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Sample records for gompertz growth model

  1. Probabilistic Gompertz model of irreversible growth.

    PubMed

    Bardos, D C

    2005-05-01

    Characterizing organism growth within populations requires the application of well-studied individual size-at-age models, such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters, may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required. Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae) where growth is irreversible. Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological length scale is then shown to yield realistic length-increment distributions.

  2. Stochastic Gompertz model of tumour cell growth.

    PubMed

    Lo, C F

    2007-09-21

    In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.

  3. Comparison of Gompertz and neural network models of broiler growth.

    PubMed

    Roush, W B; Dozier, W A; Branton, S L

    2006-04-01

    Neural networks offer an alternative to regression analysis for biological growth modeling. Very little research has been conducted to model animal growth using artificial neural networks. Twenty-five male chicks (Ross x Ross 308) were raised in an environmental chamber. Body weights were determined daily and feed and water were provided ad libitum. The birds were fed a starter diet (23% CP and 3,200 kcal of ME/kg) from 0 to 21 d, and a grower diet (20% CP and 3,200 kcal of ME/ kg) from 22 to 70 d. Dead and female birds were not included in the study. Average BW of 18 birds were used as the data points for the growth curve to be modeled. Training data consisted of alternate-day weights starting with the first day. Validation data consisted of BW at all other age periods. Comparison was made between the modeling by the Gompertz nonlinear regression equation and neural network modeling. Neural network models were developed with the Neuroshell Predictor. Accuracy of the models was determined by mean square error (MSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and bias. The Gompertz equation was fit for the data. Forecasting error measurements were based on the difference between the model and the observed values. For the training data, the lowest MSE, MAD, MAPE, and bias were noted for the neural-developed neural network. For the validation data, the lowest MSE and MAD were noted with the genetic algorithm-developed neural network. Lowest bias was for the neural-developed network. As measured by bias, the Gompertz equation underestimated the values whereas the neural- and genetic-developed neural networks produced little or no overestimation of the observed BW responses. Past studies have attempted to interpret the biological significance of the estimates of the parameters of an equation. However, it may be more practical to ignore the relevance of parameter estimates and focus on the ability to predict responses.

  4. Estimation of growth parameters using a nonlinear mixed Gompertz model.

    PubMed

    Wang, Z; Zuidhof, M J

    2004-06-01

    In order to maximize the utility of simulation models for decision making, accurate estimation of growth parameters and associated variances is crucial. A mixed Gompertz growth model was used to account for between-bird variation and heterogeneous variance. The mixed model had several advantages over the fixed effects model. The mixed model partitioned BW variation into between- and within-bird variation, and the covariance structure assumed with the random effect accounted for part of the BW correlation across ages in the same individual. The amount of residual variance decreased by over 55% with the mixed model. The mixed model reduced estimation biases that resulted from selective sampling. For analysis of longitudinal growth data, the mixed effects growth model is recommended.

  5. A proposed fractional-order Gompertz model and its application to tumour growth data.

    PubMed

    Bolton, Larisse; Cloot, Alain H J J; Schoombie, Schalk W; Slabbert, Jacobus P

    2015-06-01

    A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.

  6. Growth characteristics of pearl gray guinea fowl as predicted by the Richards, Gompertz, and logistic models.

    PubMed

    Nahashon, S N; Aggrey, S E; Adefope, N A; Amenyenu, A; Wright, D

    2006-02-01

    This study was undertaken to describe the growth pattern of the pearl gray Guinea fowl. Using BW data from hatch to 22 wk, 3 nonlinear mathematical functions (Richards, Gompertz, and logistic) were used to estimate growth patterns of the pearl gray guinea fowl. The logistic and Gompertz models are a special case of the Richards model, which has a variable point of inflection defined by the shape or growth trajectory parameter, m. The shape parameter m was 1.08 and 0.98 in males and females, respectively, suggesting that the growth pattern of the pearl gray female guinea fowl is Gompertz. The pearl gray guinea fowl exhibited sexual dimorphism for their growth characteristics. From the Gompertz model, the asymptotic BW, growth rate, and age at maximum growth were 1.62 kg, 0.22 kg/wk, and 6.65 wk in males, respectively, and 1.70 kg, 0.19 kg/wk, and 6.70 wk in females, respectively. The ages at maximum growth were 6.65, 6.47, and 8.12 wk for the Richards, Gompertz, and logistic models, respectively. The pearl gray guinea fowl females have a higher asymptotic BW compared with the males. The average asymptotic BW of about 1.57 kg for both sexes predicted by the logistic model was below the average predicted BW from the Richards (1.66 kg) and Gompertz (1.67 kg) models, respectively, at 22 wk of age. The inverse relationship between the asymptotic weight and both relative growth and age at maximum growth of the pearl gray guinea fowl is similar to that of chickens, quail, and ducks. Success in studying the growth characteristics of guinea fowl will contribute to the efforts of genetically improving this least-studied avian species.

