indicator of the possible AFB1 contamination in the commodity. Despite growth models may overestimate the presence of AFB1, their use would be a helpful tool for producers and manufacturers; from our data 5% probability of AFB1 production (initiation of production) would occur when a minimum of 60% probability of growth is observed. Legal restrictions are quite severe for these toxins, thus their control from the early stages of contamination throughout the food chain is of paramount

A model for neurite growth and neuronal morphogenesis.

PubMed

Li, G H; Qin, C D

1996-02-01

A model is presented for tensile regulation of neuritic growth. It is proposed that the neurite tension can be determined by Hooke's law and determines the growth rate of neurites. The growth of a neurite is defined as the change in its unstretched length. Neuritic growth rate is assumed to increase in proportion to tension magnitude over a certain threshold [Dennerll et al., J. Cell Biol. 107: 665-674 (1988)]. The movement of branch nodes also contributes to the neuronal morphogenesis. It is supposed that the rate of a branch-node displacement is in proportion to the resultant neuritic tension exerted on this node. To deal with the growth-cone movement, it is further supposed that the environment exerts a traction force on the growth cone and the rate of growth-cone displacement is determined by the vector sum of the neuritic tension and the traction force. A group of differential equations are used to describe the model. The key point of the model is that the traction force and the neuritic tension are in opposition to generate a temporal contrast-enhancing mechanism. Results of a simulation study suggest that the model can explain some phenomena related to neuronal morphogenesis.

Detecting Growth Shape Misspecifications in Latent Growth Models: An Evaluation of Fit Indexes

ERIC Educational Resources Information Center

Leite, Walter L.; Stapleton, Laura M.

2011-01-01

In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…

Winter drought impairs xylem phenology, anatomy and growth in Mediterranean Scots pine forests.

PubMed

Camarero, J J; Guada, G; Sánchez-Salguero, R; Cervantes, E

2016-12-01

Continental Mediterranean forests face drought but also cold spells and both climate extremes can impair the resilience capacity of these forests. Climate warming could amplify the negative effects of cold spells by inducing premature dehardening. Here we capitalize on a winter drought-induced dieback triggered by a cold spell which occurred in December 2001 affecting Scots pine forests in eastern Spain. We assessed post-dieback recovery by quantifying and comparing radial growth and xylem anatomy of non-declining (ND, crown cover >50%) and declining (D, crown cover ≤50%) trees in two sites (VP, Villarroya de los Pinares; TO, Torrijas). We also characterized xylogenesis in both sites and aboveground productivity in site VP. Dieback caused legacy effects since needle loss, a 60% reduction in litter fall and radial-growth decline characterized D-trees 3 years after dieback symptoms started appearing in spring 2002. D-trees formed collapsed tracheids in the 2002-ring, particularly in the most affected VP site where xylogenesis differences between ND and D trees were most noticeable. The lower growth rates of D-trees were caused by a shorter duration of their major xylogenesis phases. In site VP the radial-enlargement and wall-thickening of tracheids were significantly reduced in D-trees as compared to ND-trees because these xylogenesis phases tended to start earlier and end later in ND-trees. Gompertz models fitted to tracheid production predicted that maximum growth rates occurred 11-12 days earlier in ND than in D-trees. The formation of radially-enlarging tracheids was enhanced by longer days in both study sites and also by wetter conditions in the driest TO site, but xylogenesis sensitivity to climate was reduced in D-trees. Winter-drought dieback impairs xylem anatomy and phenology, aboveground productivity, xylogenesis and growth in Mediterranean Scots pine populations. Affected stands show a costly post-dieback recovery challenging their resilience ability

Modeling Pacing Behavior and Test Speededness Using Latent Growth Curve Models

ERIC Educational Resources Information Center

Kahraman, Nilufer; Cuddy, Monica M.; Clauser, Brian E.

2013-01-01

This research explores the usefulness of latent growth curve modeling in the study of pacing behavior and test speededness. Examinee response times from a high-stakes, computerized examination, collected before and after the examination was subjected to a timing change, were analyzed using a series of latent growth curve models to detect…

Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.

2010-01-01

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.

United States geological survey's reserve-growth models and their implementation

USGS Publications Warehouse

Klett, T.R.

2005-01-01

The USGS has developed several mathematical models to forecast reserve growth of fields both in the United States (U.S.) and the world. The models are based on historical reserve growth patterns of fields in the U.S. The patterns of past reserve growth are extrapolated to forecast future reserve growth. Changes of individual field sizes through time are extremely variable, therefore, the reserve growth models take on a statistical approach whereby volumetric changes for populations of fields are used in the models. Field age serves as a measure of the field-development effort that is applied to promote reserve growth. At the time of the USGS World Petroleum Assessment 2000, a reserve growth model for discovered fields of the world was not available. Reserve growth forecasts, therefore, were made based on a model of historical reserve growth of fields of the U.S. To test the feasibility of such an application, reserve growth forecasts were made of 186 giant oil fields of the world (excluding the U.S. and Canada). In addition, forecasts were made for these giant oil fields subdivided into those located in and outside of Organization of Petroleum Exporting Countries (OPEC). The model provided a reserve-growth forecast that closely matched the actual reserve growth that occurred from 1981 through 1996 for the 186 fields as a whole, as well as for both OPEC and non-OPEC subdivisions, despite the differences in reserves definition among the fields of the U.S. and the rest of the world. ?? 2005 International Association for Mathematical Geology.

Modeling delamination growth in composites

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

Reedy, E.D. Jr.; Mello, F.J.

1996-12-01

A method for modeling the initiation and growth of discrete delaminations in shell-like composite structures is presented. The laminate is divided into two or more sublaminates, with each sublaminate modeled with four-noded quadrilateral shell elements. A special, eight-noded hex constraint element connects opposing sublaminate shell elements. It supplies the nodal forces and moments needed to make the two opposing shell elements act as a single shell element until a prescribed failure criterion is satisfied. Once the failure criterion is attained, the connection is broken, creating or growing a discrete delamination. This approach has been implemented in a 3D finite elementmore » code. This code uses explicit time integration, and can analyze shell-like structures subjected to large deformations and complex contact conditions. The shell elements can use existing composite material models that include in-plane laminate failure modes. This analysis capability was developed to perform crashworthiness studies of composite structures, and is useful whenever there is a need to estimate peak loads, energy absorption, or the final shape of a highly deformed composite structure. This paper describes the eight-noded hex constraint element used to model the initiation and growth of a delamination, and discusses associated implementation issues. Particular attention is focused on the delamination growth criterion, and it is verified that calculated results do not depend on element size. In addition, results for double cantilever beam and end notched flexure specimens are presented and compared to measured data to assess the ability of the present approach to model a growing delamination.« less

Calibration of the STEMS diameter growth model using FIA data

Treesearch

Veronica C. Lessard

2000-01-01

The diameter growth model used in STEMS, the Stand and Tree Evaluation and Modeling System, was originally calibrated using data from permanent growth plots in Minnesota, Wisconsin, and Michigan. Because the model has been applied in predicting growth using Forest Inventory and Analysis (FIA) data, it was appropriate to refit the model to FIA data. The model was...

Modeling of thin film GaAs growth

NASA Technical Reports Server (NTRS)

Heinbockel, J. H.

1982-01-01

A potential scaling Monte Carlo model of crystal growth is developed. The model is a modification of the solid-on-solid method for studying crystal growth in that potentials at surface sites are continuously updated on a time scale reflecting the surface events of migration, incorporation and evaporation. The model allows for B on A type of crystal growth and lattice disregistry by the assignment of potential values at various surface sites. The surface adatoms are periodically assigned a random energy from a Boltzmann distribution and this energy determines whether the adatoms evaporate, migrate or remain stationary during the sampling interval. For each addition or migration of an adatom, the surface potentials are adjusted to reflect the adsorption, migration or desorption potential changes.

Modeling the Arrest of Tissue Growth in Epithelia

NASA Astrophysics Data System (ADS)

Golden, Alexander; Lubensky, David

The mechanisms of control and eventual arrest of growth of tissues is an area that has received considerable attention, both experimentally and in the development of quantitative models. In particular, the Drosophila wing disc epithelium appears to robustly arrive at a unique final size. One mechanism that has the potential to play a role in the eventual cessation of growth is mechanical feedback from stresses induced by nonuniform growth. There is experimental support for an effect on the tissue growth rate by such mechanical stresses, and a number of numerical or cell-based models have been proposed that show that the arrest of growth can be achieved by mechanical feedback. We introduce an analytic framework that allows us to understand different coarse-grained feedback mechanisms on the same terms. We use the framework to distinguish between families of models that do not have a unique final size and those that do and give rough estimates for how much variability in the eventual organ size can be expected in models that do not have a unique final size. NSF Grant DMR-1056456.

A tumor growth model with deformable ECM

NASA Astrophysics Data System (ADS)

Sciumè, G.; Santagiuliana, R.; Ferrari, M.; Decuzzi, P.; Schrefler, B. A.

2014-12-01

Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.

A model of urban rational growth based on grey prediction

NASA Astrophysics Data System (ADS)

Xiao, Wenjing

2017-04-01

Smart growth focuses on building sustainable cities, using compact development to prevent urban sprawl. This paper establishes a series of models to implement smart growth theories into city design. Besides two specific city design cases are shown. Firstly, We establishes Smart Growth Measure Model to measure the success of smart growth of a city. And we use Full Permutation Polygon Synthetic Indicator Method to calculate the Comprehensive Indicator (CI) which is used to measure the success of smart growth. Secondly, this paper uses the principle of smart growth to develop a new growth plan for two cities. We establish an optimization model to maximum CI value. The Particle Swarm Optimization (PSO) algorithm is used to solve the model. Combined with the calculation results and the specific circumstances of cities, we make their the smart growth plan respectively.

In silico modeling for tumor growth visualization.

PubMed

Jeanquartier, Fleur; Jean-Quartier, Claire; Cemernek, David; Holzinger, Andreas

2016-08-08

Cancer is a complex disease. Fundamental cellular based studies as well as modeling provides insight into cancer biology and strategies to treatment of the disease. In silico models complement in vivo models. Research on tumor growth involves a plethora of models each emphasizing isolated aspects of benign and malignant neoplasms. Biologists and clinical scientists are often overwhelmed by the mathematical background knowledge necessary to grasp and to apply a model to their own research. We aim to provide a comprehensive and expandable simulation tool to visualizing tumor growth. This novel Web-based application offers the advantage of a user-friendly graphical interface with several manipulable input variables to correlate different aspects of tumor growth. By refining model parameters we highlight the significance of heterogeneous intercellular interactions on tumor progression. Within this paper we present the implementation of the Cellular Potts Model graphically presented through Cytoscape.js within a Web application. The tool is available under the MIT license at https://github.com/davcem/cpm-cytoscape and http://styx.cgv.tugraz.at:8080/cpm-cytoscape/ . In-silico methods overcome the lack of wet experimental possibilities and as dry method succeed in terms of reduction, refinement and replacement of animal experimentation, also known as the 3R principles. Our visualization approach to simulation allows for more flexible usage and easy extension to facilitate understanding and gain novel insight. We believe that biomedical research in general and research on tumor growth in particular will benefit from the systems biology perspective.

Bridging process-based and empirical approaches to modeling tree growth

Treesearch

Harry T. Valentine; Annikki Makela; Annikki Makela

2005-01-01

The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the...

Regression models for linking patterns of growth to a later outcome: infant growth and childhood overweight.

PubMed

Wills, Andrew K; Strand, Bjørn Heine; Glavin, Kari; Silverwood, Richard J; Hovengen, Ragnhild

2016-04-08

Regression models are widely used to link serial measures of anthropometric size or changes in size to a later outcome. Different parameterisations of these models enable one to target different questions about the effect of growth, however, their interpretation can be challenging. Our objective was to formulate and classify several sets of parameterisations by their underlying growth pattern contrast, and to discuss their utility using an expository example. We describe and classify five sets of model parameterisations in accordance with their underlying growth pattern contrast (conditional growth; being bigger v being smaller; becoming bigger and staying bigger; growing faster v being bigger; becoming and staying bigger versus being bigger). The contrasts are estimated by including different sets of repeated measures of size and changes in size in a regression model. We illustrate these models in the setting of linking infant growth (measured on 6 occasions: birth, 6 weeks, 3, 6, 12 and 24 months) in weight-for-height-for-age z-scores to later childhood overweight at 8y using complete cases from the Norwegian Childhood Growth study (n = 900). In our expository example, conditional growth during all periods, becoming bigger in any interval and staying bigger through infancy, and being bigger from birth were all associated with higher odds of later overweight. The highest odds of later overweight occurred for individuals who experienced high conditional growth or became bigger in the 3 to 6 month period and stayed bigger, and those who were bigger from birth to 24 months. Comparisons between periods and between growth patterns require large sample sizes and need to consider how to scale associations to make comparisons fair; with respect to the latter, we show one approach. Studies interested in detrimental growth patterns may gain extra insight from reporting several sets of growth pattern contrasts, and hence an approach that incorporates several sets of

Modeling Vegetation Growth Impact on Groundwater Recharge

NASA Astrophysics Data System (ADS)

Anurag, H.; Ng, G. H. C.; Tipping, R.

2017-12-01

Vegetation growth is affected by variability in climate and land-cover / land-use over a range of temporal and spatial scales. Vegetation also modifies water budget through interception and evapotranspiration and thus has a significant impact on groundwater recharge. Most groundwater recharge assessments represent vegetation using specified, static parameter, such as for leaf-area-index, but this neglects the effect of vegetation dynamics on recharge estimates. Our study addresses this gap by including vegetation growth in model simulations of recharge. We use NCAR's Community Land Model v4.5 with its BGC module (BGC is the new CLM4.5 biogeochemistry). It integrates prognostic vegetation growth with land-surface and subsurface hydrological processes and can thus capture the effect of vegetation on groundwater. A challenge, however, is the need to resolve uncertainties in model inputs ranging from vegetation growth parameters all the way down to the water table. We have compiled diverse data spanning meteorological inputs to subsurface geology and use these to implement ensemble model simulations to evaluate the possible effects of dynamic vegetation growth (versus specified, static vegetation parameterizations) on estimating groundwater recharge. We present preliminary results for select data-intensive test locations throughout the state of Minnesota (USA), which has a sharp east-west precipitation gradient that makes it an apt testbed for examining ecohydrologic relationships across different temperate climatic settings and ecosystems. Using the ensemble simulations, we examine the effect of seasonal to interannual variability of vegetation growth on recharge and water table depths, which has implications for predicting the combined impact of climate, vegetation, and geology on groundwater resources. Future work will include distributed model simulations over the entire state, as well as conditioning uncertain vegetation and subsurface parameters on remote sensing

Modeling the effects of ozone on soybean growth and yield.

PubMed

Kobayashi, K; Miller, J E; Flagler, R B; Heck, W W

1990-01-01

A simple mechanistic model was developed based on an existing growth model in order to address the mechanisms of the effects of ozone on growth and yield of soybean [Glycine max. (L.) Merr. 'Davis'] and interacting effects of other environmental stresses. The model simulates daily growth of soybean plants using environmental data including shortwave radiation, temperature, precipitation, irrigation and ozone concentration. Leaf growth, dry matter accumulation, water budget, nitrogen input and seed growth linked to senescence and abscission of leaves are described in the model. The effects of ozone are modeled as reduced photosynthate production and accelerated senescence. The model was applied to the open-top chamber experiments in which soybean plants were exposed to ozone under two levels of soil moisture regimes. After calibrating the model to the growth data and seed yield, goodness-of-fit of the model was tested. The model fitted well for top dry weight in the vegetative growth phase and also at maturity. The effect of ozone on seen yield was also described satisfactorily by the model. The simulation showed apparent interaction between the effect of ozone and soil moisture stress on the seed yield. The model revealed that further work is needed concerning the effect of ozone on the senescence process and the consequences of alteration of canopy microclimate by the open-top chambers.

Modeling Growth of Nanostructures in Plasmas

NASA Technical Reports Server (NTRS)

Hwang, Helen H.; Bose, Deepak; Govindan, T. R.; Meyyappan, M.

2004-01-01

As semiconductor circuits shrink to CDs below 0.1 nm, it is becoming increasingly critical to replace and/or enhance existing technology with nanoscale structures, such as nanowires for interconnects. Nanowires grown in plasmas are strongly dependent on processing conditions, such as gas composition and substrate temperature. Growth occurs at specific sites, or step-edges, with the bulk growth rate of the nanowires determined from the equation of motion of the nucleating crystalline steps. Traditional front-tracking algorithms, such as string-based or level set methods, suffer either from numerical complications in higher spatial dimensions, or from difficulties in incorporating surface-intense physical and chemical phenomena. Phase field models have the robustness of the level set method, combined with the ability to implement surface-specific chemistry that is required to model crystal growth, although they do not necessarily directly solve for the advancing front location. We have adopted a phase field approach and will present results of the adatom density and step-growth location in time as a function of processing conditions, such as temperature and plasma gas composition.

Effect of high pressure on growth and bacteriocin production of Pediococcus acidilactici HA-6111-2

NASA Astrophysics Data System (ADS)

Castro, S. M.; Kolomeytseva, M.; Casquete, R.; Silva, J.; Saraiva, J. A.; Teixeira, P.

2015-10-01

This study was aimed to investigate the effect of high pressure processing (HPP, 200-600 MPa) on the (i) survival of Listeria innocua and Pediococcus acidilactici HA-6111-2; (ii) production of bacteriocin bacHA-6111-2 and (iii) activity of bacteriocin against untreated and pressure-treated L. innocua cells. Inactivation of P. acidilactici was observed for pressures of >300 MPa. However, at this pressure level, L. innocua was more sensitive. Bacteriocin crude extract was pressure stable, with a decrease for pressures of ≥400 MPa. Pressures of ≤200 MPa did not affect bacteriocin production when compared with non-pressure-treated cells, whereas higher pressures caused a 2- to 4-fold decrease on the maximum level of bacteriocin production. Growth curves of P. acidilactici were fitted with the modified Gompertz model. The lag phase period depended on the magnitude of the pressure applied: there was a delay in the exponential phase as pressure increased and, as a consequence, in the beginning of bacteriocin production. Since P. acidilactici HA-6111-2 and its bacteriocin have shown resistance to pressures up to 300-400 MPa, they could be used in combination with HPP in order to improve food safety.

Dendritic growth model of multilevel marketing

NASA Astrophysics Data System (ADS)

Pang, James Christopher S.; Monterola, Christopher P.

2017-02-01

Biologically inspired dendritic network growth is utilized to model the evolving connections of a multilevel marketing (MLM) enterprise. Starting from agents at random spatial locations, a network is formed by minimizing a distance cost function controlled by a parameter, termed the balancing factor bf, that weighs the wiring and the path length costs of connection. The paradigm is compared to an actual MLM membership data and is shown to be successful in statistically capturing the membership distribution, better than the previously reported agent based preferential attachment or analytic branching process models. Moreover, it recovers the known empirical statistics of previously studied MLM, specifically: (i) a membership distribution characterized by the existence of peak levels indicating limited growth, and (ii) an income distribution obeying the 80 - 20 Pareto principle. Extensive types of income distributions from uniform to Pareto to a "winner-take-all" kind are also modeled by varying bf. Finally, the robustness of our dendritic growth paradigm to random agent removals is explored and its implications to MLM income distributions are discussed.

When growth models are not universal: evidence from marine invertebrates

PubMed Central

Hirst, Andrew G.; Forster, Jack

2013-01-01

The accumulation of body mass, as growth, is fundamental to all organisms. Being able to understand which model(s) best describe this growth trajectory, both empirically and ultimately mechanistically, is an important challenge. A variety of equations have been proposed to describe growth during ontogeny. Recently, the West Brown Enquist (WBE) equation, formulated as part of the metabolic theory of ecology, has been proposed as a universal model of growth. This equation has the advantage of having a biological basis, but its ability to describe invertebrate growth patterns has not been well tested against other, more simple models. In this study, we collected data for 58 species of marine invertebrate from 15 different taxa. The data were fitted to three growth models (power, exponential and WBE), and their abilities were examined using an information theoretic approach. Using Akaike information criteria, we found changes in mass through time to fit an exponential equation form best (in approx. 73% of cases). The WBE model predominantly overestimates body size in early ontogeny and underestimates it in later ontogeny; it was the best fit in approximately 14% of cases. The exponential model described growth well in nine taxa, whereas the WBE described growth well in one of the 15 taxa, the Amphipoda. Although the WBE has the advantage of being developed with an underlying proximate mechanism, it provides a poor fit to the majority of marine invertebrates examined here, including species with determinate and indeterminate growth types. In the original formulation of the WBE model, it was tested almost exclusively against vertebrates, to which it fitted well; the model does not however appear to be universal given its poor ability to describe growth in benthic or pelagic marine invertebrates. PMID:23945691

A dynamic model for tumour growth and metastasis formation.

PubMed

Haustein, Volker; Schumacher, Udo

2012-07-05

A simple and fast computational model to describe the dynamics of tumour growth and metastasis formation is presented. The model is based on the calculation of successive generations of tumour cells and enables one to describe biologically important entities like tumour volume, time point of 1st metastatic growth or number of metastatic colonies at a given time. The model entirely relies on the chronology of these successive events of the metastatic cascade. The simulation calculations were performed for two embedded growth models to describe the Gompertzian like growth behaviour of tumours. The initial training of the models was carried out using an analytical solution for the size distribution of metastases of a hepatocellular carcinoma. We then show the applicability of our models to clinical data from the Munich Cancer Registry. Growth and dissemination characteristics of metastatic cells originating from cells in the primary breast cancer can be modelled thus showing its ability to perform systematic analyses relevant for clinical breast cancer research and treatment. In particular, our calculations show that generally metastases formation has already been initiated before the primary can be detected clinically.