  7. On the therapy effect for a stochastic growth Gompertz-type model.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

    2012-02-01

    We consider a diffusion model based on a generalized Gompertz deterministic growth in which carrying capacity depends on the initial size of the population. The drift of the resulting process is then modified by introducing a time-dependent function, called "therapy", in order to model the effect of an exogenous factor. The transition probability density function and the related moments for the proposed process are obtained. A study of the influence of the therapy on several characteristics of the model is performed. The first-passage-time problem through time-dependent boundaries is also analyzed. Finally, an application to real data concerning a rabbit population subject to particular therapies is presented.

  8. Parameterization of European perch Perca fluviatilis length-at-age data using stochastic Gompertz growth models.

    PubMed

    Troynikov, V S; Gorfine, H K; Ložys, L; Pūtys, Z; Jakubavičiūtė, E; Day, R W

    2011-12-01

    Three stochastic versions of the Gompertz growth model were used to parameterize total length (L(T) )-at-age data for perch Perca fluviatilis, an important target species for commercial and recreational fishers and a food species for predatory fishes and aquatic birds. Each model addresses growth heterogeneity by incorporating random parameters from a specific positive distribution: Weibull, gamma or log-normal. The modelling outputs for each version of the model provide L(T) distributions for selected ages and percentiles of L(T) at age for both males and females. The results highlight the importance of using a stochastic approach and the logistic-like growth pattern for analysing growth data for P. fluviatilis in Curonian Lagoon (Lithuania). Outputs from this modelling can be extended to a stochastic analysis of fish cohort dynamics, incorporating all length-based biological relationships, and the selectivity-related interactions between fish cohorts and fishing gear.

  9. Optimization of the cell seeding density and modeling of cell growth and metabolism using the modified Gompertz model for microencapsulated animal cell culture.

    PubMed

    Wen-tao, Qi; Ying, Zhang; Juan, Ma; Xin, Guo; Yu-bing, Xie; Wei, Wang; Xiaojun, Ma

    2006-04-05

    Cell microencapsulation is one of the promising strategies for the in vitro production of proteins or in vivo delivery of therapeutic products. In order to design and fabricate the optimized microencapsulated cell system, the Gompertz model was applied and modified to describe the growth and metabolism of microencapsulated cell, including substrate consumption and product formation. The Gompertz model successfully described the cell growth kinetics and the modified Gompertz models fitted the substrate consumption and product formation well. It was demonstrated that the optimal initial cell seeding density was about 4-5 x 10(6) cells/mL of microcapsule, in terms of the maximum specific growth rate, the glucose consumption potential and the product formation potential calculated by the Gompertz and modified Gompertz models. Modeling of cell growth and metabolism in microcapsules provides a guideline for optimizing the culture of microencapsulated cells.

  10. Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function.

    PubMed

    Vuori, Kaarina; Strandén, Ismo; Sevón-Aimonen, Marja-Liisa; Mäntysaari, Esa A

    2006-01-01

    A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.

  11. Estimation of vaginal probiotic lactobacilli growth parameters with the application of the Gompertz model.

    PubMed

    Juárez, TomásMaríaSilvina; de, LabandaElenaBru; de, RuizHolgadoAidaPesce; Nader-Macías, María Elena

    2002-01-01

    Lactobacilli are widely described as probiotic microorganisms used to restore the ecological balance of different animal or human tracts. For their use as probiotics, bacteria must show certain characteristics or properties related to the ability of adherence to mucosae or epithelia or show inhibition against pathogenic microorganisms. It is of primary interest to obtain the highest biomass and viability of the selected microorganisms. In this report, the growth of seven vaginal lactobacilli strains in four different growth media and at several inoculum percentages was compared, and the values of growth parameters (lag phase time, maximum growth rate, maximum optical density) were obtained by applying the Gompertz model to the experimental data. The application and estimation of this model is discussed, and the evaluation of the growth parameters is analyzed to compare the growth conditions of lactobacilli. Thus, these results in lab experiments provide a basis for testing different culture conditions to determine the best conditions in which to grow the probiotic lactobacilli for technological applications.