A dynamic model for tumour growth and metastasis formation

PubMed Central

2012-01-01

A simple and fast computational model to describe the dynamics of tumour growth and metastasis formation is presented. The model is based on the calculation of successive generations of tumour cells and enables one to describe biologically important entities like tumour volume, time point of 1st metastatic growth or number of metastatic colonies at a given time. The model entirely relies on the chronology of these successive events of the metastatic cascade. The simulation calculations were performed for two embedded growth models to describe the Gompertzian like growth behaviour of tumours. The initial training of the models was carried out using an analytical solution for the size distribution of metastases of a hepatocellular carcinoma. We then show the applicability of our models to clinical data from the Munich Cancer Registry. Growth and dissemination characteristics of metastatic cells originating from cells in the primary breast cancer can be modelled thus showing its ability to perform systematic analyses relevant for clinical breast cancer research and treatment. In particular, our calculations show that generally metastases formation has already been initiated before the primary can be detected clinically. PMID:22548735

Effect of high intensity ultrasound on the fermentation profile of Lactobacillus sakei in a meat model system.

PubMed

Ojha, Kumari Shikha; Kerry, Joseph P; Alvarez, Carlos; Walsh, Des; Tiwari, Brijesh K

2016-07-01

The objective of this study was to investigate the efficacy of high intensity ultrasound on the fermentation profile of Lactobacillus sakei in a meat model system. Ultrasound power level (0-68.5 W) and sonication time (0-9 min) at 20 °C were assessed against the growth of L. sakei using a Microplate reader over a period of 24h. The L. sakei growth data showed a good fit with the Gompertz model (R(2)>0.90; SE<0.042). Second order polynomial models demonstrated the effect of ultrasonic power and sonication time on the specific growth rate (SGR, μ, h(-1)) and lag phase (λ, h). A higher SGR and a shorter lag phase were observed at low power (2.99 W for 5 min) compared to control. Conversely, a decrease (p<0.05) in SGR with an increase in lag phase was observed with an increase in ultrasonic power level. Cell-free extracts obtained after 24h fermentation of ultrasound treated samples showed antimicrobial activity against Staphylococcus aureus, Listeria monocytogenes, Escherichia coli and Salmonella typhimurium at lower concentrations compared to control. No significant difference (p<0.05) among treatments was observed for lactic acid content after a 24h fermentation period. This study showed that both stimulation and retardation of L. sakei is possible, depending on the ultrasonic power and sonication time employed. Hence, fermentation process involving probiotics to develop functional food products can be tailored by selection of ultrasound processing parameters. Copyright © 2016 Elsevier B.V. All rights reserved.

Longevity and growth of Acacia tortilis; insights from 14C content and anatomy of wood

PubMed Central

Andersen, Gidske L; Krzywinski, Knut

2007-01-01

Background Acacia tortilis is a keystone species across arid ecosystems in Africa and the Middle East. Yet, its life-history, longevity and growth are poorly known, and consequently ongoing changes in tree populations cannot be managed in an appropriate manner. In other arid areas parenchymatic bands marking growth zones in the wood have made dendrochronological studies possible. The possibilities for using pre- and post-bomb 14C content in wood samples along with the presence of narrow marginal parenchymatic bands in the wood is therefore tested to gain further insight into the age, growth and growth conditions of A. tortilis in the hyper-arid Eastern Desert of Egypt. Results Based on age scenarios and the Gompertz growth equation, the age of trees studied seems to be from 200 up to 650 years. Annual radial growth estimated from calibrated dates based on the post-bomb 14C content of samples is up to 2.4 mm, but varies both spatially and temporally. Parenchymatic bands are not formed regularly. The correlation in band pattern among trees is poor, both among and within sites. Conclusion The post-bomb 14C content of A. tortilis wood gives valuable information on tree growth and is required to assess the age scenario approach applied here. This approach indicates high longevities and slow growth of trees. Special management measures should therefore be taken at sites where the trend in tree population size is negative. The possibilities for dendrochronological studies based on A. tortilis from the Eastern Desert are poor. However, marginal parenchymatic bands can give insight into fine scale variation in growth conditions and the past management of trees. PMID:17573964

Population dynamics and growth rates of endosymbionts during Diaphorina citri (Hemiptera, Liviidae) ontogeny.

PubMed

Dossi, Fabio Cleisto Alda; da Silva, Edney Pereira; Cônsoli, Fernando Luis

2014-11-01

The infection density of symbionts is among the major parameters to understand their biological effects in host-endosymbionts interactions. Diaphorina citri harbors two bacteriome-associated bacterial endosymbionts (Candidatus Carsonella ruddii and Candidatus Profftella armatura), besides the intracellular reproductive parasite Wolbachia. In this study, the density dynamics of the three endosymbionts associated with the psyllid D. citri was investigated by real-time quantitative PCR (qPCR) at different developmental stages. Bacterial density was estimated by assessing the copy number of the 16S rRNA gene for Carsonella and Profftella, and of the ftsZ gene for Wolbachia. Analysis revealed a continuous growth of the symbionts during host development. Symbiont growth and rate curves were estimated by the Gompertz equation, which indicated a negative correlation between the degree of symbiont-host specialization and the time to achieve the maximum growth rate (t*). Carsonella densities were significantly lower than those of Profftella at all host developmental stages analyzed, even though they both displayed a similar trend. The growth rates of Wolbachia were similar to those of Carsonella, but Wolbachia was not as abundant. Adult males displayed higher symbiont densities than females. However, females showed a much more pronounced increase in symbiont density as they aged if compared to males, regardless of the incorporation of symbionts into female oocytes and egg laying. The increased density of endosymbionts in aged adults differs from the usual decrease observed during host aging in other insect-symbiont systems.

Alexandrium minutum growth controlled by phosphorus . An applied model

NASA Astrophysics Data System (ADS)

Chapelle, A.; Labry, C.; Sourisseau, M.; Lebreton, C.; Youenou, A.; Crassous, M. P.

2010-11-01

Toxic algae are a worldwide problem threatening aquaculture, public health and tourism. Alexandrium, a toxic dinoflagellate proliferates in Northwest France estuaries (i.e. the Penzé estuary) causing Paralytic Shellfish Poisoning events. Vegetative growth, and in particular the role of nutrient uptake and growth rate, are crucial parameters to understand toxic blooms. With the goal of modelling in situ Alexandrium blooms related to environmental parameters, we first try to calibrate a zero-dimensional box model of Alexandrium growth. This work focuses on phosphorus nutrition. Our objective is to calibrate Alexandrium minutum as well as Heterocapsa triquetra (a non-toxic dinoflagellate) growth under different rates of phosphorus supply, other factors being optimal and constant. Laboratory experiments are used to calibrate two growth models and three uptake models for each species. Models are then used to simulate monospecific batch and semi-continuous experiments as well as competition between the two algae (mixed cultures). Results show that the Droop growth model together with linear uptake versus quota can represent most of our observations, although a power law uptake function can more accurately simulate our phosphorus uptake data. We note that such models have limitations in non steady-state situations and cell quotas can depend on a variety of factors, so care must be taken in extrapolating these results beyond the specific conditions studied.

A mathematical model of microalgae growth in cylindrical photobioreactor

NASA Astrophysics Data System (ADS)

Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana

2017-08-01

Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.

Localisation in a Growth Model with Interaction

NASA Astrophysics Data System (ADS)

Costa, M.; Menshikov, M.; Shcherbakov, V.; Vachkovskaia, M.

2018-05-01

This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interaction. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.

Localisation in a Growth Model with Interaction

NASA Astrophysics Data System (ADS)

Costa, M.; Menshikov, M.; Shcherbakov, V.; Vachkovskaia, M.

2018-06-01

This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interaction. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.

Comparison of statistical models to estimate parasite growth rate in the induced blood stage malaria model.

PubMed

Wockner, Leesa F; Hoffmann, Isabell; O'Rourke, Peter; McCarthy, James S; Marquart, Louise

2017-08-25

The efficacy of vaccines aimed at inhibiting the growth of malaria parasites in the blood can be assessed by comparing the growth rate of parasitaemia in the blood of subjects treated with a test vaccine compared to controls. In studies using induced blood stage malaria (IBSM), a type of controlled human malaria infection, parasite growth rate has been measured using models with the intercept on the y-axis fixed to the inoculum size. A set of statistical models was evaluated to determine an optimal methodology to estimate parasite growth rate in IBSM studies. Parasite growth rates were estimated using data from 40 subjects published in three IBSM studies. Data was fitted using 12 statistical models: log-linear, sine-wave with the period either fixed to 48 h or not fixed; these models were fitted with the intercept either fixed to the inoculum size or not fixed. All models were fitted by individual, and overall by study using a mixed effects model with a random effect for the individual. Log-linear models and sine-wave models, with the period fixed or not fixed, resulted in similar parasite growth rate estimates (within 0.05 log 10 parasites per mL/day). Average parasite growth rate estimates for models fitted by individual with the intercept fixed to the inoculum size were substantially lower by an average of 0.17 log 10 parasites per mL/day (range 0.06-0.24) compared with non-fixed intercept models. Variability of parasite growth rate estimates across the three studies analysed was substantially higher (3.5 times) for fixed-intercept models compared with non-fixed intercept models. The same tendency was observed in models fitted overall by study. Modelling data by individual or overall by study had minimal effect on parasite growth estimates. The analyses presented in this report confirm that fixing the intercept to the inoculum size influences parasite growth estimates. The most appropriate statistical model to estimate the growth rate of blood-stage parasites

Diameter Growth Models for Inventory Applications

Treesearch

Ronald E. McRoberts; Christopher W. Woodall; Veronica C. Lessard; Margaret R. Holdaway

2002-01-01

Distant-independent, individual-tree, diametar growth models were constructed to update information for forest inventory plots measured in previous years. The models are nonlinear in the parameters and were calibrated weighted nonlinear least squares techniques and forest inventory plot data. Analyses of residuals indicated that model predictions compare favorably to...

Growth rate in the dynamical dark energy models.

PubMed

Avsajanishvili, Olga; Arkhipova, Natalia A; Samushia, Lado; Kahniashvili, Tina

Dark energy models with a slowly rolling cosmological scalar field provide a popular alternative to the standard, time-independent cosmological constant model. We study the simultaneous evolution of background expansion and growth in the scalar field model with the Ratra-Peebles self-interaction potential. We use recent measurements of the linear growth rate and the baryon acoustic oscillation peak positions to constrain the model parameter [Formula: see text] that describes the steepness of the scalar field potential.

Nonlinear Growth Models in M"plus" and SAS

ERIC Educational Resources Information Center

Grimm, Kevin J.; Ram, Nilam

2009-01-01

Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…

Modeling duckweed growth in wastewater treatment systems

USGS Publications Warehouse

Landesman, L.; Parker, N.C.; Fedler, C.B.; Konikoff, M.

2005-01-01

Species of the genera Lemnaceae, or duckweeds, are floating aquatic plants that show great promise for both wastewater treatment and livestock feed production. Research conducted in the Southern High Plains of Texas has shown that Lemna obscura grew well in cattle feedlot runoff water and produced leaf tissue with a high protein content. A model or mathematical expression derived from duckweed growth data was used to fit data from experiments conducted in a greenhouse in Lubbock, Texas. The relationship between duckweed growth and the total nitrogen concentration in the mediium follows the Mitscherlich Function and is similar to that of other plants. Empirically derived model equations have successfully predicted the growth response of Lemna obscura.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

A Stochastic Model of Eye Lens Growth

PubMed Central

Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana; Bassnett, Steven

2015-01-01

The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between various proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function. PMID:25816743

Extended Eden model reproduces growth of an acellular slime mold.

PubMed

Wagner, G; Halvorsrud, R; Meakin, P

1999-11-01

A stochastic growth model was used to simulate the growth of the acellular slime mold Physarum polycephalum on substrates where the nutrients were confined in separate drops. Growth of Physarum on such substrates was previously studied experimentally and found to produce a range of different growth patterns [Phys. Rev. E 57, 941 (1998)]. The model represented the aging of cluster sites and differed from the original Eden model in that the occupation probability of perimeter sites depended on the time of occupation of adjacent cluster sites. This feature led to a bias in the selection of growth directions. A moderate degree of persistence was found to be crucial to reproduce the biological growth patterns under various conditions. Persistence in growth combined quick propagation in heterogeneous environments with a high probability of locating sources of nutrients.

Extended Eden model reproduces growth of an acellular slime mold

NASA Astrophysics Data System (ADS)

Wagner, Geri; Halvorsrud, Ragnhild; Meakin, Paul

1999-11-01

A stochastic growth model was used to simulate the growth of the acellular slime mold Physarum polycephalum on substrates where the nutrients were confined in separate drops. Growth of Physarum on such substrates was previously studied experimentally and found to produce a range of different growth patterns [Phys. Rev. E 57, 941 (1998)]. The model represented the aging of cluster sites and differed from the original Eden model in that the occupation probability of perimeter sites depended on the time of occupation of adjacent cluster sites. This feature led to a bias in the selection of growth directions. A moderate degree of persistence was found to be crucial to reproduce the biological growth patterns under various conditions. Persistence in growth combined quick propagation in heterogeneous environments with a high probability of locating sources of nutrients.

Selection, calibration, and validation of models of tumor growth.

PubMed

Lima, E A B F; Oden, J T; Hormuth, D A; Yankeelov, T E; Almeida, R C

2016-11-01

This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology ( in vivo ). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory

Local Solutions in the Estimation of Growth Mixture Models

ERIC Educational Resources Information Center

Hipp, John R.; Bauer, Daniel J.

2006-01-01

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

Parameter Estimates in Differential Equation Models for Population Growth

ERIC Educational Resources Information Center

Winkel, Brian J.

2011-01-01

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

Analysis of a novel class of predictive microbial growth models and application to coculture growth.

PubMed

Poschet, F; Vereecken, K M; Geeraerd, A H; Nicolaï, B M; Van Impe, J F

2005-04-15

In this paper, a novel class of microbial growth models is analysed. In contrast with the currently used logistic type models (e.g., the model of Baranyi and Roberts [Baranyi, J., Roberts, T.A., 1994. A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology 23, 277-294]), the novel model class, presented in Van Impe et al. (Van Impe, J.F., Poschet, F., Geeraerd, A.H., Vereecken, K.M., 2004. Towards a novel class of predictive microbial growth models. International Journal of Food Microbiology, this issue), explicitly incorporates nutrient exhaustion and/or metabolic waste product effects inducing stationary phase behaviour. As such, these novel model types can be extended in a natural way towards microbial interactions in cocultures and microbial growth in structured foods. Two illustrative case studies of the novel model types are thoroughly analysed and compared to the widely used model of Baranyi and Roberts. In a first case study, the stationary phase is assumed to be solely resulting from toxic product inhibition and is described as a function of the pH-evolution. In the second case study, substrate exhaustion is the sole cause of the stationary phase. Finally, a more complex case study of a so-called P-model is presented, dealing with a coculture inhibition of Listeria innocua mediated by lactic acid production of Lactococcus lactis.

Monte Carlo grain growth modeling with local temperature gradients

NASA Astrophysics Data System (ADS)

Tan, Y.; Maniatty, A. M.; Zheng, C.; Wen, J. T.

2017-09-01

This work investigated the development of a Monte Carlo (MC) simulation approach to modeling grain growth in the presence of non-uniform temperature field that may vary with time. We first scale the MC model to physical growth processes by fitting experimental data. Based on the scaling relationship, we derive a grid site selection probability (SSP) function to consider the effect of a spatially varying temperature field. The SSP function is based on the differential MC step, which allows it to naturally consider time varying temperature fields too. We verify the model and compare the predictions to other existing formulations (Godfrey and Martin 1995 Phil. Mag. A 72 737-49 Radhakrishnan and Zacharia 1995 Metall. Mater. Trans. A 26 2123-30) in simple two-dimensional cases with only spatially varying temperature fields, where the predicted grain growth in regions of constant temperature are expected to be the same as for the isothermal case. We also test the model in a more realistic three-dimensional case with a temperature field varying in both space and time, modeling grain growth in the heat affected zone of a weld. We believe the newly proposed approach is promising for modeling grain growth in material manufacturing processes that involves time-dependent local temperature gradient.

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth.

PubMed

Armstrong, Michelle Hine; Buganza Tepole, Adrián; Kuhl, Ellen; Simon, Bruce R; Vande Geest, Jonathan P

2016-01-01

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

A Finite Element Model for Mixed Porohyperelasticity with Transport, Swelling, and Growth

PubMed Central

Armstrong, Michelle Hine; Buganza Tepole, Adrián; Kuhl, Ellen; Simon, Bruce R.; Vande Geest, Jonathan P.

2016-01-01

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentration-driven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues. PMID:27078495

Random-growth urban model with geographical fitness

NASA Astrophysics Data System (ADS)

Kii, Masanobu; Akimoto, Keigo; Doi, Kenji

2012-12-01

This paper formulates a random-growth urban model with a notion of geographical fitness. Using techniques of complex-network theory, we study our system as a type of preferential-attachment model with fitness, and we analyze its macro behavior to clarify the properties of the city-size distributions it predicts. First, restricting the geographical fitness to take positive values and using a continuum approach, we show that the city-size distributions predicted by our model asymptotically approach Pareto distributions with coefficients greater than unity. Then, allowing the geographical fitness to take negative values, we perform local coefficient analysis to show that the predicted city-size distributions can deviate from Pareto distributions, as is often observed in actual city-size distributions. As a result, the model we propose can generate a generic class of city-size distributions, including but not limited to Pareto distributions. For applications to city-population projections, our simple model requires randomness only when new cities are created, not during their subsequent growth. This property leads to smooth trajectories of city population growth, in contrast to other models using Gibrat’s law. In addition, a discrete form of our dynamical equations can be used to estimate past city populations based on present-day data; this fact allows quantitative assessment of the performance of our model. Further study is needed to determine appropriate formulas for the geographical fitness.

Adaptive non-linear control for cancer therapy through a Fokker-Planck observer.

PubMed

Shakeri, Ehsan; Latif-Shabgahi, Gholamreza; Esmaeili Abharian, Amir

2018-04-01

In recent years, many efforts have been made to present optimal strategies for cancer therapy through the mathematical modelling of tumour-cell population dynamics and optimal control theory. In many cases, therapy effect is included in the drift term of the stochastic Gompertz model. By fitting the model with empirical data, the parameters of therapy function are estimated. The reported research works have not presented any algorithm to determine the optimal parameters of therapy function. In this study, a logarithmic therapy function is entered in the drift term of the Gompertz model. Using the proposed control algorithm, the therapy function parameters are predicted and adaptively adjusted. To control the growth of tumour-cell population, its moments must be manipulated. This study employs the probability density function (PDF) control approach because of its ability to control all the process moments. A Fokker-Planck-based non-linear stochastic observer will be used to determine the PDF of the process. A cost function based on the difference between a predefined desired PDF and PDF of tumour-cell population is defined. Using the proposed algorithm, the therapy function parameters are adjusted in such a manner that the cost function is minimised. The existence of an optimal therapy function is also proved. The numerical results are finally given to demonstrate the effectiveness of the proposed method.

A toy model of sea ice growth

NASA Technical Reports Server (NTRS)

Thorndike, Alan S.

1992-01-01

My purpose here is to present a simplified treatment of the growth of sea ice. By ignoring many details, it is possible to obtain several results that help to clarify the ways in which the sea ice cover will respond to climate change. Three models are discussed. The first deals with the growth of sea ice during the cold season. The second describes the cycle of growth and melting for perennial ice. The third model extends the second to account for the possibility that the ice melts away entirely in the summer. In each case, the objective is to understand what physical processes are most important, what ice properties determine the ice behavior, and to which climate variables the system is most sensitive.

A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.

Computational modeling of hypertensive growth in the human carotid artery

NASA Astrophysics Data System (ADS)

Sáez, Pablo; Peña, Estefania; Martínez, Miguel Angel; Kuhl, Ellen

2014-06-01

Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

Analyzing The Uncertainty Of Diameter Growth Model Predictions

Treesearch

Ronald E. McRoberts; Veronica C. Lessard; Margaret R. Holdaway

1999-01-01

The North Central Research Station of the USDA Forest Service is developing a new set of individual tree, diameter growth models to be used as a component of an annual forest inventory system. The criterion for selection of predictor variables for these models is the uncertainty in 5-, 10-, and 20-year diameter growth predictions estimated using Monte Carlo simulations...

Adjusting the Stems Regional Forest Growth Model to Improve Local Predictions

Treesearch

W. Brad Smith

1983-01-01

A simple procedure using double sampling is described for adjusting growth in the STEMS regional forest growth model to compensate for subregional variations. Predictive accuracy of the STEMS model (a distance-independent, individual tree growth model for Lake States forests) was improved by using this procedure

Individual tree-diameter growth model for the Northeastern United States

Treesearch

Richard M. Teck; Donald E. Hilt

1991-01-01

Describes a distance-independent individual-tree diameter growth model for the Northeastern United States. Diameter growth is predicted in two steps using a two parameter, sigmoidal growth function modified by a one parameter exponential decay function with species-specific coefficients. Coefficients are presented for 28 species groups. The model accounts for...

On the validity of Zeeman's classification for three dimensional competitive differential equations with linearly determined nullclines

NASA Astrophysics Data System (ADS)

Jiang, Jifa; Niu, Lei

2017-12-01

We study three dimensional competitive differential equations with linearly determined nullclines and prove that they always have 33 stable nullcline classes in total. Each class is given in terms of inequalities on the intrinsic growth rates and competitive coefficients and is independent of generating functions. The common characteristics are that every trajectory converges to an equilibrium in classes 1-25, that Hopf bifurcations do not occur within class 32, and that there is always a heteroclinic cycle in class 27. Nontrivial dynamical behaviors, such as the existence and multiplicity of limit cycles, only may occur in classes 26-33, but these nontrivial dynamical behaviors depend on generating functions. We show that Hopf bifurcation can occur within each of classes 26-31 for continuous-time Leslie/Gower system and Ricker system, the same as Lotka-Volterra system; but it only occurs in classes 26 and 27 for continuous-time Atkinson/Allen system and Gompertz system. There is an apparent distinction between Lotka-Volterra system and Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate. Lotka-Volterra system with the identical growth rate has no limit cycle, but admits a center on the carrying simplex in classes 26 and 27. But Leslie/Gower system, Ricker system, Atkinson/Allen system, and Gompertz system with the identical growth rate do possess limit cycles. At last, we provide examples to show that Leslie/Gower system and Ricker system can also admit two limit cycles. This general classification greatly widens applications of Zeeman's method and makes it possible to investigate the existence and multiplicity of limit cycles, centers and stability of heteroclinic cycles for three dimensional competitive systems with linearly determined nullclines, as done in planar systems.

A size-structured model of bacterial growth and reproduction.

PubMed

Ellermeyer, S F; Pilyugin, S S

2012-01-01

We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.

Adjusting STEMS growth model for Wisconsin forests.

Treesearch

Margaret R. Holdaway

1985-01-01

Describes a simple procedure for adjusting growth in the STEMS regional tree growth model to compensate for subregional differences. Coefficients are reported to adjust Lake States STEMS to the forests of Northern and Central Wisconsin--an area of essentially uniform climate and similar broad physiographic features. Errors are presented for various combinations of...

Stochastic growth logistic model with aftereffect for batch fermentation process

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

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Investigating Stage-Sequential Growth Mixture Models with Multiphase Longitudinal Data

ERIC Educational Resources Information Center

Kim, Su-Young; Kim, Jee-Seon

2012-01-01

This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand…

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth

Flower Power: Sunflowers as a Model for Logistic Growth

ERIC Educational Resources Information Center

Fernandez, Eileen; Geist, Kristi A.

2011-01-01

Logistic growth displays an interesting pattern: It starts fast, exhibiting the rapid growth characteristic of exponential models. As time passes, it slows in response to constraints such as limited resources or reallocation of energy. The growth continues to slow until it reaches a limit, called capacity. When the growth describes a population,…

Teacher Evaluation Models: Compliance or Growth Oriented?

ERIC Educational Resources Information Center

Clenchy, Kelly R.

2017-01-01

This research study reviewed literature specific to the evolution of teacher evaluation models and explored the effectiveness of standards-based evaluation models' potential to facilitate professional growth. The researcher employed descriptive phenomenology to conduct a study of teachers' perceptions of a standard-based evaluation model's…

Modelling human skull growth: a validated computational model

PubMed Central

Marghoub, Arsalan; Johnson, David; Khonsari, Roman H.; Fagan, Michael J.; Moazen, Mehran

2017-01-01

During the first year of life, the brain grows rapidly and the neurocranium increases to about 65% of its adult size. Our understanding of the relationship between the biomechanical forces, especially from the growing brain, the craniofacial soft tissue structures and the individual bone plates of the skull vault is still limited. This basic knowledge could help in the future planning of craniofacial surgical operations. The aim of this study was to develop a validated computational model of skull growth, based on the finite-element (FE) method, to help understand the biomechanics of skull growth. To do this, a two-step validation study was carried out. First, an in vitro physical three-dimensional printed model and an in silico FE model were created from the same micro-CT scan of an infant skull and loaded with forces from the growing brain from zero to two months of age. The results from the in vitro model validated the FE model before it was further developed to expand from 0 to 12 months of age. This second FE model was compared directly with in vivo clinical CT scans of infants without craniofacial conditions (n = 56). The various models were compared in terms of predicted skull width, length and circumference, while the overall shape was quantified using three-dimensional distance plots. Statistical analysis yielded no significant differences between the male skull models. All size measurements from the FE model versus the in vitro physical model were within 5%, with one exception showing a 7.6% difference. The FE model and in vivo data also correlated well, with the largest percentage difference in size being 8.3%. Overall, the FE model results matched well with both the in vitro and in vivo data. With further development and model refinement, this modelling method could be used to assist in preoperative planning of craniofacial surgery procedures and could help to reduce reoperation rates. PMID:28566514

Modelling human skull growth: a validated computational model.

PubMed

Libby, Joseph; Marghoub, Arsalan; Johnson, David; Khonsari, Roman H; Fagan, Michael J; Moazen, Mehran

2017-05-01

During the first year of life, the brain grows rapidly and the neurocranium increases to about 65% of its adult size. Our understanding of the relationship between the biomechanical forces, especially from the growing brain, the craniofacial soft tissue structures and the individual bone plates of the skull vault is still limited. This basic knowledge could help in the future planning of craniofacial surgical operations. The aim of this study was to develop a validated computational model of skull growth, based on the finite-element (FE) method, to help understand the biomechanics of skull growth. To do this, a two-step validation study was carried out. First, an in vitro physical three-dimensional printed model and an in silico FE model were created from the same micro-CT scan of an infant skull and loaded with forces from the growing brain from zero to two months of age. The results from the in vitro model validated the FE model before it was further developed to expand from 0 to 12 months of age. This second FE model was compared directly with in vivo clinical CT scans of infants without craniofacial conditions ( n = 56). The various models were compared in terms of predicted skull width, length and circumference, while the overall shape was quantified using three-dimensional distance plots. Statistical analysis yielded no significant differences between the male skull models. All size measurements from the FE model versus the in vitro physical model were within 5%, with one exception showing a 7.6% difference. The FE model and in vivo data also correlated well, with the largest percentage difference in size being 8.3%. Overall, the FE model results matched well with both the in vitro and in vivo data. With further development and model refinement, this modelling method could be used to assist in preoperative planning of craniofacial surgery procedures and could help to reduce reoperation rates. © 2017 The Author(s).

Class Enumeration and Parameter Recovery of Growth Mixture Modeling and Second-Order Growth Mixture Modeling in the Presence of Measurement Noninvariance between Latent Classes

PubMed Central

Kim, Eun Sook; Wang, Yan

2017-01-01

Population heterogeneity in growth trajectories can be detected with growth mixture modeling (GMM). It is common that researchers compute composite scores of repeated measures and use them as multiple indicators of growth factors (baseline performance and growth) assuming measurement invariance between latent classes. Considering that the assumption of measurement invariance does not always hold, we investigate the impact of measurement noninvariance on class enumeration and parameter recovery in GMM through a Monte Carlo simulation study (Study 1). In Study 2, we examine the class enumeration and parameter recovery of the second-order growth mixture modeling (SOGMM) that incorporates measurement models at the first order level. Thus, SOGMM estimates growth trajectory parameters with reliable sources of variance, that is, common factor variance of repeated measures and allows heterogeneity in measurement parameters between latent classes. The class enumeration rates are examined with information criteria such as AIC, BIC, sample-size adjusted BIC, and hierarchical BIC under various simulation conditions. The results of Study 1 showed that the parameter estimates of baseline performance and growth factor means were biased to the degree of measurement noninvariance even when the correct number of latent classes was extracted. In Study 2, the class enumeration accuracy of SOGMM depended on information criteria, class separation, and sample size. The estimates of baseline performance and growth factor mean differences between classes were generally unbiased but the size of measurement noninvariance was underestimated. Overall, SOGMM is advantageous in that it yields unbiased estimates of growth trajectory parameters and more accurate class enumeration compared to GMM by incorporating measurement models. PMID:28928691

Simulating unstressed crop development and growth using the Unified Plant Growth Model (UPGM)

USDA-ARS?s Scientific Manuscript database

Since development of the EPIC model in 1989, many versions of the plant growth component have been incorporated into other erosion and crop management models and subsequently modified to meet model objectives (e.g., WEPS, WEPP, SWAT, ALMANAC, GPFARM). This has resulted in different versions of the ...

Unified Plant Growth Model (UPGM). 1. Background, objectives, and vision.

USDA-ARS?s Scientific Manuscript database

Since the development of the Environmental Policy Integrated Climate (EPIC) model in 1988, the EPIC-based plant growth code has been incorporated and modified into many agro-ecosystem models. The goals of the Unified Plant Growth Model (UPGM) project are: 1) integrating into one platform the enhance...

Mathematical foundations of the dendritic growth models.

PubMed

Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos

2007-11-01

At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.

Predicting growth of the healthy infant using a genome scale metabolic model.

PubMed

Nilsson, Avlant; Mardinoglu, Adil; Nielsen, Jens

2017-01-01

An estimated 165 million children globally have stunted growth, and extensive growth data are available. Genome scale metabolic models allow the simulation of molecular flux over each metabolic enzyme, and are well adapted to analyze biological systems. We used a human genome scale metabolic model to simulate the mechanisms of growth and integrate data about breast-milk intake and composition with the infant's biomass and energy expenditure of major organs. The model predicted daily metabolic fluxes from birth to age 6 months, and accurately reproduced standard growth curves and changes in body composition. The model corroborates the finding that essential amino and fatty acids do not limit growth, but that energy is the main growth limiting factor. Disruptions to the supply and demand of energy markedly affected the predicted growth, indicating that elevated energy expenditure may be detrimental. The model was used to simulate the metabolic effect of mineral deficiencies, and showed the greatest growth reduction for deficiencies in copper, iron, and magnesium ions which affect energy production through oxidative phosphorylation. The model and simulation method were integrated to a platform and shared with the research community. The growth model constitutes another step towards the complete representation of human metabolism, and may further help improve the understanding of the mechanisms underlying stunting.

Modeling the Growth Rates of Tetragonal Lysozyme Crystal Faces

NASA Technical Reports Server (NTRS)

Li, Meirong; Nadarajah, Arunan; Pusey, Marc L.

1998-01-01

with respect to its concentration at saturation in order to apply growth rate models to this process. The measured growth rates were then compared with the predicted ones from several dislocation and 2D nucleation growth models, employing tetramer and octamer growth units in polydisperse solutions and monomer units in monodisperse solutions. For the (110) face, the calculations consistently showed that the measured growth rates followed the expected model relations with octamer growth units. For the (101) face, it is not possible to obtain a clear agreement between the predicted and measured growth rates for a single growth unit as done for the (110) face. However, the calculations do indicate that the average size of the growth unit is between a tetramer and an octamer. This suggests that tetramers, octamers and other intermediate size growth units all participate in the growth process for this face. These calculations show that it is possible to model the macroscopic protein crystal growth rates if the molecular level processes can be account for, particularly protein aggregation processes in the bulk solution. Our recent investigations of tetragonal lysozyme crystals employing high resolution atomic force microscopy scans have further confirmed the growth of these crystals by aggregate growth units corresponding to 4(sub 3) helices.

Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots

ERIC Educational Resources Information Center

Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.

2013-01-01

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…

Derivation and application of a mathematical model for long bone growth.

PubMed

Seetharam, Suneil; Bhatia, Sujata K

2012-01-01

The objective of this work was to develop a mathematical model of long bone growth and to gain insights regarding growth disorders. A cell balance (mass balance of moving cells) assessment was performed on the three regions of the growth plate, to determine the variables (including number of proliferating cells, and division rate of proliferating cells) that influence tibia growth rate. Once this relationship was established, clinical data were used to understand how tibia growth rate and number of proliferating cells change with time. These equations were then inserted into the model to determine how cell division rate changes with time. The model was utilized to determine the influence of growth time, and to measure changes in vitamin C deficiency, Indian hedgehog (IHH) expression, and bone morphogenetic protein-2 (BMP-2) implants on tibia length. According to the model, a 10-month discrepancy in growth time between the two tibias is required to produce clinically significant leg asymmetry. In addition, vitamin C deficiency, IHH overexpression, and BMP-2 implants can all affect tibia length. These bioactive molecules have the greatest effect on tibia growth rate when these perturbations occur early in life for extended periods of time. The results are significant for modeling and predicting the effects of perturbations, including bioactive implants, on long bone growth.

Mechanical model for filament buckling and growth by phase ordering.

PubMed

Rey, Alejandro D; Abukhdeir, Nasser M

2008-02-05

A mechanical model of open filament shape and growth driven by phase ordering is formulated. For a given phase-ordering driving force, the model output is the filament shape evolution and the filament end-point kinematics. The linearized model for the slope of the filament is the Cahn-Hilliard model of spinodal decomposition, where the buckling corresponds to concentration fluctuations. Two modes are predicted: (i) sequential growth and buckling and (ii) simultaneous buckling and growth. The relation among the maximum buckling rate, filament tension, and matrix viscosity is given. These results contribute to ongoing work in smectic A filament buckling.

Agent-Based Modeling of Growth Processes

ERIC Educational Resources Information Center

Abraham, Ralph

2014-01-01

Growth processes abound in nature, and are frequently the target of modeling exercises in the sciences. In this article we illustrate an agent-based approach to modeling, in the case of a single example from the social sciences: bullying.

Growth modeling of Listeria monocytogenes in pasteurized liquid egg.

PubMed

Ohkochi, Miho; Koseki, Shigenobu; Kunou, Masaaki; Sugiura, Katsuaki; Tsubone, Hirokazu

2013-09-01

The growth kinetics of Listeria monocytogenes and natural flora in commercially produced pasteurized liquid egg was examined at 4.1 to 19.4°C, and a growth simulation model that can estimate the range of the number of L. monocytogenes bacteria was developed. The experimental kinetic data were fitted to the Baranyi model, and growth parameters, such as maximum specific growth rate (μ(max)), maximum population density (N(max)), and lag time (λ), were estimated. As a result of estimating these parameters, we found that L. monocytogenes can grow without spoilage below 12.2°C, and we then focused on storage temperatures below 12.2°C in developing our secondary models. The temperature dependency of the μ(max) was described by Ratkowsky's square root model. The N(max) of L. monocytogenes was modeled as a function of temperature, because the N(max) of L. monocytogenes decreased as storage temperature increased. A tertiary model of L. monocytogenes was developed using the Baranyi model and μ(max) and N(max) secondary models. The ranges of the numbers of L. monocytogenes bacteria were simulated using Monte Carlo simulations with an assumption that these parameters have variations that follow a normal distribution. Predictive simulations under both constant and fluctuating temperature conditions demonstrated a high accuracy, represented by root mean square errors of 0.44 and 0.34, respectively. The predicted ranges also seemed to show a reasonably good estimation, with 55.8 and 51.5% of observed values falling into the prediction range of the 25th to 75th percentile, respectively. These results suggest that the model developed here can be used to estimate the kinetics and range of L. monocytogenes growth in pasteurized liquid egg under refrigerated temperature.

Modeling effects of overstory density and competing vegetation on tree height growth

Treesearch

Christian Salas; Albert R. Stage; Andrew P. Robinson

2007-01-01

We developed and evaluated an individual-tree height growth model for Douglas-fir [Pseudotsuga menziesii (Mirbel) Franco] in the Inland Northwest United States. The model predicts growth for all tree sizes continuously, rather than requiring a transition between independent models for juvenile and mature growth phases. The model predicts the effects...

How to improve breeding value prediction for feed conversion ratio in the case of incomplete longitudinal body weights.

PubMed

Tran, V H Huynh; Gilbert, H; David, I

2017-01-01

quite similar for miss_FCR, Gomp_FCR, and interp_FCR. In conclusion, when the proportion of missing BW is high, genetic parameters of FCR are not well estimated. In French Large White pigs, in the growing period extending from d 65 to 168, prediction of missing BW using a Gompertz growth model slightly improved the estimations, but the linear interpolation improved the estimation to a greater extent. This result is due to the linear rather than sigmoidal increase in BW over the study period.

Modeling the growth of Salmonella in raw poultry stored under aerobic conditions.

PubMed

Dominguez, Silvia A; Schaffner, Donald W

2008-12-01

The presence of Salmonella in raw poultry is a well-recognized risk factor for foodborne illness. The objective of this study was to develop and validate a mathematical model that predicts the growth of Salmonella in raw poultry stored under aerobic conditions at a variety of temperatures. One hundred twelve Salmonella growth rates were extracted from 12 previously published studies. These growth rates were used to develop a square-root model relating the growth rate of Salmonella to storage temperature. Model predictions were compared to growth rate measurements collected in our laboratory for four poultry-specific Salmonella strains (two antibiotic-resistant and two nonresistant strains) inoculated onto raw chicken tenderloins. Chicken was inoculated at two levels (10(3) CFU/cm2 and < or = 10 CFU/cm2) and incubated at temperatures ranging from 10 to 37 degrees C. Visual inspection of the data, bias and accuracy factors, and comparison with two other published models were used to analyze the performance of the new model. Neither antibiotic resistance nor inoculum size affected Salmonella growth rates. The presence of spoilage microflora did not appear to slow the growth of Salmonella. Our model provided intermediate predicted growth rates when compared with the two other published models. Our model predicted slightly faster growth rates than those observed in inoculated chicken in the temperature range of 10 to 28 degrees C but slightly slower growth rates than those observed between 30 and 37 degrees C. Slightly negative bias factors were obtained in every case (-5 to -3%); however, application of the model may be considered fail-safe for storage temperatures below 28 degrees C.

Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves

NASA Technical Reports Server (NTRS)

Mengshoel, Ole Jakob

2009-01-01

Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using

A New Model for Root Growth in Soil with Macropores

NASA Astrophysics Data System (ADS)

Landl, M.; Huber, K.; Schnepf, A.; Vanderborght, J.; Javaux, M.; Bengough, G.; Vereecken, H.

2016-12-01

In order to study soil-root interaction processes, dynamic root architecture models which are linked to models that simulate water flow and nutrient transport in the soil-root system are needed. Such models can be used to predict the impact of soil structural features, e.g. the presence of macropores in dense subsoil, on water and nutrient uptake by plants. In dynamic root architecture models, root growth is represented by moving root tips whose growth trajectory results in the creation of linear root segments. Typically, the direction of each new root segment is calculated as the vector sum of various direction-affecting components. The use of these established methods to simulate root growth in soil containing macropores, however, failed to reproduce experimentally observed root growth patterns. We therefore developed an alternative modelling approach where we distinguish between, firstly, the driving force for root growth which is determined by the orientation of the previous root segment as well as the influence of gravitropism and, secondly, soil mechanical resistance to root growth. The latter is expressed by root conductance which represents the inverse of soil penetration resistance and is treated similarly to hydraulic conductivity in Darcy's law. At the presence of macropores, root conductance is anisotropic which leads to a difference between the direction of the driving force and the direction of the root tip movement. The model was tested using data from the literature, at pot scale, at macropore scale, and in a series of simulations where sensitivity to gravity and macropore orientation was evaluated. The model simulated root growth trajectories in structured soil at both single root and whole root-system scales, generating root systems that were similar to images from experiments. Its implementation in the three dimensional soil and root water uptake model R-SWMS enables the use of the model in the future to evaluate the effect of macropores on crop

Leptin administration affects growth and skeletal development in a rat intrauterine growth restriction model: preliminary study.

PubMed

Bar-El Dadon, Shimrit; Shahar, Ron; Katalan, Vered; Monsonego-Ornan, Efrat; Reifen, Ram

2011-09-01

Skeletal abnormalities are one of the hallmarks of growth delay during gestation. The aim of this study was to determine changes induced by leptin in skeletal growth and development in a rat model of intrauterine growth retardation (IUGR) and to elucidate the possible underlying mechanisms. Intrauterine growth retardation was induced prepartum and the effects of leptin to mothers prenatally or to offspring postnatally were studied. Radii were harvested and tested mechanically and structurally. Tibias were evaluated for growth-plate morphometry. On day 40 postpartum, total bone length and mineral density and tibial growth-plate width and numbers of cells within its zones of offspring treated with leptin were significantly greater than in the control group. Postnatal leptin administration in an IUGR model improves the structural properties and elongation rate of bone. These findings could pave the way to preventing some phenotypic presentations of IUGR. Copyright © 2011 Elsevier Inc. All rights reserved.

Evaluating growth models: A case study using PrognosisBC

Treesearch

Peter Marshall; Pablo Parysow; Shadrach Akindele

2008-01-01

The ability of the PrognosisBC (Version 3.0) growth model to predict tree and stand growth was assessed against a series of remeasured permanent sample plots, including some which had been precommercially thinned. In addition, the model was evaluated for logical consistency across a variety of stand structures using simulation. By the end of the...

Human growth and body weight dynamics: an integrative systems model.

PubMed

Rahmandad, Hazhir

2014-01-01

Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%-24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations.

Human Growth and Body Weight Dynamics: An Integrative Systems Model

PubMed Central

Rahmandad, Hazhir

2014-01-01

Quantifying human weight and height dynamics due to growth, aging, and energy balance can inform clinical practice and policy analysis. This paper presents the first mechanism-based model spanning full individual life and capturing changes in body weight, composition and height. Integrating previous empirical and modeling findings and validated against several additional empirical studies, the model replicates key trends in human growth including A) Changes in energy requirements from birth to old ages. B) Short and long-term dynamics of body weight and composition. C) Stunted growth with chronic malnutrition and potential for catch up growth. From obesity policy analysis to treating malnutrition and tracking growth trajectories, the model can address diverse policy questions. For example I find that even without further rise in obesity, the gap between healthy and actual Body Mass Indexes (BMIs) has embedded, for different population groups, a surplus of 14%–24% in energy intake which will be a source of significant inertia in obesity trends. In another analysis, energy deficit percentage needed to reduce BMI by one unit is found to be relatively constant across ages. Accompanying documented and freely available simulation model facilitates diverse applications customized to different sub-populations. PMID:25479101

A Three-Level Hierarchical Linear Model Using Student Growth Curve Modeling and Contextual Data

ERIC Educational Resources Information Center

Giorgio, Dorian

2012-01-01

Educational experts have criticized status models of school accountability, as required by the No Child Left Behind Act (NCLB), describing them as ineffectual in measuring achievement because their one-time assessment of student knowledge ignores student growth. Research on student achievement has instead identified growth models as superior…

Modelling breast cancer tumour growth for a stable disease population.

PubMed

Isheden, Gabriel; Humphreys, Keith

2017-01-01

Statistical models of breast cancer tumour progression have been used to further our knowledge of the natural history of breast cancer, to evaluate mammography screening in terms of mortality, to estimate overdiagnosis, and to estimate the impact of lead-time bias when comparing survival times between screen detected cancers and cancers found outside of screening programs. Multi-state Markov models have been widely used, but several research groups have proposed other modelling frameworks based on specifying an underlying biological continuous tumour growth process. These continuous models offer some advantages over multi-state models and have been used, for example, to quantify screening sensitivity in terms of mammographic density, and to quantify the effect of body size covariates on tumour growth and time to symptomatic detection. As of yet, however, the continuous tumour growth models are not sufficiently developed and require extensive computing to obtain parameter estimates. In this article, we provide a detailed description of the underlying assumptions of the continuous tumour growth model, derive new theoretical results for the model, and show how these results may help the development of this modelling framework. In illustrating the approach, we develop a model for mammography screening sensitivity, using a sample of 1901 post-menopausal women diagnosed with invasive breast cancer.

Evaluating the Predictive Value of Growth Prediction Models

ERIC Educational Resources Information Center

Murphy, Daniel L.; Gaertner, Matthew N.

2014-01-01

This study evaluates four growth prediction models--projection, student growth percentile, trajectory, and transition table--commonly used to forecast (and give schools credit for) middle school students' future proficiency. Analyses focused on vertically scaled summative mathematics assessments, and two performance standards conditions (high…

The AFIS tree growth model for updating annual forest inventories in Minnesota

Treesearch

Margaret R. Holdaway

2000-01-01

As the Forest Service moves towards annual inventories, states may use model predictions of growth to update unmeasured plots. A tree growth model (AFIS) based on the scaled Weibull function and using the average-adjusted model form is presented. Annual diameter growth for four species was modeled using undisturbed plots from Minnesota's Aspen-Birch and Northern...

Residual Structures in Latent Growth Curve Modeling

ERIC Educational Resources Information Center

Grimm, Kevin J.; Widaman, Keith F.

2010-01-01

Several alternatives are available for specifying the residual structure in latent growth curve modeling. Two specifications involve uncorrelated residuals and represent the most commonly used residual structures. The first, building on repeated measures analysis of variance and common specifications in multilevel models, forces residual variances…

Forest Growth and Yield Models Viewed From a Different Perspective

Treesearch

Jeffery C. Goelz

2002-01-01

Typically, when different forms of growth and yield models are considered, they are grouped into convenient discrete classes. As a heuristic device, I chose to use a contrasting perspective, that all growth and yield models are diameter distribution models that merely differ in regard to which diameter distribution is employed and how the distribution is projected to...

Modeling the growth and branching of plants: A simple rod-based model

NASA Astrophysics Data System (ADS)

Faruk Senan, Nur Adila; O'Reilly, Oliver M.; Tresierras, Timothy N.

A rod-based model for plant growth and branching is developed in this paper. Specifically, Euler's theory of the elastica is modified to accommodate growth and remodeling. In addition, branching is characterized using a configuration force and evolution equations are postulated for the flexural stiffness and intrinsic curvature. The theory is illustrated with examples of multiple static equilibria of a branched plant and the remodeling and tip growth of a plant stem under gravitational loading.

Response surface models for effects of temperature and previous growth sodium chloride on growth kinetics of Salmonella typhimurium on cooked chicken breast.

PubMed

Oscar, T P

1999-12-01

Response surface models were developed and validated for effects of temperature (10 to 40 degrees C) and previous growth NaCl (0.5 to 4.5%) on lag time (lambda) and specific growth rate (mu) of Salmonella Typhimurium on cooked chicken breast. Growth curves for model development (n = 55) and model validation (n = 16) were fit to a two-phase linear growth model to obtain lambda and mu of Salmonella Typhimurium on cooked chicken breast. Response surface models for natural logarithm transformations of lambda and mu as a function of temperature and previous growth NaCl were obtained by regression analysis. Both lambda and mu of Salmonella Typhimurium were affected (P < 0.0001) by temperature but not by previous growth NaCl. Models were validated against data not used in their development. Mean absolute relative error of predictions (model accuracy) was 26.6% for lambda and 15.4% for mu. Median relative error of predictions (model bias) was 0.9% for lambda and 5.2% for mu. Results indicated that the models developed provided reliable predictions of lambda and mu of Salmonella Typhimurium on cooked chicken breast within the matrix of conditions modeled. In addition, results indicated that previous growth NaCl (0.5 to 4.5%) was not a major factor affecting subsequent growth kinetics of Salmonella Typhimurium on cooked chicken breast. Thus, inclusion of previous growth NaCl in predictive models may not significantly improve our ability to predict growth of Salmonella spp. on food subjected to temperature abuse.

On Fitting a Multivariate Two-Part Latent Growth Model

PubMed Central

Xu, Shu; Blozis, Shelley A.; Vandewater, Elizabeth A.

2017-01-01

A 2-part latent growth model can be used to analyze semicontinuous data to simultaneously study change in the probability that an individual engages in a behavior, and if engaged, change in the behavior. This article uses a Monte Carlo (MC) integration algorithm to study the interrelationships between the growth factors of 2 variables measured longitudinally where each variable can follow a 2-part latent growth model. A SAS macro implementing Mplus is developed to estimate the model to take into account the sampling uncertainty of this simulation-based computational approach. A sample of time-use data is used to show how maximum likelihood estimates can be obtained using a rectangular numerical integration method and an MC integration method. PMID:29333054

New simulation model of multicomponent crystal growth and inhibition.

PubMed

Wathen, Brent; Kuiper, Michael; Walker, Virginia; Jia, Zongchao

2004-04-02

We review a novel computational model for the study of crystal structures both on their own and in conjunction with inhibitor molecules. The model advances existing Monte Carlo (MC) simulation techniques by extending them from modeling 3D crystal surface patches to modeling entire 3D crystals, and by including the use of "complex" multicomponent molecules within the simulations. These advances makes it possible to incorporate the 3D shape and non-uniform surface properties of inhibitors into simulations, and to study what effect these inhibitor properties have on the growth of whole crystals containing up to tens of millions of molecules. The application of this extended MC model to the study of antifreeze proteins (AFPs) and their effects on ice formation is reported, including the success of the technique in achieving AFP-induced ice-growth inhibition with concurrent changes to ice morphology that mimic experimental results. Simulations of ice-growth inhibition suggest that the degree of inhibition afforded by an AFP is a function of its ice-binding position relative to the underlying anisotropic growth pattern of ice. This extended MC technique is applicable to other crystal and crystal-inhibitor systems, including more complex crystal systems such as clathrates.

Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

PubMed Central

Westermark, Stefanie; Steuer, Ralf

2016-01-01

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes. PMID:28083530

Slow crack growth: Models and experiments

NASA Astrophysics Data System (ADS)

Santucci, S.; Vanel, L.; Ciliberto, S.

2007-07-01

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.

Mathematical modelling of growth of Listeria  monocytogenes in raw chilled pork.

PubMed

Ye, K; Wang, K; Liu, M; Liu, J; Zhu, L; Zhou, G

2017-04-01

The aim of this study was to analyse the growth kinetics of Listeria monocytogenes in naturally contaminated chilled pork. A cocktail of 26 meat-borne L. monocytogenes was inoculated to raw or sterile chilled pork to observe its growth at 4, 10, 16, 22 and 28°C respectively. The growth data were fitted by the Baranyi model and Ratkowsky square-root model. Results showed that the Baranyi model and Ratkowsky square-root model could describe the growth characteristics of L. monocytogenes at different temperatures reasonably well in raw chilled pork (1·0 ≤ Bf ≤ Af ≤ 1·1). Compared with the growth of L. monocytogenes in sterile chilled pork, the background microflora had no impact on the growth parameters of L. monocytogenes, except for the lag phase at low temperature storage. The microbial predictive models developed in this study can be used to predict the growth of L. monocytogenes during natural spoilage, and construct quantitative risk assessments in chilled pork. This study simulated the actual growth of Listeria monocytogenes in chilled pork to the maximum extent, and described its growth characteristics of L. monocytogenes during natural spoilage. This study showed that the background microflora had no impact on the growth parameters of L. monocytogenes, except for the lag phase at low temperature storage. The models developed in this study can be used to predict the growth of L. monocytogenes during refrigerated storage. © 2017 The Society for Applied Microbiology.

Dynamic model for predicting growth of salmonella spp. in ground sterile pork

USDA-ARS?s Scientific Manuscript database

Predictive model for Salmonella spp. growth in ground pork was developed and validated using kinetic growth data. Salmonella spp. kinetic growth data in ground pork was collected at several isothermal conditions (between 10 and 45C) and Baranyi model was fitted to describe the growth at each temper...

Bayesian Inference and Application of Robust Growth Curve Models Using Student's "t" Distribution

ERIC Educational Resources Information Center

Zhang, Zhiyong; Lai, Keke; Lu, Zhenqiu; Tong, Xin

2013-01-01

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy.

PubMed

He, Yixuan; Kodali, Anita; Wallace, Dorothy I

2018-06-14

Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.

Using a laboratory-based growth model to estimate mass- and temperature-dependent growth parameters across populations of juvenile Chinook Salmon

USGS Publications Warehouse

Perry, Russell W.; Plumb, John M.; Huntington, Charles

2015-01-01

To estimate the parameters that govern mass- and temperature-dependent growth, we conducted a meta-analysis of existing growth data from juvenile Chinook Salmon Oncorhynchus tshawytscha that were fed an ad libitum ration of a pelleted diet. Although the growth of juvenile Chinook Salmon has been well studied, research has focused on a single population, a narrow range of fish sizes, or a narrow range of temperatures. Therefore, we incorporated the Ratkowsky model for temperature-dependent growth into an allometric growth model; this model was then fitted to growth data from 11 data sources representing nine populations of juvenile Chinook Salmon. The model fit the growth data well, explaining 98% of the variation in final mass. The estimated allometric mass exponent (b) was 0.338 (SE = 0.025), similar to estimates reported for other salmonids. This estimate of b will be particularly useful for estimating mass-standardized growth rates of juvenile Chinook Salmon. In addition, the lower thermal limit, optimal temperature, and upper thermal limit for growth were estimated to be 1.8°C (SE = 0.63°C), 19.0°C (SE = 0.27°C), and 24.9°C (SE = 0.02°C), respectively. By taking a meta-analytical approach, we were able to provide a growth model that is applicable across populations of juvenile Chinook Salmon receiving an ad libitum ration of a pelleted diet.

Modelling grain growth in the framework of Rational Extended Thermodynamics

NASA Astrophysics Data System (ADS)

Kertsch, Lukas; Helm, Dirk

2016-05-01

Grain growth is a significant phenomenon for the thermomechanical processing of metals. Since the mobility of the grain boundaries is thermally activated and energy stored in the grain boundaries is released during their motion, a mutual interaction with the process conditions occurs. To model such phenomena, a thermodynamic framework for the representation of thermomechanical coupling phenomena in metals including a microstructure description is required. For this purpose, Rational Extended Thermodynamics appears to be a useful tool. We apply an entropy principle to derive a thermodynamically consistent model for grain coarsening due to the growth and shrinkage of individual grains. Despite the rather different approaches applied, we obtain a grain growth model which is similar to existing ones and can be regarded as a thermodynamic extension of that by Hillert (1965) to more general systems. To demonstrate the applicability of the model, we compare our simulation results to grain growth experiments in pure copper by different authors, which we are able to reproduce very accurately. Finally, we study the implications of the energy release due to grain growth on the energy balance. The present unified approach combining a microstructure description and continuum mechanics is ready to be further used to develop more elaborate material models for complex thermo-chemo-mechanical coupling phenomena.

Quantitative model of the growth of floodplains by vertical accretion

USGS Publications Warehouse

Moody, J.A.; Troutman, B.M.

2000-01-01

A simple one-dimensional model is developed to quantitatively predict the change in elevation, over a period of decades, for vertically accreting floodplains. This unsteady model approximates the monotonic growth of a floodplain as an incremental but constant increase of net sediment deposition per flood for those floods of a partial duration series that exceed a threshold discharge corresponding to the elevation of the floodplain. Sediment deposition from each flood increases the elevation of the floodplain and consequently the magnitude of the threshold discharge resulting in a decrease in the number of floods and growth rate of the floodplain. Floodplain growth curves predicted by this model are compared to empirical growth curves based on dendrochronology and to direct field measurements at five floodplain sites. The model was used to predict the value of net sediment deposition per flood which best fits (in a least squares sense) the empirical and field measurements; these values fall within the range of independent estimates of the net sediment deposition per flood based on empirical equations. These empirical equations permit the application of the model to estimate of floodplain growth for other floodplains throughout the world which do not have detailed data of sediment deposition during individual floods. Copyright (C) 2000 John Wiley and Sons, Ltd.

Modeling plasma-assisted growth of graphene-carbon nanotube hybrid

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

Tewari, Aarti

2016-08-15

A theoretical model describing the growth of graphene-CNT hybrid in a plasma medium is presented. Using the model, the growth of carbon nanotube (CNT) on a catalyst particle and thereafter the growth of the graphene on the CNT is studied under the purview of plasma sheath and number density kinetics of different plasma species. It is found that the plasma parameter such as ion density; gas ratios and process parameter such as source power affect the CNT and graphene dimensions. The variation in growth rates of graphene and CNT under different plasma power, gas ratios, and ion densities is analyzed.more » Based on the results obtained, it can be concluded that higher hydrocarbon ion densities and gas ratios of hydrocarbon to hydrogen favor the growth of taller CNTs and graphene, respectively. In addition, the CNT tip radius reduces with hydrogen ion density and higher plasma power favors graphene with lesser thickness. The present study can help in better understanding of the graphene-CNT hybrid growth in a plasma medium.« less

Plant growth and architectural modelling and its applications

PubMed Central

Guo, Yan; Fourcaud, Thierry; Jaeger, Marc; Zhang, Xiaopeng; Li, Baoguo

2011-01-01

Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels. PMID:21638797

A Gompertzian model with random effects to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

2015-05-15

In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

Onset of mortality increase with age and age trajectories of mortality from all diseases in the four Nordic countries.

PubMed

Dolejs, Josef; Marešová, Petra

2017-01-01

The answer to the question "At what age does aging begin?" is tightly related to the question "Where is the onset of mortality increase with age?" Age affects mortality rates from all diseases differently than it affects mortality rates from nonbiological causes. Mortality increase with age in adult populations has been modeled by many authors, and little attention has been given to mortality decrease with age after birth. Nonbiological causes are excluded, and the category "all diseases" is studied. It is analyzed in Denmark, Finland, Norway, and Sweden during the period 1994-2011, and all possible models are screened. Age trajectories of mortality are analyzed separately: before the age category where mortality reaches its minimal value and after the age category. Resulting age trajectories from all diseases showed a strong minimum, which was hidden in total mortality. The inverse proportion between mortality and age fitted in 54 of 58 cases before mortality minimum. The Gompertz model with two parameters fitted as mortality increased with age in 17 of 58 cases after mortality minimum, and the Gompertz model with a small positive quadratic term fitted data in the remaining 41 cases. The mean age where mortality reached minimal value was 8 (95% confidence interval 7.05-8.95) years. The figures depict an age where the human population has a minimal risk of death from biological causes. Inverse proportion and the Gompertz model fitted data on both sides of the mortality minimum, and three parameters determined the shape of the age-mortality trajectory. Life expectancy should be determined by the two standard Gompertz parameters and also by the single parameter in the model c/x. All-disease mortality represents an alternative tool to study the impact of age. All results are based on published data.

A laboratory-calibrated model of coho salmon growth with utility for ecological analyses

USGS Publications Warehouse

Manhard, Christopher V.; Som, Nicholas A.; Perry, Russell W.; Plumb, John M.

2018-01-01

We conducted a meta-analysis of laboratory- and hatchery-based growth data to estimate broadly applicable parameters of mass- and temperature-dependent growth of juvenile coho salmon (Oncorhynchus kisutch). Following studies of other salmonid species, we incorporated the Ratkowsky growth model into an allometric model and fit this model to growth observations from eight studies spanning ten different populations. To account for changes in growth patterns with food availability, we reparameterized the Ratkowsky model to scale several of its parameters relative to ration. The resulting model was robust across a wide range of ration allocations and experimental conditions, accounting for 99% of the variation in final body mass. We fit this model to growth data from coho salmon inhabiting tributaries and constructed ponds in the Klamath Basin by estimating habitat-specific indices of food availability. The model produced evidence that constructed ponds provided higher food availability than natural tributaries. Because of their simplicity (only mass and temperature are required as inputs) and robustness, ration-varying Ratkowsky models have utility as an ecological tool for capturing growth in freshwater fish populations.

Density-dependence as a size-independent regulatory mechanism.

PubMed

de Vladar, Harold P

2006-01-21

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.

Modeling Gas Exchange in a Closed Plant Growth Chamber

NASA Technical Reports Server (NTRS)

Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.

1994-01-01

Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant a growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.

Modeling gas exchange in a closed plant growth chamber

NASA Technical Reports Server (NTRS)

Cornett, J. D.; Hendrix, J. E.; Wheeler, R. M.; Ross, C. W.; Sadeh, W. Z.

1994-01-01

Fluid transport models for fluxes of water vapor and CO2 have been developed for one crop of wheat and three crops of soybean grown in a closed plant growth chamber. Correspondence among these fluxes is discussed. Maximum fluxes of gases are provided for engineering design requirements of fluid recycling equipment in growth chambers. Furthermore, to investigate the feasibility of generalized crop models, dimensionless representations of water vapor fluxes are presented. The feasibility of such generalized models and the need for additional data are discussed.

Analysis of models for two solution crystal growth problems

NASA Technical Reports Server (NTRS)

Fehribach, Joseph D.; Rosenberger, Franz

1989-01-01

Two diffusive solution crystal growth models are considered which are characterized by two phases separated by an interface, a lack of convective mixing in either phase, and the presence of diffusion components differing widely in diffusivity. The first model describes precipitant-driven solution crystal growth and the second model describes a hanging drop evaporation problem. It is shown that for certain proteins sharp concentration gradients may develop in the drop during evaporation, while under the same conditions the concentrations of other proteins remain uniform.

Relation between germination and mycelium growth of individual fungal spores.

PubMed

Gougouli, Maria; Koutsoumanis, Konstantinos P

2013-02-15

The relation between germination time and lag time of mycelium growth of individual spores was studied by combining microscopic and macroscopic techniques. The radial growth of a large number (100-200) of Penicillium expansum and Aspergillus niger mycelia originating from single spores was monitored macroscopically at isothermal conditions ranging from 0 to 30°C and 10 to 41.5°C, respectively. The radial growth curve for each mycelium was fitted to a linear model for the estimation of mycelium lag time. The results showed that the lag time varied significantly among single spores. The cumulative frequency distributions of the lag times were fitted to the modified Gompertz model and compared with the respective distributions for the germination time, which were obtained microscopically. The distributions of the measured mycelium lag time were found to be similar to the germination time distributions under the same conditions but shifted in time with the lag times showing a significant delay compared to germination times. A numerical comparison was also performed based on the distribution parameters λ(m) and λ(g), which indicate the time required from the spores to start the germination process and the completion of the lag phase, respectively. The relative differences %(λ(m)-λ(g))/λ(m) were not found to be significantly affected by temperatures tested with mean values of 72.5±5.1 and 60.7±2.1 for P. expansum for A. niger, respectively. In order to investigate the source of the above difference, a time-lapse microscopy method was developed providing videos with the behavior of single fungal spore from germination until mycelium formation. The distances of the apexes of the first germ tubes that emerged from the swollen spore were measured in each frame of the videos and these data were expressed as a function of time. The results showed that in the early hyphal development, the measured radii appear to increase exponentially, until a certain time, where

Modeling of dislocation dynamics in germanium Czochralski growth

NASA Astrophysics Data System (ADS)

Artemyev, V. V.; Smirnov, A. D.; Kalaev, V. V.; Mamedov, V. M.; Sidko, A. P.; Podkopaev, O. I.; Kravtsova, E. D.; Shimansky, A. F.

2017-06-01

Obtaining very high-purity germanium crystals with low dislocation density is a practically difficult problem, which requires knowledge and experience in growth processes. Dislocation density is one of the most important parameters defining the quality of germanium crystal. In this paper, we have performed experimental study of dislocation density during 4-in. germanium crystal growth using the Czochralski method and comprehensive unsteady modeling of the same crystal growth processes, taking into account global heat transfer, melt flow and melt/crystal interface shape evolution. Thermal stresses in the crystal and their relaxation with generation of dislocations within the Alexander-Haasen model have been calculated simultaneously with crystallization dynamics. Comparison to experimental data showed reasonable agreement for the temperature, interface shape and dislocation density in the crystal between calculation and experiment.

Modeling water scarcity over south Asia: Incorporating crop growth and irrigation models into the Variable Infiltration Capacity (VIC) model

NASA Astrophysics Data System (ADS)

Troy, Tara J.; Ines, Amor V. M.; Lall, Upmanu; Robertson, Andrew W.

2013-04-01

Large-scale hydrologic models, such as the Variable Infiltration Capacity (VIC) model, are used for a variety of studies, from drought monitoring to projecting the potential impact of climate change on the hydrologic cycle decades in advance. The majority of these models simulates the natural hydrological cycle and neglects the effects of human activities such as irrigation, which can result in streamflow withdrawals and increased evapotranspiration. In some parts of the world, these activities do not significantly affect the hydrologic cycle, but this is not the case in south Asia where irrigated agriculture has a large water footprint. To address this gap, we incorporate a crop growth model and irrigation model into the VIC model in order to simulate the impacts of irrigated and rainfed agriculture on the hydrologic cycle over south Asia (Indus, Ganges, and Brahmaputra basin and peninsular India). The crop growth model responds to climate signals, including temperature and water stress, to simulate the growth of maize, wheat, rice, and millet. For the primarily rainfed maize crop, the crop growth model shows good correlation with observed All-India yields (0.7) with lower correlations for the irrigated wheat and rice crops (0.4). The difference in correlation is because irrigation provides a buffer against climate conditions, so that rainfed crop growth is more tied to climate than irrigated crop growth. The irrigation water demands induce hydrologic water stress in significant parts of the region, particularly in the Indus, with the streamflow unable to meet the irrigation demands. Although rainfall can vary significantly in south Asia, we find that water scarcity is largely chronic due to the irrigation demands rather than being intermittent due to climate variability.

Phase-field model of vapor-liquid-solid nanowire growth

NASA Astrophysics Data System (ADS)

Wang, Nan; Upmanyu, Moneesh; Karma, Alain

2018-03-01

We present a multiphase-field model to describe quantitatively nanowire growth by the vapor-liquid-solid (VLS) process. The free-energy functional of this model depends on three nonconserved order parameters that distinguish the vapor, liquid, and solid phases and describe the energetic properties of various interfaces, including arbitrary forms of anisotropic γ plots for the solid-vapor and solid-liquid interfaces. The evolution equations for those order parameters describe basic kinetic processes including the rapid (quasi-instantaneous) equilibration of the liquid catalyst to a droplet shape with constant mean curvature, the slow incorporation of growth atoms at the droplet surface, and crystallization within the droplet. The standard constraint that the sum of the phase fields equals unity and the conservation of the number of catalyst atoms, which relates the catalyst volume to the concentration of growth atoms inside the droplet, are handled via separate Lagrange multipliers. An analysis of the model is presented that rigorously maps the phase-field equations to a desired set of sharp-interface equations for the evolution of the phase boundaries under the constraint of force balance at three-phase junctions (triple points) given by the Young-Herring relation that includes torque term related to the anisotropy of the solid-liquid and solid-vapor interface excess free energies. Numerical examples of growth in two dimensions are presented for the simplest case of vanishing crystalline anisotropy and the more realistic case of a solid-liquid γ plot with cusped minima corresponding to two sets of (10 ) and (11 ) facets. The simulations reproduce many of the salient features of nanowire growth observed experimentally, including growth normal to the substrate with tapering of the side walls, transitions between different growth orientations, and crawling growth along the substrate. They also reproduce different observed relationships between the nanowire growth

Dynamic modeling of Listeria monocytogenes growth in pasteurized vanilla cream after postprocessing contamination.

PubMed

Panagou, Efstathios Z; Nychas, George-John E

2008-09-01

A product-specific model was developed and validated under dynamic temperature conditions for predicting the growth of Listeria monocytogenes in pasteurized vanilla cream, a traditional milk-based product. Model performance was also compared with Growth Predictor and Sym'Previus predictive microbiology software packages. Commercially prepared vanilla cream samples were artificially inoculated with a five-strain cocktail of L. monocytogenes, with an initial concentration of 102 CFU g(-1), and stored at 3, 5, 10, and 15 degrees C for 36 days. The growth kinetic parameters at each temperature were determined by the primary model of Baranyi and Roberts. The maximum specific growth rate (mu(max)) was further modeled as a function of temperature by means of a square root-type model. The performance of the model in predicting the growth of the pathogen under dynamic temperature conditions was based on two different temperature scenarios with periodic changes from 4 to 15 degrees C. Growth prediction for dynamic temperature profiles was based on the square root model and the differential equations of the Baranyi and Roberts model, which were numerically integrated with respect to time. Model performance was based on the bias factor (B(f)), the accuracy factor (A(f)), the goodness-of-fit index (GoF), and the percent relative errors between observed and predicted growth. The product-specific model developed in the present study accurately predicted the growth of L. monocytogenes under dynamic temperature conditions. The average values for the performance indices were 1.038, 1.068, and 0.397 for B(f), A(f), and GoF, respectively for both temperature scenarios assayed. Predictions from Growth Predictor and Sym'Previus overestimated pathogen growth. The average values of B(f), A(f), and GoF were 1.173, 1.174, 1.162, and 0.956, 1.115, 0.713 for [corrected] Growth Predictor and Sym'Previus, respectively.

Modeling Tree Growth Taking into Account Carbon Source and Sink Limitations.

PubMed

Hayat, Amaury; Hacket-Pain, Andrew J; Pretzsch, Hans; Rademacher, Tim T; Friend, Andrew D

2017-01-01

Increasing CO 2 concentrations are strongly controlled by the behavior of established forests, which are believed to be a major current sink of atmospheric CO 2 . There are many models which predict forest responses to environmental changes but they are almost exclusively carbon source (i.e., photosynthesis) driven. Here we present a model for an individual tree that takes into account the intrinsic limits of meristems and cellular growth rates, as well as control mechanisms within the tree that influence its diameter and height growth over time. This new framework is built on process-based understanding combined with differential equations solved by numerical method. Our aim is to construct a model framework of tree growth for replacing current formulations in Dynamic Global Vegetation Models, and so address the issue of the terrestrial carbon sink. Our approach was successfully tested for stands of beech trees in two different sites representing part of a long-term forest yield experiment in Germany. This model provides new insights into tree growth and limits to tree height, and addresses limitations of previous models with respect to sink-limited growth.

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Age structure and capital dilution effects in neo-classical growth models.

PubMed

Blanchet, D

1988-01-01

Economists often over estimate capital dilution effects when applying neoclassical growth models which use age structured population and depreciation of capital stock. This occurs because capital stock is improperly characterized. A standard model which assumes a constant depreciation of capital intimates that a population growth rate equal to a negative constant savings ratio is preferable to any higher growth rate. Growth rates which are lower than a negative constant savings ratio suggest an ever growing capital/labor ratio and an ever growing standard of living, even if people do not save. This is suggested because the natural reduction of the capital stock through depreciation is slower than the population decrease which is simply unrealistic. This model overlooks the fact that low or negative growth rates result in an ageing of the capital stock, and this ageing subsequently results in an increase of the overall rate of capital depreciation. In that overly simplistic model, depreciation was assumed independent of the age of the captial stock. Incorporating depreciation as a variable into a model allows a more symmetric treatment of capital. Using models with heterogenous capital, this article explores what occurs when more than 1 kind of capital good is involved in production and when these various captial goods have different lengths of life. Applying economic models, it also examines what occurs when the length of life of capital may vary. These variations correct the negative impact that population growth can have on per capital production and consumption.

The Unified Plant Growth Model (UPGM): software framework overview and model application

USDA-ARS?s Scientific Manuscript database

Since the Environmental Policy Integrated Climate (EPIC) model was developed in 1989, the EPIC plant growth component has been incorporated into other erosion and crop management models (e.g., WEPS, WEPP, SWAT, ALMANAC, and APEX) and modified to meet model developer research objectives. This has re...

Plant growth modeling at the JSC variable pressure growth chamber - An application of experimental design

NASA Technical Reports Server (NTRS)

Miller, Adam M.; Edeen, Marybeth; Sirko, Robert J.

1992-01-01

This paper describes the approach and results of an effort to characterize plant growth under various environmental conditions at the Johnson Space Center variable pressure growth chamber. Using a field of applied mathematics and statistics known as design of experiments (DOE), we developed a test plan for varying environmental parameters during a lettuce growth experiment. The test plan was developed using a Box-Behnken approach to DOE. As a result of the experimental runs, we have developed empirical models of both the transpiration process and carbon dioxide assimilation for Waldman's Green lettuce over specified ranges of environmental parameters including carbon dioxide concentration, light intensity, dew-point temperature, and air velocity. This model also predicts transpiration and carbon dioxide assimilation for different ages of the plant canopy.

A smart growth evaluation model based on data envelopment analysis

NASA Astrophysics Data System (ADS)

Zhang, Xiaokun; Guan, Yongyi

2018-04-01

With the rapid spread of urbanization, smart growth (SG) has attracted plenty of attention from all over the world. In this paper, by the establishment of index system for smart growth, data envelopment analysis (DEA) model was suggested to evaluate the SG level of the current growth situation in cities. In order to further improve the information of both radial direction and non-radial detection, we introduced the non-Archimedean infinitesimal to form C2GS2 control model. Finally, we evaluated the SG level in Canberra and identified a series of problems, which can verify the applicability of the model and provide us more improvement information.

A monomer-trimer model supports intermittent glucagon fibril growth

NASA Astrophysics Data System (ADS)

Košmrlj, Andrej; Cordsen, Pia; Kyrsting, Anders; Otzen, Daniel E.; Oddershede, Lene B.; Jensen, Mogens H.

2015-03-01

We investigate in vitro fibrillation kinetics of the hormone peptide glucagon at various concentrations using confocal microscopy and determine the glucagon fibril persistence length 60μm. At all concentrations we observe that periods of individual fibril growth are interrupted by periods of stasis. The growth probability is large at high and low concentrations and is reduced for intermediate glucagon concentrations. To explain this behavior we propose a simple model, where fibrils come in two forms, one built entirely from glucagon monomers and one entirely from glucagon trimers. The opposite building blocks act as fibril growth blockers, and this generic model reproduces experimental behavior well.

An individual-based growth and competition model for coastal redwood forest restoration

USGS Publications Warehouse

van Mantgem, Phillip J.; Das, Adrian J.

2014-01-01

Thinning treatments to accelerate coastal redwood forest stand development are in wide application, but managers have yet to identify prescriptions that might best promote Sequoia sempervirens (Lamb. ex D. Don) Endl. (redwood) growth. The creation of successful thinning prescriptions would be aided by identifying the underlying mechanisms governing how individual tree growth responds to competitive environments in coastal redwood forests. We created a spatially explicit individual-based model of tree competition and growth parameterized using surveys of upland redwood forests at Redwood National Park, California. We modeled competition for overstory trees (stems ≥ 20 cm stem diameter at breast height, 1.37 m (dbh)) as growth reductions arising from sizes, distances, and species identity of competitor trees. Our model explained up to half of the variation in individual tree growth, suggesting that neighborhood crowding is an important determinant of growth in this forest type. We used our model to simulate the effects of novel thinning prescriptions (e.g., 40% stand basal area removal) for redwood forest restoration, concluding that these treatments could lead to substantial growth releases, particularly for S. sempervirens. The results of this study, along with continued improvements to our model, will help to determine spacing and species composition that best encourage growth.

Discrete and continuous models for tissue growth and shrinkage.

PubMed

Yates, Christian A

2014-06-07

The incorporation of domain growth into stochastic models of biological processes is of increasing interest to mathematical modellers and biologists alike. In many situations, especially in developmental biology, the growth of the underlying tissue domain plays an important role in the redistribution of particles (be they cells or molecules) which may move and react atop the domain. Although such processes have largely been modelled using deterministic, continuum models there is an increasing appetite for individual-based stochastic models which can capture the fine details of the biological movement processes which are being elucidated by modern experimental techniques, and also incorporate the inherent stochasticity of such systems. In this work we study a simple stochastic model of domain growth. From a basic version of this model, Hywood et al. (2013) were able to derive a Fokker-Plank equation (FPE) (in this case an advection-diffusion partial differential equation on a growing domain) which describes the evolution of the probability density of some tracer particles on the domain. We extend their work so that a variety of different domain growth mechanisms can be incorporated and demonstrate a good agreement between the mean tracer density and the solution of the FPE in each case. In addition we incorporate domain shrinkage (via element death) into our individual-level model and demonstrate that we are able to derive coefficients for the FPE in this case as well. For situations in which the drift and diffusion coefficients are not readily available we introduce a numerical coefficient estimation approach and demonstrate the accuracy of this approach by comparing it with situations in which an analytical solution is obtainable. Copyright © 2014 Elsevier Ltd. All rights reserved.

Development and validation of an extensive growth and growth boundary model for psychrotolerant Lactobacillus spp. in seafood and meat products.

PubMed

Mejlholm, Ole; Dalgaard, Paw

2013-10-15

A new and extensive growth and growth boundary model for psychrotolerant Lactobacillus spp. was developed and validated for processed and unprocessed products of seafood and meat. The new model was developed by refitting and expanding an existing cardinal parameter model for growth and the growth boundary of lactic acid bacteria (LAB) in processed seafood (O. Mejlholm and P. Dalgaard, J. Food Prot. 70. 2485-2497, 2007). Initially, to estimate values for the maximum specific growth rate at the reference temperature of 25 °C (μref) and the theoretical minimum temperature that prevents growth of psychrotolerant LAB (T(min)), the existing LAB model was refitted to data from experiments with seafood and meat products reported not to include nitrite or any of the four organic acids evaluated in the present study. Next, dimensionless terms modelling the antimicrobial effect of nitrite, and acetic, benzoic, citric and sorbic acids on growth of Lactobacillus sakei were added to the refitted model, together with minimum inhibitory concentrations determined for the five environmental parameters. The new model including the effect of 12 environmental parameters, as well as their interactive effects, was successfully validated using 229 growth rates (μ(max) values) for psychrotolerant Lactobacillus spp. in seafood and meat products. Average bias and accuracy factor values of 1.08 and 1.27, respectively, were obtained when observed and predicted μ(max) values of psychrotolerant Lactobacillus spp. were compared. Thus, on average μ(max) values were only overestimated by 8%. The performance of the new model was equally good for seafood and meat products, and the importance of including the effect of acetic, benzoic, citric and sorbic acids and to a lesser extent nitrite in order to accurately predict growth of psychrotolerant Lactobacillus spp. was clearly demonstrated. The new model can be used to predict growth of psychrotolerant Lactobacillus spp. in seafood and meat

Application of enthalpy model for floating zone silicon crystal growth

NASA Astrophysics Data System (ADS)

Krauze, A.; Bergfelds, K.; Virbulis, J.

2017-09-01

A 2D simplified crystal growth model based on the enthalpy method and coupled with a low-frequency harmonic electromagnetic model is developed to simulate the silicon crystal growth near the external triple point (ETP) and crystal melting on the open melting front of a polycrystalline feed rod in FZ crystal growth systems. Simulations of the crystal growth near the ETP show significant influence of the inhomogeneities of the EM power distribution on the crystal growth rate for a 4 in floating zone (FZ) system. The generated growth rate fluctuations are shown to be larger in the system with higher crystal pull rate. Simulations of crystal melting on the open melting front of the polycrystalline rod show the development of melt-filled grooves at the open melting front surface. The distance between the grooves is shown to grow with the increase of the skin-layer depth in the solid material.

Incorporating temporal heterogeneity in environmental conditions into a somatic growth model

USGS Publications Warehouse

Dzul, Maria C.; Yackulic, Charles B.; Korman, Josh; Yard, Michael D.; Muehlbauer, Jeffrey D.

2017-01-01

Evaluating environmental effects on fish growth can be challenging because environmental conditions may vary at relatively fine temporal scales compared to sampling occasions. Here we develop a Bayesian state-space growth model to evaluate effects of monthly environmental data on growth of fish that are observed less frequently (e.g., from mark-recapture data where time between captures can range from months to years). We assess effects of temperature, turbidity duration, food availability, flow variability, and trout abundance on subadult humpback chub (Gila cypha) growth in two rivers, the Colorado River (CR) and the Little Colorado River (LCR), and we use out-of-sample prediction to rank competing models. Environmental covariates explained a high proportion of the variation in growth in both rivers; however, the best growth models were river-specific and included either positive temperature and turbidity duration effects (CR) or positive temperature and food availability effects (LCR). Our approach to analyzing environmental controls on growth should be applicable in other systems where environmental data vary over relatively short time scales compared to animal observations.

Eye growth and myopia development: Unifying theory and Matlab model.

PubMed

Hung, George K; Mahadas, Kausalendra; Mohammad, Faisal

2016-03-01

The aim of this article is to present an updated unifying theory of the mechanisms underlying eye growth and myopia development. A series of model simulation programs were developed to illustrate the mechanism of eye growth regulation and myopia development. Two fundamental processes are presumed to govern the relationship between physiological optics and eye growth: genetically pre-programmed signaling and blur feedback. Cornea/lens is considered to have only a genetically pre-programmed component, whereas eye growth is considered to have both a genetically pre-programmed and a blur feedback component. Moreover, based on the Incremental Retinal-Defocus Theory (IRDT), the rate of change of blur size provides the direction for blur-driven regulation. The various factors affecting eye growth are shown in 5 simulations: (1 - unregulated eye growth): blur feedback is rendered ineffective, as in the case of form deprivation, so there is only genetically pre-programmed eye growth, generally resulting in myopia; (2 - regulated eye growth): blur feedback regulation demonstrates the emmetropization process, with abnormally excessive or reduced eye growth leading to myopia and hyperopia, respectively; (3 - repeated near-far viewing): simulation of large-to-small change in blur size as seen in the accommodative stimulus/response function, and via IRDT as well as nearwork-induced transient myopia (NITM), leading to the development of myopia; (4 - neurochemical bulk flow and diffusion): release of dopamine from the inner plexiform layer of the retina, and the subsequent diffusion and relay of neurochemical cascade show that a decrease in dopamine results in a reduction of proteoglycan synthesis rate, which leads to myopia; (5 - Simulink model): model of genetically pre-programmed signaling and blur feedback components that allows for different input functions to simulate experimental manipulations that result in hyperopia, emmetropia, and myopia. These model simulation programs

A Novel Modelling Approach for Predicting Forest Growth and Yield under Climate Change.

PubMed

Ashraf, M Irfan; Meng, Fan-Rui; Bourque, Charles P-A; MacLean, David A

2015-01-01

Global climate is changing due to increasing anthropogenic emissions of greenhouse gases. Forest managers need growth and yield models that can be used to predict future forest dynamics during the transition period of present-day forests under a changing climatic regime. In this study, we developed a forest growth and yield model that can be used to predict individual-tree growth under current and projected future climatic conditions. The model was constructed by integrating historical tree growth records with predictions from an ecological process-based model using neural networks. The new model predicts basal area (BA) and volume growth for individual trees in pure or mixed species forests. For model development, tree-growth data under current climatic conditions were obtained using over 3000 permanent sample plots from the Province of Nova Scotia, Canada. Data to reflect tree growth under a changing climatic regime were projected with JABOWA-3 (an ecological process-based model). Model validation with designated data produced model efficiencies of 0.82 and 0.89 in predicting individual-tree BA and volume growth. Model efficiency is a relative index of model performance, where 1 indicates an ideal fit, while values lower than zero means the predictions are no better than the average of the observations. Overall mean prediction error (BIAS) of basal area and volume growth predictions was nominal (i.e., for BA: -0.0177 cm(2) 5-year(-1) and volume: 0.0008 m(3) 5-year(-1)). Model variability described by root mean squared error (RMSE) in basal area prediction was 40.53 cm(2) 5-year(-1) and 0.0393 m(3) 5-year(-1) in volume prediction. The new modelling approach has potential to reduce uncertainties in growth and yield predictions under different climate change scenarios. This novel approach provides an avenue for forest managers to generate required information for the management of forests in transitional periods of climate change. Artificial intelligence technology

A Novel Modelling Approach for Predicting Forest Growth and Yield under Climate Change

PubMed Central

Ashraf, M. Irfan; Meng, Fan-Rui; Bourque, Charles P.-A.; MacLean, David A.

2015-01-01

Global climate is changing due to increasing anthropogenic emissions of greenhouse gases. Forest managers need growth and yield models that can be used to predict future forest dynamics during the transition period of present-day forests under a changing climatic regime. In this study, we developed a forest growth and yield model that can be used to predict individual-tree growth under current and projected future climatic conditions. The model was constructed by integrating historical tree growth records with predictions from an ecological process-based model using neural networks. The new model predicts basal area (BA) and volume growth for individual trees in pure or mixed species forests. For model development, tree-growth data under current climatic conditions were obtained using over 3000 permanent sample plots from the Province of Nova Scotia, Canada. Data to reflect tree growth under a changing climatic regime were projected with JABOWA-3 (an ecological process-based model). Model validation with designated data produced model efficiencies of 0.82 and 0.89 in predicting individual-tree BA and volume growth. Model efficiency is a relative index of model performance, where 1 indicates an ideal fit, while values lower than zero means the predictions are no better than the average of the observations. Overall mean prediction error (BIAS) of basal area and volume growth predictions was nominal (i.e., for BA: -0.0177 cm2 5-year-1 and volume: 0.0008 m3 5-year-1). Model variability described by root mean squared error (RMSE) in basal area prediction was 40.53 cm2 5-year-1 and 0.0393 m3 5-year-1 in volume prediction. The new modelling approach has potential to reduce uncertainties in growth and yield predictions under different climate change scenarios. This novel approach provides an avenue for forest managers to generate required information for the management of forests in transitional periods of climate change. Artificial intelligence technology has substantial

Evaluation of portfolio credit risk based on survival analysis for progressive censored data

NASA Astrophysics Data System (ADS)

Jaber, Jamil J.; Ismail, Noriszura; Ramli, Siti Norafidah Mohd

2017-04-01

In credit risk management, the Basel committee provides a choice of three approaches to the financial institutions for calculating the required capital: the standardized approach, the Internal Ratings-Based (IRB) approach, and the Advanced IRB approach. The IRB approach is usually preferred compared to the standard approach due to its higher accuracy and lower capital charges. This paper use several parametric models (Exponential, log-normal, Gamma, Weibull, Log-logistic, Gompertz) to evaluate the credit risk of the corporate portfolio in the Jordanian banks based on the monthly sample collected from January 2010 to December 2015. The best model is selected using several goodness-of-fit criteria (MSE, AIC, BIC). The results indicate that the Gompertz distribution is the best model parametric model for the data.

Twin-singleton developmental study of brain white matter anatomy.

PubMed

Sadeghi, Neda; Gilmore, John H; Gerig, Guido

2017-02-01

Twin studies provide valuable insights into the analysis of genetic and environmental factors influencing human brain development. However, these findings may not generalize to singletons due to differences in pre- and postnatal environments. One would expect the effect of these differences to be greater during the early years of life. To address this concern, we compare longitudinal diffusion data of white matter regions for 26 singletons and 76 twins (monozygotic and dizygotic) from birth to 2 years of age. We use nonlinear mixed effect modeling where the temporal changes in the diffusion parameters are described by the Gompertz function. The Gompertz function describes growth trajectory in terms of intuitive parameters: asymptote, delay, and speed. We analyzed fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD) for 21 regions of interest (ROIs). These ROIs included areas in the association, projection, and commissural fiber tracts. We did not find any differences in the diffusion parameters between monozygotic and dizygotic twins. In addition, FA and RD showed no developmental differences between singletons and twins for the regions analyzed. However, the delay parameter of the Gompertz function of AD for the anterior limb of the internal capsule and anterior corona radiata was significantly different between singletons and twins. Further analysis indicated that the differences are small, and twins "catch up" by the first few months of life. These results suggest that the effects of differences of pre- and postnatal environments between twins and singletons are minimal on white matter development and disappear early in life. Hum Brain Mapp 38:1009-1024, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

A generalized system of models forecasting Central States tree growth.

Treesearch

Stephen R. Shifley

1987-01-01

Describes the development and testing of a system of individual tree-based growth projection models applicable to species in Indiana, Missouri, and Ohio. Annual tree basal area growth is estimated as a function of tree size, crown ratio, stand density, and site index. Models are compatible with the STEMS and TWIGS Projection System.

Multiscale modeling of growth plate cartilage mechanobiology.

PubMed

Gao, Jie; Williams, John L; Roan, Esra

2017-04-01

Growth plate chondrocytes are responsible for bone growth through proliferation and differentiation. However, the way they experience physiological loads and regulate bone formation, especially during the later developmental phase in the mature growth plate, is still under active investigation. In this study, a previously developed multiscale finite element model of the growth plate is utilized to study the stress and strain distributions within the cartilage at the cellular level when rapidly compressed to 20 %. Detailed structures of the chondron are included in the model to examine the hypothesis that the same combination of mechanoregulatory signals shown to maintain cartilage or stimulate osteogenesis or fibrogenesis in the cartilage anlage or fracture callus also performs the same function at the cell level within the chondrons of growth plate cartilage. Our cell-level results are qualitatively and quantitatively in agreement with tissue-level theories when both hydrostatic cellular stress and strain are considered simultaneously in a mechanoregulatory phase diagram similar to that proposed at the tissue level by Claes and Heigele for fracture healing. Chondrocytes near the reserve/proliferative zone border are subjected to combinations of high compressive hydrostatic stresses ([Formula: see text] MPa), and cell height and width strains of [Formula: see text] to [Formula: see text] respectively, that maintain cartilage and keep chondrocytes from differentiating and provide conditions favorable for cell division, whereas chondrocytes closer to the hypertrophic/calcified zone undergo combinations of lower compressive hydrostatic stress ([Formula: see text] MPa) and cell height and width strains as low as [Formula: see text] to +4 %, respectively, that promote cell differentiation toward osteogenesis; cells near the outer periphery of the growth plate structure experience a combination of low compressive hydrostatic stress (0 to [Formula: see text] MPa) and

Modelling the growth of Leuconostoc mesenteroides by Artificial Neural Networks.

PubMed

García-Gimeno, R M; Hervás-Martínez, C; Rodríguez-Pérez, R; Zurera-Cosano, G

2005-12-15

The combined effect of temperature (10.5 to 24.5 degrees C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the predicted specific growth rate (Gr), lag-time (Lag) and maximum population density (yEnd) of Leuconostoc mesenteroides under aerobic and anaerobic conditions, was studied using an Artificial Neural Network-based model (ANN) in comparison with Response Surface Methodology (RS). For both aerobic and anaerobic conditions, two types of ANN model were elaborated, unidimensional for each of the growth parameters, and multidimensional in which the three parameters Gr, Lag, and yEnd are combined. Although in general no significant statistical differences were observed between both types of model, we opted for the unidimensional model, because it obtained the lowest mean value for the standard error of prediction for generalisation. The ANN models developed provided reliable estimates for the three kinetic parameters studied; the SEP values in aerobic conditions ranged from between 2.82% for Gr, 6.05% for Lag and 10% for yEnd, a higher degree accuracy than those of the RS model (Gr: 9.54%; Lag: 8.89%; yEnd: 10.27%). Similar results were observed for anaerobic conditions. During external validation, a higher degree of accuracy (Af) and bias (Bf) were observed for the ANN model compared with the RS model. ANN predictive growth models are a valuable tool, enabling swift determination of L. mesenteroides growth parameters.

Isotropic model for cluster growth on a regular lattice

NASA Astrophysics Data System (ADS)

Yates, Christian A.; Baker, Ruth E.

2013-08-01

There exists a plethora of mathematical models for cluster growth and/or aggregation on regular lattices. Almost all suffer from inherent anisotropy caused by the regular lattice upon which they are grown. We analyze the little-known model for stochastic cluster growth on a regular lattice first introduced by Ferreira Jr. and Alves [J. Stat. Mech. Theo. & Exp.1742-546810.1088/1742-5468/2006/11/P11007 (2006) P11007], which produces circular clusters with no discernible anisotropy. We demonstrate that even in the noise-reduced limit the clusters remain circular. We adapt the model by introducing a specific rearrangement algorithm so that, rather than adding elements to the cluster from the outside (corresponding to apical growth), our model uses mitosis-like cell splitting events to increase the cluster size. We analyze the surface scaling properties of our model and compare it to the behavior of more traditional models. In “1+1” dimensions we discover and explore a new, nonmonotonic surface thickness scaling relationship which differs significantly from the Family-Vicsek scaling relationship. This suggests that, for models whose clusters do not grow through particle additions which are solely dependent on surface considerations, the traditional classification into “universality classes” may not be appropriate.

Modeling Synergistic Drug Inhibition of Mycobacterium tuberculosis Growth in Murine Macrophages

DTIC Science & Technology

2011-01-01

important application of metabolic network modeling is the ability to quantitatively model metabolic enzyme inhibition and predict bacterial growth...describe the extensions of this framework to model drug- induced growth inhibition of M. tuberculosis in macrophages.39 Mathematical framework Fig. 1 shows...starting point, we used the previously developed iNJ661v model to represent the metabolic Fig. 1 Mathematical framework: a set of coupled models used to

The Effects of Autocorrelation on the Curve-of-Factors Growth Model

ERIC Educational Resources Information Center

Murphy, Daniel L.; Beretvas, S. Natasha; Pituch, Keenan A.

2011-01-01

This simulation study examined the performance of the curve-of-factors model (COFM) when autocorrelation and growth processes were present in the first-level factor structure. In addition to the standard curve-of factors growth model, 2 new models were examined: one COFM that included a first-order autoregressive autocorrelation parameter, and a…

Evaluating Teachers and Schools Using Student Growth Models

ERIC Educational Resources Information Center

Schafer, William D.; Lissitz, Robert W.; Zhu, Xiaoshu; Zhang, Yuan; Hou, Xiaodong; Li, Ying

2012-01-01

Interest in Student Growth Modeling (SGM) and Value Added Modeling (VAM) arises from educators concerned with measuring the effectiveness of teaching and other school activities through changes in student performance as a companion and perhaps even an alternative to status. Several formal statistical models have been proposed for year-to-year…

2D Process-based Microbialite Growth Model

NASA Astrophysics Data System (ADS)

Airo, A.; Smith, A.

2007-12-01

A 2D process-based microbialite growth model (MGM) has been developed that integrates the coupled effects of the microbialite growth and sediment distribution within a two-dimensional cross-section of a subaqueous bedrock profile. Sediment transport is realized through particle erosion and deposition that are a function of local wave energy which is computed on the basis of linear wave theory. Surface-normal microbialite growth is directly correlated to light intensity, which is computed for every point of the microbialite surface by using a Henyey- Greenstein-type relation for scattering and the Beer's Law for absorption in the water column. Shadowing effects by surrounding obstacles and/or overlying sediment are also considered. Sediment particles can be incorporated into the microbialite framework if growth occurs in the presence of sediment. The resulting meter-size microbialite constructs develop morphologies that correspond well to natural microbialites. Furthermore, changes of environmental factors such as light intensity, wave energy, and bedrock profile result in morphological variations of the microbialites that would be expected on the basis of the current understanding of microbialite growth and development.

Bayesian modeling of Clostridium perfringens growth in beef-in-sauce products.

PubMed

Jaloustre, S; Cornu, M; Morelli, E; Noël, V; Delignette-Muller, M L

2011-04-01

Models on Clostridium perfringens growth which have been published to date have all been deterministic. A probabilistic model describing growth under non-isothermal conditions was thus proposed for predicting C. perfringens growth in beef-in-sauce products cooked and distributed in a French hospital. Model parameters were estimated from different types of data from various studies. A Bayesian approach was proposed to model the overall uncertainty regarding parameters and potential variability on the 'work to be done' (h(0)) during the germination, outgrowth and lag phase. Three models which differed according to their description of this parameter h(0) were tested. The model with inter-curve variability on h(0) was found to be the best one, on the basis of goodness-of-fit assessment and validation with literature data on results obtained under non-isothermal conditions. This model was used in two-dimensional Monte Carlo simulations to predict C. perfringens growth throughout the preparation of beef-in-sauce products, using temperature profiles recorded in a hospital kitchen. The median predicted growth was 7.8×10(-2) log(10) cfu·g(-1) (95% credibility interval [2.4×10(-2), 0.8]) despite the fact that for more than 50% of the registered temperature profiles cooling steps were longer than those required by French regulations. Copyright © 2010 Elsevier Ltd. All rights reserved.

Cylindrically symmetric Green's function approach for modeling the crystal growth morphology of ice.

PubMed

Libbrecht, K G

1999-08-01

We describe a front-tracking Green's function approach to modeling cylindrically symmetric crystal growth. This method is simple to implement, and with little computer power can adequately model a wide range of physical situations. We apply the method to modeling the hexagonal prism growth of ice crystals, which is governed primarily by diffusion along with anisotropic surface kinetic processes. From ice crystal growth observations in air, we derive measurements of the kinetic growth coefficients for the basal and prism faces as a function of temperature, for supersaturations near the water saturation level. These measurements are interpreted in the context of a model for the nucleation and growth of ice, in which the growth dynamics are dominated by the structure of a disordered layer on the ice surfaces.

Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Graphic comparison of reserve-growth models for conventional oil and accumulation

USGS Publications Warehouse

Klett, T.R.

2003-01-01

The U.S. Geological Survey (USGS) periodically assesses crude oil, natural gas, and natural gas liquids resources of the world. The assessment procedure requires estimated recover-able oil and natural gas volumes (field size, cumulative production plus remaining reserves) in discovered fields. Because initial reserves are typically conservative, subsequent estimates increase through time as these fields are developed and produced. The USGS assessment of petroleum resources makes estimates, or forecasts, of the potential additions to reserves in discovered oil and gas fields resulting from field development, and it also estimates the potential fully developed sizes of undiscovered fields. The term ?reserve growth? refers to the commonly observed upward adjustment of reserve estimates. Because such additions are related to increases in the total size of a field, the USGS uses field sizes to model reserve growth. Future reserve growth in existing fields is a major component of remaining U.S. oil and natural gas resources and has therefore become a necessary element of U.S. petroleum resource assessments. Past and currently proposed reserve-growth models compared herein aid in the selection of a suitable set of forecast functions to provide an estimate of potential additions to reserves from reserve growth in the ongoing National Oil and Gas Assessment Project (NOGA). Reserve growth is modeled by construction of a curve that represents annual fractional changes of recoverable oil and natural gas volumes (for fields and reservoirs), which provides growth factors. Growth factors are used to calculate forecast functions, which are sets of field- or reservoir-size multipliers. Comparisons of forecast functions were made based on datasets used to construct the models, field type, modeling method, and length of forecast span. Comparisons were also made between forecast functions based on field-level and reservoir- level growth, and between forecast functions based on older

Dynamic predictive model for growth of Salmonella spp. in scrambled egg mix.

PubMed

Li, Lin; Cepeda, Jihan; Subbiah, Jeyamkondan; Froning, Glenn; Juneja, Vijay K; Thippareddi, Harshavardhan

2017-06-01

Liquid egg products can be contaminated with Salmonella spp. during processing. A dynamic model for the growth of Salmonella spp. in scrambled egg mix - high solids (SEM) was developed and validated. SEM was prepared and inoculated with ca. 2 log CFU/mL of a five serovar Salmonella spp. cocktail. Salmonella spp. growth data at isothermal temperatures (10, 15, 20, 25, 30, 35, 37, 39, 41, 43, 45, and 47 °C) in SEM were collected. Baranyi model was used (primary model) to fit growth data and the maximum growth rate and lag phase duration for each temperature were determined. A secondary model was developed with maximum growth rate as a function of temperature. The model performance measures, root mean squared error (RMSE, 0.09) and pseudo-R 2 (1.00) indicated good fit for both primary and secondary models. A dynamic model was developed by integrating the primary and secondary models and validated using two sinusoidal temperature profiles, 5-15 °C (low temperature) for 480 h and 10-40 °C (high temperature) for 48 h. The RMSE values for the sinusoidal low and high temperature profiles were 0.47 and 0.42 log CFU/mL, respectively. The model can be used to predict Salmonella spp. growth in case of temperature abuse during liquid egg processing. Copyright © 2016. Published by Elsevier Ltd.

Modelling the growth of Listeria monocytogenes in Mediterranean fish species from aquaculture production.

PubMed

Bolívar, Araceli; Costa, Jean Carlos Correia Peres; Posada-Izquierdo, Guiomar D; Valero, Antonio; Zurera, Gonzalo; Pérez-Rodríguez, Fernando

2018-04-02

Over the last couple of decades, several studies have evaluated growth dynamics of L. monocytogenes in lightly processed and ready-to-eat (RTE) fishery products mostly consumed in Nordic European countries. Other fish species from aquaculture production are of special interest since their relevant consumption patterns and added value in Mediterranean countries, such as sea bream and sea bass. In the present study, the growth of L. monocytogenes was evaluated in fish-based juice (FBJ) by means of optical density (OD) measurements in a temperature range 2-20 °C under different atmosphere conditions (i.e. reduced oxygen and aerobic). The Baranyi and Roberts model was used to estimate the maximum growth rate (μ max ) from the observed growth curves. The effect of storage temperature on μ max was modelled using the Ratkowsky square root model. The developed models were validated using experimental growth data for L. monocytogenes in sea bream and sea bass fillets stored under static and dynamic temperature conditions. Overall, models developed in FBJ provided fail-safe predictions for L. monocytogenes growth. For the model generated under reduced oxygen conditions, bias and accuracy factor for growth rate predictions were 1.15 and 1.25, respectively, showing good performance to adequately predict L. monocytogenes growth in Mediterranean fish products. The present study provides validated predictive models for L. monocytogenes growth in Mediterranean fish species to be used in microbial risk assessment and shelf-life studies. Copyright © 2018 Elsevier B.V. All rights reserved.

Experimental analysis and modeling of melt growth processes

NASA Astrophysics Data System (ADS)

Müller, Georg

2002-04-01

Melt growth processes provide the basic crystalline materials for many applications. The research and development of crystal growth processes is therefore driven by the demands which arise from these specific applications; however, common goals include an increased uniformity of the relevant crystal properties at the micro- and macro-scale, a decrease of deleterious crystal defects, and an increase of crystal dimensions. As melt growth equipment and experimentation becomes more and more expensive, little room remains for improvements by trial and error procedures. A more successful strategy is to optimize the crystal growth process by a combined use of experimental process analysis and computer modeling. This will be demonstrated in this paper by several examples from the bulk growth of silicon, gallium arsenide, indium phosphide, and calcium fluoride. These examples also involve the most important melt growth techniques, crystal pulling (Czochralski methods) and vertical gradient freeze (Bridgman-type methods). The power and success of the above optimization strategy, however, is not limited only to the given examples but can be generalized and applied to many types of bulk crystal growth.

Comparison of Primary Models to Predict Microbial Growth by the Plate Count and Absorbance Methods.

PubMed

Pla, María-Leonor; Oltra, Sandra; Esteban, María-Dolores; Andreu, Santiago; Palop, Alfredo

2015-01-01

The selection of a primary model to describe microbial growth in predictive food microbiology often appears to be subjective. The objective of this research was to check the performance of different mathematical models in predicting growth parameters, both by absorbance and plate count methods. For this purpose, growth curves of three different microorganisms (Bacillus cereus, Listeria monocytogenes, and Escherichia coli) grown under the same conditions, but with different initial concentrations each, were analysed. When measuring the microbial growth of each microorganism by optical density, almost all models provided quite high goodness of fit (r(2) > 0.93) for all growth curves. The growth rate remained approximately constant for all growth curves of each microorganism, when considering one growth model, but differences were found among models. Three-phase linear model provided the lowest variation for growth rate values for all three microorganisms. Baranyi model gave a variation marginally higher, despite a much better overall fitting. When measuring the microbial growth by plate count, similar results were obtained. These results provide insight into predictive microbiology and will help food microbiologists and researchers to choose the proper primary growth predictive model.

The Multigroup Multilevel Categorical Latent Growth Curve Models

ERIC Educational Resources Information Center

Hung, Lai-Fa

2010-01-01

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

A Kinetic Model for GaAs Growth by Hydride Vapor Phase Epitaxy

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

Schulte, Kevin L.; Simon, John; Jain, Nikhil

2016-11-21

Precise control of the growth of III-V materials by hydride vapor phase epitaxy (HVPE) is complicated by the fact that the growth rate depends on the concentrations of nearly all inputs to the reactor and also the reaction temperature. This behavior is in contrast to metalorganic vapor phase epitaxy (MOVPE), which in common practice operates in a mass transport limited regime where growth rate and alloy composition are controlled almost exclusively by flow of the Group III precursor. In HVPE, the growth rate and alloy compositions are very sensitive to temperature and reactant concentrations, which are strong functions of themore » reactor geometry. HVPE growth, particularly the growth of large area materials and devices, will benefit from the development of a growth model that can eventually be coupled with a computational fluid dynamics (CFD) model of a specific reactor geometry. In this work, we develop a growth rate law using a Langmuir-Hinshelwood (L-H) analysis, fitting unknown parameters to growth rate data from the literature that captures the relevant kinetic and thermodynamic phenomena of the HVPE process. We compare the L-H rate law to growth rate data from our custom HVPE reactor, and develop quantitative insight into reactor performance, demonstrating the utility of the growth model.« less

Individual tree basal-area growth parameter estimates for four models

Treesearch

J.J. Colbert; Michael Schuckers; Desta Fekedulegn; James Rentch; Mairtin MacSiurtain; Kurt Gottschalk

2004-01-01

Four sigmoid growth models are fit to basal-area data derived from increment cores and disks taken at breast height from oak trees. Models are rated on their ability to fit growth data from five datasets that are obtained from 10 locations along a longitudinal gradient across the states of Delaware, Pennsylvania, West Virginia, and Ohio in the USA. We examine and...

The importance of expressing antimicrobial agents on water basis in growth/no growth interface models: a case study for Zygosaccharomyces bailii.

PubMed

Dang, T D T; Vermeulen, A; Mertens, L; Geeraerd, A H; Van Impe, J F; Devlieghere, F

2011-01-31

In a previous study on Zygosaccharomyces bailii, three growth/no growth models have been developed, predicting growth probability of the yeast at different conditions typical for acidified foods (Dang, T.D.T., Mertens, L., Vermeulen, A., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2010. Modeling the growth/no growth boundary of Z. bailii in acidic conditions: A contribution to the alternative method to preserve foods without using chemical preservatives. International Journal of Food Microbiology 137, 1-12). In these broth-based models, the variables were pH, water activity and acetic acid, with acetic acid concentration expressed in volume % on the total culture medium (i.e., broth). To continue the previous study, validation experiments were performed for 15 selected combinations of intrinsic factors to assess the performance of the model at 22°C (60days) in a real food product (ketchup). Although the majority of experimental results were consistent, some remarkable deviations between prediction and validation were observed, e.g., Z. bailii growth occurred in conditions where almost no growth had been predicted. A thorough investigation revealed that the difference between two ways of expressing acetic acid concentration (i.e., on broth basis and on water basis) is rather significant, particularly for media containing high amounts of dry matter. Consequently, the use of broth-based concentrations in the models was not appropriate. Three models with acetic acid concentration expressed on water basis were established and it was observed that predictions by these models well matched the validation results; therefore a "systematic error" in broth-based models was recognized. In practice, quantities of antimicrobial agents are often calculated based on the water content of food products. Hence, to assure reliable predictions and facilitate the application of models (developed from lab media with high dry matter contents), it is important to express

A diameter growth model for the SRS FIA

Treesearch

David Gartner

2015-01-01

Changes in the national Forest Inventory and Analysis (FIA) processing system required the Southern Research Station’s FIA unit to create a diameter growth model to estimate the growth of trees that could not be measured at both ends of a measurement interval. Examples of such trees are trees that have died or been harvested, and trees that grow over the minimum...

Crystal plasticity modeling of irradiation growth in Zircaloy-2

DOE PAGES

Patra, Anirban; Tome, Carlos; Golubov, Stanislav I.

2017-05-10

A reaction-diffusion based mean field rate theory model is implemented in the viscoplastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. A novel scheme is proposed to model the evolution (both number density and radius) of irradiation-induced dislocation loops that can be informed directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behavior of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture, and external stress onmore » the coupled irradiation growth and creep behavior are also studied.« less

Crystal plasticity modeling of irradiation growth in Zircaloy-2

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

Patra, Anirban; Tome, Carlos; Golubov, Stanislav I.

A reaction-diffusion based mean field rate theory model is implemented in the viscoplastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. A novel scheme is proposed to model the evolution (both number density and radius) of irradiation-induced dislocation loops that can be informed directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behavior of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture, and external stress onmore » the coupled irradiation growth and creep behavior are also studied.« less

Simultaneous saccharification and bioethanol production from corn cobs: Process optimization and kinetic studies.

PubMed

Sewsynker-Sukai, Yeshona; Gueguim Kana, E B

2018-08-01

This study investigates the simultaneous saccharification and fermentation (SSF) process for bioethanol production from corn cobs with prehydrolysis (PSSF) and without prehydrolysis (OSSF). Two response surface models were developed with high coefficients of determination (>0.90). Process optimization gave high bioethanol concentrations and bioethanol conversions for the PSSF (36.92 ± 1.34 g/L and 62.36 ± 2.27%) and OSSF (35.04 ± 0.170 g/L and 58.13 ± 0.283%) models respectively. Additionally, the logistic and modified Gompertz models were used to study the kinetics of microbial cell growth and ethanol formation under microaerophilic and anaerobic conditions. Cell growth in the OSSF microaerophilic process gave the highest maximum specific growth rate (µ max ) of 0.274 h -1 . The PSSF microaerophilic bioprocess gave the highest potential maximum bioethanol concentration (P m ) (42.24 g/L). This study demonstrated that microaerophilic rather than anaerobic culture conditions enhanced cell growth and bioethanol production, and that additional prehydrolysis steps do not significantly impact on the bioethanol concentration and conversion in SSF process. Copyright © 2018 Elsevier Ltd. All rights reserved.

Crystal plasticity modeling of irradiation growth in Zircaloy-2

NASA Astrophysics Data System (ADS)

Patra, Anirban; Tomé, Carlos N.; Golubov, Stanislav I.

2017-08-01

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.

A new reserve growth model for United States oil and gas fields

USGS Publications Warehouse

Verma, M.K.

2005-01-01

Reserve (or field) growth, which is an appreciation of total ultimate reserves through time, is a well-recognized phenomenon, particularly in mature petroleum provinces. The importance of forecasting reserve growth accurately in a mature petroleum province made it necessary to develop improved growth functions, and a critical review of the original Arrington method was undertaken. During a five-year (1992-1996), the original Arrington method gave 1.03% higher than the actual oil reserve growth, whereas the proposed modified method gave a value within 0.3% of the actual growth, and therefore it was accepted for the development for reserve growth models. During a five-year (1992-1996), the USGS 1995 National Assessment gave 39.3% higher oil and 33.6% lower gas than the actual growths, whereas the new model based on Modified Arrington method gave 11.9% higher oil and 29.8% lower gas than the actual growths. The new models forecast predict reserve growths of 4.2 billion barrels of oil (2.7%) and 30.2 trillion cubic feet of gas (5.4%) for the conterminous U.S. for the next five years (1997-2001). ?? 2005 International Association for Mathematical Geology.

Modelling the interaction between flooding events and economic growth

NASA Astrophysics Data System (ADS)

Grames, J.; Prskawetz, A.; Grass, D.; Blöschl, G.

2015-06-01

Socio-hydrology describes the interaction between the socio-economy and water. Recent models analyze the interplay of community risk-coping culture, flooding damage and economic growth (Di Baldassarre et al., 2013; Viglione et al., 2014). These models descriptively explain the feedbacks between socio-economic development and natural disasters like floods. Contrary to these descriptive models, our approach develops an optimization model, where the intertemporal decision of an economic agent interacts with the hydrological system. In order to build this first economic growth model describing the interaction between the consumption and investment decisions of an economic agent and the occurrence of flooding events, we transform an existing descriptive stochastic model into an optimal deterministic model. The intermediate step is to formulate and simulate a descriptive deterministic model. We develop a periodic water function to approximate the former discrete stochastic time series of rainfall events. Due to the non-autonomous exogenous periodic rainfall function the long-term path of consumption and investment will be periodic.

Developmental trajectories of adolescent popularity: a growth curve modelling analysis.

PubMed

Cillessen, Antonius H N; Borch, Casey

2006-12-01

Growth curve modelling was used to examine developmental trajectories of sociometric and perceived popularity across eight years in adolescence, and the effects of gender, overt aggression, and relational aggression on these trajectories. Participants were 303 initially popular students (167 girls, 136 boys) for whom sociometric data were available in Grades 5-12. The popularity and aggression constructs were stable but non-overlapping developmental dimensions. Growth curve models were run with SAS MIXED in the framework of the multilevel model for change [Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis. Oxford, UK: Oxford University Press]. Sociometric popularity showed a linear change trajectory; perceived popularity showed nonlinear change. Overt aggression predicted low sociometric popularity but an increase in perceived popularity in the second half of the study. Relational aggression predicted a decrease in sociometric popularity, especially for girls, and continued high-perceived popularity for both genders. The effect of relational aggression on perceived popularity was the strongest around the transition from middle to high school. The importance of growth curve models for understanding adolescent social development was discussed, as well as specific issues and challenges of growth curve analyses with sociometric data.

Modeling the atomistic growth behavior of gold nanoparticles in solution

NASA Astrophysics Data System (ADS)

Turner, C. Heath; Lei, Yu; Bao, Yuping

2016-04-01

The properties of gold nanoparticles strongly depend on their three-dimensional atomic structure, leading to an increased emphasis on controlling and predicting nanoparticle structural evolution during the synthesis process. In order to provide this atomistic-level insight and establish a link to the experimentally-observed growth behavior, a kinetic Monte Carlo simulation (KMC) approach is developed for capturing Au nanoparticle growth characteristics. The advantage of this approach is that, compared to traditional molecular dynamics simulations, the atomistic nanoparticle structural evolution can be tracked on time scales that approach the actual experiments. This has enabled several different comparisons against experimental benchmarks, and it has helped transition the KMC simulations from a hypothetical toy model into a more experimentally-relevant test-bed. The model is initially parameterized by performing a series of automated comparisons of Au nanoparticle growth curves versus the experimental observations, and then the refined model allows for detailed structural analysis of the nanoparticle growth behavior. Although the Au nanoparticles are roughly spherical, the maximum/minimum dimensions deviate from the average by approximately 12.5%, which is consistent with the corresponding experiments. Also, a surface texture analysis highlights the changes in the surface structure as a function of time. While the nanoparticles show similar surface structures throughout the growth process, there can be some significant differences during the initial growth at different synthesis conditions.

Numerical Modeling of Physical Vapor Transport in Contactless Crystal Growth Geometry

NASA Technical Reports Server (NTRS)

Palosz, W.; Lowry, S.; Krishnam, A.; Przekwas, A.; Grasza, K.

1998-01-01

Growth from the vapor under conditions of limited contact with the walls of the growth ampoule is beneficial for the quality of the growing crystal due to reduced stress and contamination which may be caused by interactions with the growth container. The technique may be of a particular interest for studies on crystal growth under microgravity conditions: elimination of some factors affecting the crystal quality may make interpretation of space-conducted processes more conclusive and meaningful. For that reason, and as a part of our continuing studies on 'contactless' growth technique, we have developed a computational model of crystal growth process in such system. The theoretical model was built, and simulations were performed using the commercial computational fluid dynamics code, (CFD) ACE. The code uses an implicit finite volume formulation with a gray discrete ordinate method radiation model which accounts for the diffuse absorption and reflection of radiation throughout the furnace. The three-dimensional model computes the heat transfer through the crystal, quartz, and gas both inside and outside the ampoule, and mass transport from the source to the crystal and the sink. The heat transport mechanisms by conduction, natural convection, and radiation, and mass transport by diffusion and convection are modeled simultaneously and include the heat of the phase transition at the solid-vapor interfaces. As the thermal boundary condition, temperature profile along the walls of the furnace is used. For different thermal profiles and furnace and ampoule dimensions, the crystal growth rate and development of the crystal-vapor and source-vapor interfaces (change of the interface shape and location with time) are obtained. Super/under-saturation in the ampoule is determined and critical factors determining the 'contactless' growth conditions are identified and discussed. The relative importance of the ampoule dimensions and geometry, the furnace dimensions and its

Modeling and predicting the biofilm formation of Salmonella Virchow with respect to temperature and pH.

PubMed

Ariafar, M Nima; Buzrul, Sencer; Akçelik, Nefise

2016-03-01

Biofilm formation of Salmonella Virchow was monitored with respect to time at three different temperature (20, 25 and 27.5 °C) and pH (5.2, 5.9 and 6.6) values. As the temperature increased at a constant pH level, biofilm formation decreased while as the pH level increased at a constant temperature, biofilm formation increased. Modified Gompertz equation with high adjusted determination coefficient (Radj(2)) and low mean square error (MSE) values produced reasonable fits for the biofilm formation under all conditions. Parameters of the modified Gompertz equation could be described in terms of temperature and pH by use of a second order polynomial function. In general, as temperature increased maximum biofilm quantity, maximum biofilm formation rate and time of acceleration of biofilm formation decreased; whereas, as pH increased; maximum biofilm quantity, maximum biofilm formation rate and time of acceleration of biofilm formation increased. Two temperature (23 and 26 °C) and pH (5.3 and 6.3) values were used up to 24 h to predict the biofilm formation of S. Virchow. Although the predictions did not perfectly match with the data, reasonable estimates were obtained. In principle, modeling and predicting the biofilm formation of different microorganisms on different surfaces under various conditions could be possible.

Nanowire growth process modeling and reliability models for nanodevices

NASA Astrophysics Data System (ADS)

Fathi Aghdam, Faranak

Nowadays, nanotechnology is becoming an inescapable part of everyday life. The big barrier in front of its rapid growth is our incapability of producing nanoscale materials in a reliable and cost-effective way. In fact, the current yield of nano-devices is very low (around 10 %), which makes fabrications of nano-devices very expensive and uncertain. To overcome this challenge, the first and most important step is to investigate how to control nano-structure synthesis variations. The main directions of reliability research in nanotechnology can be classified either from a material perspective or from a device perspective. The first direction focuses on restructuring materials and/or optimizing process conditions at the nano-level (nanomaterials). The other direction is linked to nano-devices and includes the creation of nano-electronic and electro-mechanical systems at nano-level architectures by taking into account the reliability of future products. In this dissertation, we have investigated two topics on both nano-materials and nano-devices. In the first research work, we have studied the optimization of one of the most important nanowire growth processes using statistical methods. Research on nanowire growth with patterned arrays of catalyst has shown that the wire-to-wire spacing is an important factor affecting the quality of resulting nanowires. To improve the process yield and the length uniformity of fabricated nanowires, it is important to reduce the resource competition between nanowires during the growth process. We have proposed a physical-statistical nanowire-interaction model considering the shadowing effect and shared substrate diffusion area to determine the optimal pitch that would ensure the minimum competition between nanowires. A sigmoid function is used in the model, and the least squares estimation method is used to estimate the model parameters. The estimated model is then used to determine the optimal spatial arrangement of catalyst arrays

Tissue-scale, personalized modeling and simulation of prostate cancer growth

NASA Astrophysics Data System (ADS)

Lorenzo, Guillermo; Scott, Michael A.; Tew, Kevin; Hughes, Thomas J. R.; Zhang, Yongjie Jessica; Liu, Lei; Vilanova, Guillermo; Gomez, Hector

2016-11-01

Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed “predictive medicine.” Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.

Fractional differential equations based modeling of microbial survival and growth curves: model development and experimental validation.

PubMed

Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M

2008-10-01

A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.

Correcting Model Fit Criteria for Small Sample Latent Growth Models with Incomplete Data

ERIC Educational Resources Information Center

McNeish, Daniel; Harring, Jeffrey R.

2017-01-01

To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor…

Visualized modeling platform for virtual plant growth and monitoring on the internet

NASA Astrophysics Data System (ADS)

Zhou, De-fu; Tian, Feng-qui; Ren, Ping

2009-07-01

Virtual plant growth is a key research topic in Agriculture Information Technique and Computer Graphics. It has been applied in botany, agronomy, environmental sciences, computre sciences and applied mathematics. Modeling leaf color dynamics in plant is of significant importance for realizing virtual plant growth. Using systematic analysis method and dynamic modeling technology, a SPAD-based leaf color dynamic model was developed to simulate time-course change characters of leaf SPAD on the plant. In addition, process of plant growth can be computer-stimulated using Virtual Reality Modeling Language (VRML) to establish a vivid and visible model, including shooting, rooting, blooming, as well as growth of the stems and leaves. In the resistance environment, e.g., lacking of water, air or nutrient substances, high salt or alkaline, freezing injury, high temperature, suffering from diseases and insect pests, the changes from the level of whole plant to organs, tissues and cells could be computer-stimulated. Changes from physiological and biochemistry could also be described. When a series of indexes were input by the costumers, direct view and microcosmic changes could be shown. Thus, the model has a good performance in predicting growth condition of the plant, laying a foundation for further constructing virtual plant growth system. The results revealed that realistic physiological and pathological processes of 3D virtual plants could be demonstrated by proper design and effectively realized in the internet.

Analysis of longitudinal data of beef cattle raised on pasture from northern Brazil using nonlinear models.

PubMed

Lopes, Fernando B; da Silva, Marcelo C; Marques, Ednira G; McManus, Concepta M

2012-12-01

This study was undertaken to aim of estimating the genetic parameters and trends for asymptotic weight (A) and maturity rate (k) of Nellore cattle from northern Brazil. The data set was made available by the Brazilian Association of Zebu Breeders and collected between the years of 1997 and 2007. The Von Bertalanffy, Brody, Gompertz, and logistic nonlinear models were fitted by the Gauss-Newton method to weight-age data of 45,895 animals collected quarterly of the birth to 750 days old. The curve parameters were analyzed using the procedures GLM and CORR. The estimation of (co)variance components and genetic parameters was obtained using the MTDFREML software. The estimated heritability coefficients were 0.21 ± 0.013 and 0.25 ± 0.014 for asymptotic weight and maturity rate, respectively. This indicates that selection for any trait shall results in genetic progress in the herd. The genetic correlation between A and k was negative (-0.57 ± 0.03) and indicated that animals selected for high maturity rate shall result in low asymptotic weight. The Von Bertalanffy function is adequate to establish the mean growth patterns and to predict the adult weight of Nellore cattle. This model is more accurate in predicting the birth weight of these animals and has better overall fit. The prediction of adult weight using nonlinear functions can be accurate when growth curve parameters and their (co)variance components are estimated jointly. The model used in this study can be applied to the prediction of mature weight in herds where a portion of the animals are culled before they reach the adult age.

Kinetic Model of the Initial Stage of the Nanowire Growth

NASA Astrophysics Data System (ADS)

Filimonov, S. N.; Hervieu, Yu. Yu.

2018-03-01

A kinetic model of the formation of pyramid-like bulges (pedestals) at the bases of vertical nanowires is proposed. The formation of the pedestals at the early stage of the nanowire growth is assumed to be induced by a higher nucleation rate of two-dimensional islands under the catalyst droplet, as compared to the nucleation rate at the non-activated surface areas. Kinetics of the nucleation and propagation of the steps in the pyramid is described with a model of the multilayer growth, taking into account that the catalyst droplet at the nanowire top is a strong sink for adatoms. It is shown that the transition from the growth of the pyramid to the axial growth of the nanowire is possible if the appearance of a nucleus of the new layer under the catalyst droplet results in a partial dissolution of the underlying layer. In this case a segment of the nanowire sidewall is formed, preventing the lateral growth of the layers generated by the droplet.

Stochastic nonlinear dynamics pattern formation and growth models

PubMed Central

Yaroslavsky, Leonid P

2007-01-01

Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature. PMID:17908341

Development of a program to fit data to a new logistic model for microbial growth.

PubMed

Fujikawa, Hiroshi; Kano, Yoshihiro

2009-06-01

Recently we developed a mathematical model for microbial growth in food. The model successfully predicted microbial growth at various patterns of temperature. In this study, we developed a program to fit data to the model with a spread sheet program, Microsoft Excel. Users can instantly get curves fitted to the model by inputting growth data and choosing the slope portion of a curve. The program also could estimate growth parameters including the rate constant of growth and the lag period. This program would be a useful tool for analyzing growth data and further predicting microbial growth.

Evolutionary model of the growth and size of firms

NASA Astrophysics Data System (ADS)

Kaldasch, Joachim

2012-07-01

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size-variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.

A stochastic model of firm growth

NASA Astrophysics Data System (ADS)

Bottazzi, Giulio; Secchi, Angelo

2003-06-01

Recently from analyses on different databases the tent-shape of the distribution of firm growth rates has emerged as a robust and universal characteristic of the time evolution of corporates. We add new evidence on this topic and we present a new stochastic model that, under rather general assumptions, provides a robust explanation for the observed regularity.

Modelling volumetric growth in a thick walled fibre reinforced artery

NASA Astrophysics Data System (ADS)

Eriksson, T. S. E.; Watton, P. N.; Luo, X. Y.; Ventikos, Y.

2014-12-01

A novel framework for simulating growth and remodelling (G&R) of a fibre-reinforced artery, including volumetric adaption, is proposed. We show how to implement this model into a finite element framework and propose and examine two underlying assumptions for modelling growth, namely constant individual density (CID) or adaptive individual density (AID). Moreover, we formulate a novel approach which utilises a combination of both AID and CID to simulate volumetric G&R for a tissue composed of several different constituents. We consider a special case of the G&R of an artery subjected to prescribed elastin degradation and we theorise on the assumptions and suitability of CID, AID and the mixed approach for modelling arterial biology. For simulating the volumetric changes that occur during aneurysm enlargement, we observe that it is advantageous to describe the growth of collagen using CID whilst it is preferable to model the atrophy of elastin using AID.

Biofilm growth in porous media: Experiments, computational modeling at the porescale, and upscaling

NASA Astrophysics Data System (ADS)

Peszynska, Malgorzata; Trykozko, Anna; Iltis, Gabriel; Schlueter, Steffen; Wildenschild, Dorthe

2016-09-01

Biofilm growth changes many physical properties of porous media such as porosity, permeability and mass transport parameters. The growth depends on various environmental conditions, and in particular, on flow rates. Modeling the evolution of such properties is difficult both at the porescale where the phase morphology can be distinguished, as well as during upscaling to the corescale effective properties. Experimental data on biofilm growth is also limited because its collection can interfere with the growth, while imaging itself presents challenges. In this paper we combine insight from imaging, experiments, and numerical simulations and visualization. The experimental dataset is based on glass beads domain inoculated by biomass which is subjected to various flow conditions promoting the growth of biomass and the appearance of a biofilm phase. The domain is imaged and the imaging data is used directly by a computational model for flow and transport. The results of the computational flow model are upscaled to produce conductivities which compare well with the experimentally obtained hydraulic properties of the medium. The flow model is also coupled to a newly developed biomass-nutrient growth model, and the model reproduces morphologies qualitatively similar to those observed in the experiment.

Individual-tree diameter growth model for managed, even-aged, upland oak stands

Treesearch

Donald E. Hilt

1983-01-01

A distance-independent, individual-tree diameter growth model was developed for managed, even-aged, upland oak stands. The 5-year basal-area growth of individual trees is first modeled as a function of dbh squared for given stands. Parameters from these models are then modeled as a function of mean stand diameter, percent stocking of the stand, and site index. A...

Modeling of scale-dependent bacterial growth by chemical kinetics approach.

PubMed

Martínez, Haydee; Sánchez, Joaquín; Cruz, José-Manuel; Ayala, Guadalupe; Rivera, Marco; Buhse, Thomas

2014-01-01

We applied the so-called chemical kinetics approach to complex bacterial growth patterns that were dependent on the liquid-surface-area-to-volume ratio (SA/V) of the bacterial cultures. The kinetic modeling was based on current experimental knowledge in terms of autocatalytic bacterial growth, its inhibition by the metabolite CO2, and the relief of inhibition through the physical escape of the inhibitor. The model quantitatively reproduces kinetic data of SA/V-dependent bacterial growth and can discriminate between differences in the growth dynamics of enteropathogenic E. coli, E. coli JM83, and Salmonella typhimurium on one hand and Vibrio cholerae on the other hand. Furthermore, the data fitting procedures allowed predictions about the velocities of the involved key processes and the potential behavior in an open-flow bacterial chemostat, revealing an oscillatory approach to the stationary states.

A dynamic model for predicting growth in zinc-deficient stunted infants given supplemental zinc.

PubMed

Wastney, Meryl E; McDonald, Christine M; King, Janet C

2018-05-01

Zinc deficiency limits infant growth and increases susceptibility to infections, which further compromises growth. Zinc supplementation improves the growth of zinc-deficient stunted infants, but the amount, frequency, and duration of zinc supplementation required to restore growth in an individual child is unknown. A dynamic model of zinc metabolism that predicts changes in weight and length of zinc-deficient, stunted infants with dietary zinc would be useful to define effective zinc supplementation regimens. The aims of this study were to develop a dynamic model for zinc metabolism in stunted, zinc-deficient infants and to use that model to predict the growth response when those infants are given zinc supplements. A model of zinc metabolism was developed using data on zinc kinetics, tissue zinc, and growth requirements for healthy 9-mo-old infants. The kinetic model was converted to a dynamic model by replacing the rate constants for zinc absorption and excretion with functions for these processes that change with zinc intake. Predictions of the dynamic model, parameterized for zinc-deficient, stunted infants, were compared with the results of 5 published zinc intervention trials. The model was then used to predict the results for zinc supplementation regimes that varied in the amount, frequency, and duration of zinc dosing. Model predictions agreed with published changes in plasma zinc after zinc supplementation. Predictions of weight and length agreed with 2 studies, but overpredicted values from a third study in which other nutrient deficiencies may have been growth limiting; the model predicted that zinc absorption was impaired in that study. The model suggests that frequent, smaller doses (5-10 mg Zn/d) are more effective for increasing growth in stunted, zinc-deficient 9-mo-old infants than are larger, less-frequent doses. The dose amount affects the duration of dosing necessary to restore and maintain plasma zinc concentration and growth.

Human body shape index based on an experimentally derived model of human growth.

PubMed

Lebiedowska, Maria K; Alter, Katharine E; Stanhope, Steven J

2008-01-01

To test the assumption of geometrically similar growth by developing experimentally derived models of human body growth during the age interval of 5 to 18 years; to use these derived growth models to establish a new human body shape index (HBSI) based on natural age-related changes in human body shape (HBS); and to compare various metrics of relative body weight (body mass index [BMI], ponderal index [PI], and HBSI) in a sample of 5- to 18-year-old children. Nondisabled Polish children (n = 847) participated in this descriptive study. To model growth, the best fit between body height (H) and body mass (M) was calculated for each sex using the allometric equation M = m(i) H(chi). HBSI was calculated separately for girls and boys, using sex-specific values for chi and a general HBSI from combined data. The customary BMI and PI were calculated and compared with HBSI values. The models of growth were M = 13.11H(2.84) (R2 = 0.90) for girls and M = 13.64H(2.68) (R2 = 0.91) for boys. HBSI values contained less inherent variability and were less influenced by growth (age and height) compared with BMI and PI. Age-related growth during childhood is sex-specific and not geometrically similar. Therefore, indices of HBS formulated from experimentally derived models of human growth are superior to customary geometric similarity-based indices for characterizing HBS in children during the formative growth years.

Multimodel ensembles of wheat growth: many models are better than one.

PubMed

Martre, Pierre; Wallach, Daniel; Asseng, Senthold; Ewert, Frank; Jones, James W; Rötter, Reimund P; Boote, Kenneth J; Ruane, Alex C; Thorburn, Peter J; Cammarano, Davide; Hatfield, Jerry L; Rosenzweig, Cynthia; Aggarwal, Pramod K; Angulo, Carlos; Basso, Bruno; Bertuzzi, Patrick; Biernath, Christian; Brisson, Nadine; Challinor, Andrew J; Doltra, Jordi; Gayler, Sebastian; Goldberg, Richie; Grant, Robert F; Heng, Lee; Hooker, Josh; Hunt, Leslie A; Ingwersen, Joachim; Izaurralde, Roberto C; Kersebaum, Kurt Christian; Müller, Christoph; Kumar, Soora Naresh; Nendel, Claas; O'leary, Garry; Olesen, Jørgen E; Osborne, Tom M; Palosuo, Taru; Priesack, Eckart; Ripoche, Dominique; Semenov, Mikhail A; Shcherbak, Iurii; Steduto, Pasquale; Stöckle, Claudio O; Stratonovitch, Pierre; Streck, Thilo; Supit, Iwan; Tao, Fulu; Travasso, Maria; Waha, Katharina; White, Jeffrey W; Wolf, Joost

2015-02-01

Crop models of crop growth are increasingly used to quantify the impact of global changes due to climate or crop management. Therefore, accuracy of simulation results is a major concern. Studies with ensembles of crop models can give valuable information about model accuracy and uncertainty, but such studies are difficult to organize and have only recently begun. We report on the largest ensemble study to date, of 27 wheat models tested in four contrasting locations for their accuracy in simulating multiple crop growth and yield variables. The relative error averaged over models was 24-38% for the different end-of-season variables including grain yield (GY) and grain protein concentration (GPC). There was little relation between error of a model for GY or GPC and error for in-season variables. Thus, most models did not arrive at accurate simulations of GY and GPC by accurately simulating preceding growth dynamics. Ensemble simulations, taking either the mean (e-mean) or median (e-median) of simulated values, gave better estimates than any individual model when all variables were considered. Compared to individual models, e-median ranked first in simulating measured GY and third in GPC. The error of e-mean and e-median declined with an increasing number of ensemble members, with little decrease beyond 10 models. We conclude that multimodel ensembles can be used to create new estimators with improved accuracy and consistency in simulating growth dynamics. We argue that these results are applicable to other crop species, and hypothesize that they apply more generally to ecological system models. © 2014 John Wiley & Sons Ltd.

Multimodel Ensembles of Wheat Growth: More Models are Better than One

NASA Technical Reports Server (NTRS)

Martre, Pierre; Wallach, Daniel; Asseng, Senthold; Ewert, Frank; Jones, James W.; Rotter, Reimund P.; Boote, Kenneth J.; Ruane, Alex C.; Thorburn, Peter J.; Cammarano, Davide;

Multimodel Ensembles of Wheat Growth: Many Models are Better than One

NASA Technical Reports Server (NTRS)

Martre, Pierre; Wallach, Daniel; Asseng, Senthold; Ewert, Frank; Jones, James W.; Rotter, Reimund P.; Boote, Kenneth J.; Ruane, Alexander C.; Thorburn, Peter J.; Cammarano, Davide;

Modeling of growth and laccase production by Pycnoporus sanguineus.

PubMed

Saat, Muhammad Naziz; Annuar, Mohamad Suffian Mohamad; Alias, Zazali; Chuan, Ling Tau; Chisti, Yusuf

2014-05-01

Production of extracellular laccase by the white-rot fungus Pycnoporus sanguineus was examined in batch submerged cultures in shake flasks, baffled shake flasks and a stirred tank bioreactor. The biomass growth in the various culture systems closely followed a logistic growth model. The production of laccase followed a Luedeking-Piret model. A modified Luedeking-Piret model incorporating logistic growth effectively described the consumption of glucose. Biomass productivity, enzyme productivity and substrate consumption were enhanced in baffled shake flasks relative to the cases for the conventional shake flasks. This was associated with improved oxygen transfer in the presence of the baffles. The best results were obtained in the stirred tank bioreactor. At 28 °C, pH 4.5, an agitation speed of 600 rpm and a dissolved oxygen concentration of ~25 % of air saturation, the laccase productivity in the bioreactor exceeded 19 U L(-1 )days(-1), or 1.5-fold better than the best case for the baffled shake flask. The final concentration of the enzyme was about 325 U L(-1).

Mathematical model for Trametes versicolor growth in submerged cultivation.

PubMed

Tisma, Marina; Sudar, Martina; Vasić-Racki, Durda; Zelić, Bruno

2010-08-01

Trametes versicolor is a white-rot fungus known as a producer of extracellular enzymes such as laccase, manganese-peroxidase, and lignin-peroxidase. The production of these enzymes requires detailed knowledge of the growth characteristics and physiology of the fungus. Submerged cultivations of T. versicolor on glucose, fructose, and sucrose as sole carbon sources were performed in shake flasks. Sucrose hydrolysis catalyzed by the whole cells of T. versicolor was considered as one-step enzymatic reaction described with Michaelis-Menten kinetics. Kinetic parameters of invertase-catalyzed sucrose hydrolysis were estimated (K (m) = 7.99 g dm(-3) and V (m) = 0.304 h(-1)). Monod model was used for description of kinetics of T. versicolor growth on glucose and fructose as sole carbon sources. Growth associated model parameters were estimated from the experimental results obtained by independent experiments (mu(G)(max) = 0.14 h(-1), K(G)(S) = 8.06 g dm(-3), mu(F)(max) = 0.37 h(-1) and K(F)(S) = 54.8 g dm(-3)). Developed mathematical model is in good agreement with the experimental results.

The Effect of Data Quality on Short-term Growth Model Projections

Treesearch

David Gartner

2005-01-01

This study was designed to determine the effect of FIA's data quality on short-term growth model projections. The data from Georgia's 1996 statewide survey were used for the Southern variant of the Forest Vegetation Simulator to predict Georgia's first annual panel. The effect of several data error sources on growth modeling prediction errors...

Strategies for the coupling of global and local crystal growth models

NASA Astrophysics Data System (ADS)

Derby, Jeffrey J.; Lun, Lisa; Yeckel, Andrew

2007-05-01

The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

GROWTH AND INEQUALITY: MODEL EVALUATION BASED ON AN ESTIMATION-CALIBRATION STRATEGY

PubMed Central

Jeong, Hyeok; Townsend, Robert

2010-01-01

This paper evaluates two well-known models of growth with inequality that have explicit micro underpinnings related to household choice. With incomplete markets or transactions costs, wealth can constrain investment in business and the choice of occupation and also constrain the timing of entry into the formal financial sector. Using the Thai Socio-Economic Survey (SES), we estimate the distribution of wealth and the key parameters that best fit cross-sectional data on household choices and wealth. We then simulate the model economies for two decades at the estimated initial wealth distribution and analyze whether the model economies at those micro-fit parameter estimates can explain the observed macro and sectoral aspects of income growth and inequality change. Both models capture important features of Thai reality. Anomalies and comparisons across the two distinct models yield specific suggestions for improved research on the micro foundations of growth and inequality. PMID:20448833

Transient Mobility on Submonolayer Island Growth: An Exploration of Asymptotic Effects in Modeling

NASA Astrophysics Data System (ADS)

Morales-Cifuentes, Josue; Einstein, Theodore L.; Pimpinelli, Alberto

In studies of epitaxial growth, modeling of the smallest stable cluster (i+1 monomers, with i the critical nucleus size), is paramount in understanding growth dynamics. Our previous work has tackled submonolayer growth by modeling the effect of ballistic monomers, hot-precursors, on diffusive dynamics. Different scaling regimes and energies were predicted, with initial confirmation by applying to para-hexaphenyl submonolayer studies. Lingering questions about the applicability and behavior of the model are addressed. First, we show how an asymptotic approximation based on the growth exponent, α (N Fα) allows for robustness of modeling to experimental data; second, we answer questions about non-monotonicity by exploring the behavior of the growth exponent across realizable parameter spaces; third, we revisit our previous para-hexaphenyl work and examine relevant physical parameters, namely the speed of the hot-monomers. We conclude with an exploration of how the new asymptotic approximation can be used to strengthen the application of our model to other physical systems.

The Diffusion Model Is Not a Deterministic Growth Model: Comment on Jones and Dzhafarov (2014)

PubMed Central

Smith, Philip L.; Ratcliff, Roger; McKoon, Gail

2015-01-01

Jones and Dzhafarov (2014) claim that several current models of speeded decision making in cognitive tasks, including the diffusion model, can be viewed as special cases of other general models or model classes. The general models can be made to match any set of response time (RT) distribution and accuracy data exactly by a suitable choice of parameters and so are unfalsifiable. The implication of their claim is that models like the diffusion model are empirically testable only by artificially restricting them to exclude unfalsifiable instances of the general model. We show that Jones and Dzhafarov’s argument depends on enlarging the class of “diffusion” models to include models in which there is little or no diffusion. The unfalsifiable models are deterministic or near-deterministic growth models, from which the effects of within-trial variability have been removed or in which they are constrained to be negligible. These models attribute most or all of the variability in RT and accuracy to across-trial variability in the rate of evidence growth, which is permitted to be distributed arbitrarily and to vary freely across experimental conditions. In contrast, in the standard diffusion model, within-trial variability in evidence is the primary determinant of variability in RT. Across-trial variability, which determines the relative speed of correct responses and errors, is theoretically and empirically constrained. Jones and Dzhafarov’s attempt to include the diffusion model in a class of models that also includes deterministic growth models misrepresents and trivializes it and conveys a misleading picture of cognitive decision-making research. PMID:25347314

Application of Impedance Microbiology for Evaluating Potential Acidifying Performances of Starter Lactic Acid Bacteria to Employ in Milk Transformation.

PubMed

Bancalari, Elena; Bernini, Valentina; Bottari, Benedetta; Neviani, Erasmo; Gatti, Monica

2016-01-01

Impedance microbiology is a method that enables tracing microbial growth by measuring the change in the electrical conductivity. Different systems, able to perform this measurement, are available in commerce and are commonly used for food control analysis by mean of measuring a point of the impedance curve, defined "time of detection." With this work we wanted to find an objective way to interpret the metabolic significance of impedance curves and propose it as a valid approach to evaluate the potential acidifying performances of starter lactic acid bacteria to be employed in milk transformation. To do this it was firstly investigated the possibility to use the Gompertz equation to describe the data coming from the impedance curve obtained by mean of BacTrac 4300®. Lag time (λ), maximum specific M% rate (μmax), and maximum value of M% (Yend) have been calculated and, given the similarity of the impedance fitted curve to the bacterial growth curve, their meaning has been interpreted. Potential acidifying performances of eighty strains belonging to Lactobacillus helveticus, Lactobacillus delbrueckii subsp. bulgaricus, Lactococcus lactis , and Streptococcus thermophilus species have been evaluated by using the kinetics parameters, obtained from Excel add-in DMFit version 2.1. The novelty and importance of our findings, obtained by means of BacTrac 4300®, is that they can also be applied to data obtained from other devices. Moreover, the meaning of λ, μmax, and Yend that we have extrapolated from Modified Gompertz equation and discussed for lactic acid bacteria in milk, can be exploited also to other food environment or other bacteria, assuming that they can give a curve and that curve is properly fitted with Gompertz equation.

Population growth and economic growth.

PubMed

Narayana, D L

1984-01-01

This discussion of the issues relating to the problem posed by population explosion in the developing countries and economic growth in the contemporary world covers the following: predictions of economic and social trends; the Malthusian theory of population; the classical or stationary theory of population; the medical triage model; ecological disaster; the Global 2000 study; the limits to growth; critiques of the Limits to Growth model; nonrenewable resources; food and agriculture; population explosion and stabilization; space and ocean colonization; and the limits perspective. The Limits to Growth model, a general equilibrium anti-growth model, is the gloomiest economic model ever constructed. None of the doomsday models, the Malthusian theory, the classical stationary state, the neo-Malthusian medical triage model, the Global 2000 study, are so far reaching in their consequences. The course of events that followed the publication of the "Limits to Growth" in 1972 in the form of 2 oil shocks, food shock, pollution shock, and price shock seemed to bear out formally the gloomy predictions of the thesis with a remarkable speed. The 12 years of economic experience and the knowledge of resource trends postulate that even if the economic pressures visualized by the model are at work they are neither far reaching nor so drastic. Appropriate action can solve them. There are several limitations to the Limits to Growth model. The central theme of the model, which is overshoot and collapse, is unlikely to be the course of events. The model is too aggregative to be realistic. It exaggerates the ecological disaster arising out of the exponential growth of population and industry. The gross underestimation of renewable resources is a basic flaw of the model. The most critical weakness of the model is its gross underestimation of the historical trend of technological progress and the technological possiblities within industry and agriculture. The model does correctly emphasize

Development and validation of a mathematical model for growth of pathogens in cut melons.

PubMed

Li, Di; Friedrich, Loretta M; Danyluk, Michelle D; Harris, Linda J; Schaffner, Donald W

2013-06-01

Many outbreaks of foodborne illness associated with the consumption of fresh-cut melons have been reported. The objective of our research was to develop a mathematical model that predicts the growth rate of Salmonella on fresh-cut cantaloupe over a range of storage temperatures and to validate that model by using Salmonella and Escherichia coli O157:H7 on cantaloupe, honeydew, and watermelon, using both new data and data from the published studies. The growth of Salmonella on honeydew and watermelon and E. coli O157:H7 on cantaloupe, honeydew, and watermelon was monitored at temperatures of 4 to 25°C. The Ratkowsky (or square-root model) was used to describe Salmonella growth on cantaloupe as a function of storage temperature. Our results show that the levels of Salmonella on fresh-cut cantaloupe with an initial load of 3 log CFU/g can reach over 7 log CFU/g at 25°C within 24 h. No growth was observed at 4°C. A linear correlation was observed between the square root of Salmonella growth rate and temperature, such that √growth rate = 0.026 × (T - 5.613), R(2) = 0.9779. The model was generally suitable for predicting the growth of both Salmonella and E. coli O157:H7 on cantaloupe, honeydew, and watermelon, for both new data and data from the published literature. When compared with existing models for growth of Salmonella, the new model predicts a theoretic minimum growth temperature similar to the ComBase Predictive Models and Pathogen Modeling Program models but lower than other food-specific models. The ComBase Prediction Models results are very similar to the model developed in this study. Our research confirms that Salmonella can grow quickly and reach high concentrations when cut cantaloupe is stored at ambient temperatures, without visual signs of spoilage. Our model provides a fast and cost-effective method to estimate the effects of storage temperature on fresh-cut melon safety and could also be used in subsequent quantitative microbial risk

Escaping the snare of chronological growth and launching a free curve alternative: general deviance as latent growth model.

PubMed

Wood, Phillip Karl; Jackson, Kristina M

2013-08-01

Researchers studying longitudinal relationships among multiple problem behaviors sometimes characterize autoregressive relationships across constructs as indicating "protective" or "launch" factors or as "developmental snares." These terms are used to indicate that initial or intermediary states of one problem behavior subsequently inhibit or promote some other problem behavior. Such models are contrasted with models of "general deviance" over time in which all problem behaviors are viewed as indicators of a common linear trajectory. When fit of the "general deviance" model is poor and fit of one or more autoregressive models is good, this is taken as support for the inhibitory or enhancing effect of one construct on another. In this paper, we argue that researchers consider competing models of growth before comparing deviance and time-bound models. Specifically, we propose use of the free curve slope intercept (FCSI) growth model (Meredith & Tisak, 1990) as a general model to typify change in a construct over time. The FCSI model includes, as nested special cases, several statistical models often used for prospective data, such as linear slope intercept models, repeated measures multivariate analysis of variance, various one-factor models, and hierarchical linear models. When considering models involving multiple constructs, we argue the construct of "general deviance" can be expressed as a single-trait multimethod model, permitting a characterization of the deviance construct over time without requiring restrictive assumptions about the form of growth over time. As an example, prospective assessments of problem behaviors from the Dunedin Multidisciplinary Health and Development Study (Silva & Stanton, 1996) are considered and contrasted with earlier analyses of Hussong, Curran, Moffitt, and Caspi (2008), which supported launch and snare hypotheses. For antisocial behavior, the FCSI model fit better than other models, including the linear chronometric growth curve

Escaping the snare of chronological growth and launching a free curve alternative: General deviance as latent growth model

PubMed Central

WOOD, PHILLIP KARL; JACKSON, KRISTINA M.

2014-01-01

Researchers studying longitudinal relationships among multiple problem behaviors sometimes characterize autoregressive relationships across constructs as indicating “protective” or “launch” factors or as “developmental snares.” These terms are used to indicate that initial or intermediary states of one problem behavior subsequently inhibit or promote some other problem behavior. Such models are contrasted with models of “general deviance” over time in which all problem behaviors are viewed as indicators of a common linear trajectory. When fit of the “general deviance” model is poor and fit of one or more autoregressive models is good, this is taken as support for the inhibitory or enhancing effect of one construct on another. In this paper, we argue that researchers consider competing models of growth before comparing deviance and time-bound models. Specifically, we propose use of the free curve slope intercept (FCSI) growth model (Meredith & Tisak, 1990) as a general model to typify change in a construct over time. The FCSI model includes, as nested special cases, several statistical models often used for prospective data, such as linear slope intercept models, repeated measures multivariate analysis of variance, various one-factor models, and hierarchical linear models. When considering models involving multiple constructs, we argue the construct of “general deviance” can be expressed as a single-trait multimethod model, permitting a characterization of the deviance construct over time without requiring restrictive assumptions about the form of growth over time. As an example, prospective assessments of problem behaviors from the Dunedin Multidisciplinary Health and Development Study (Silva & Stanton, 1996) are considered and contrasted with earlier analyses of Hussong, Curran, Moffitt, and Caspi (2008), which supported launch and snare hypotheses. For antisocial behavior, the FCSI model fit better than other models, including the linear

Modeling Fish Growth in Low Dissolved Oxygen

ERIC Educational Resources Information Center

Neilan, Rachael Miller

2013-01-01

This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

Revisiting a model of ontogenetic growth: estimating model parameters from theory and data.

PubMed

Moses, Melanie E; Hou, Chen; Woodruff, William H; West, Geoffrey B; Nekola, Jeffery C; Zuo, Wenyun; Brown, James H

2008-05-01

The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the M(1/4) scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the M(3/4) scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research.

Modeling and Forecasting Mortality With Economic Growth: A Multipopulation Approach.

PubMed

Boonen, Tim J; Li, Hong

2017-10-01

Research on mortality modeling of multiple populations focuses mainly on extrapolating past mortality trends and summarizing these trends by one or more common latent factors. This article proposes a multipopulation stochastic mortality model that uses the explanatory power of economic growth. In particular, we extend the Li and Lee model (Li and Lee 2005) by including economic growth, represented by the real gross domestic product (GDP) per capita, to capture the common mortality trend for a group of populations with similar socioeconomic conditions. We find that our proposed model provides a better in-sample fit and an out-of-sample forecast performance. Moreover, it generates lower (higher) forecasted period life expectancy for countries with high (low) GDP per capita than the Li and Lee model.

Mediation Analysis in a Latent Growth Curve Modeling Framework

ERIC Educational Resources Information Center