  12. Growth curve by Gompertz nonlinear regression model in female and males in tambaqui (Colossoma macropomum).

    PubMed

    De Mello, Fernanda; Oliveira, Carlos A L; Ribeiro, Ricardo P; Resende, Emiko K; Povh, Jayme A; Fornari, Darci C; Barreto, Rogério V; McManus, Concepta; Streit, Danilo

    2015-01-01

    Was evaluated the pattern of growth among females and males of tambaqui by Gompertz nonlinear regression model. Five traits of economic importance were measured on 145 animals during the three years, totaling 981 morphometric data analyzed. Different curves were adjusted between males and females for body weight, height and head length and only one curve was adjusted to the width and body length. The asymptotic weight (a) and relative growth rate to maturity (k) were different between sexes in animals with ± 5 kg; slaughter weight practiced by a specific niche market, very profitable. However, there was no difference between males and females up to ± 2 kg; slaughter weight established to supply the bigger consumer market. Females showed weight greater than males (± 280 g), which are more suitable for fish farming purposes defined for the niche market to larger animals. In general, males had lower maximum growth rate (8.66 g / day) than females (9.34 g / day), however, reached faster than females, 476 and 486 days growth rate, respectively. The height and length body are the traits that contributed most to the weight at 516 days (P <0.001).

  13. Global stability of Gompertz model of three competing populations

    NASA Astrophysics Data System (ADS)

    Yu, Yumei; Wang, Wendi; Lu, Zhengyi

    2007-10-01

    The model of three competitive populations with Gompertz growth is studied. The periodic solutions are ruled out by generalized Dulac criteria. On the basis of the analysis, we obtain conditions that ensure the asymptotic behavior of the model is simple.

  14. Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.

    PubMed

    Di Crescenzo, Antonio; Spina, Serena

    2016-12-01

    We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.

  15. Impact of electro-stimulation on denitrifying bacterial growth and analysis of bacterial growth kinetics using a modified Gompertz model in a bio-electrochemical denitrification reactor.

    PubMed

    Liu, Hengyuan; Chen, Nan; Feng, Chuanping; Tong, Shuang; Li, Rui

    2017-05-01

    This study aimed to investigate the effect of electro-stimulation on denitrifying bacterial growth in a bio-electrochemical reactor, and the growth were modeled using modified Gompertz model under different current densities at three C/Ns. It was found that the similar optimum current density of 250mA/m(2) was obtained at C/N=0.75, 1.00 and 1.25, correspondingly the maximum nitrate removal efficiencies were 98.0%, 99.2% and 99.9%. Moreover, ATP content and cell membrane permeability of denitrifying bacteria were significantly increased at optimum current density. Furthermore, modified Gompertz model fitted well with the microbial growth curves, and the highest maximum growth rates (µmax) and shorter lag time were obtained at the optimum current density for all C/Ns. This study demonstrated that the modified Gompertz model could be used for describing microbial growth under different current densities and C/Ns in a bio-electrochemical denitrification reactor, and it provided an alternative for improving the performance of denitrification process.

  16. Probabilistic neural networks using Bayesian decision strategies and a modified Gompertz model for growth phase classification in the batch culture of Bacillus subtilis.

    PubMed

    Simon; Nazmul Karim M

    2001-01-01

    Probabilistic neural networks (PNNs) were used in conjunction with the Gompertz model for bacterial growth to classify the lag, logarithmic, and stationary phases in a batch process. Using the fermentation time and the optical density of diluted cell suspensions, sampled from a culture of Bacillus subtilis, PNNs enabled a reliable determination of the growth phases. Based on a Bayesian decision strategy, the Gompertz based PNN used newly proposed definition of the lag and logarithmic phases to estimate the latent, logarithmic and stationary phases. This network topology has the potential for use with on-line turbidimeter for the automation and control of cultivation processes.

  17. On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

    2013-09-01

    A Gompertz-type diffusion process characterized by the presence of exogenous factors in the drift term is considered. Such a process is able to describe the dynamics of populations in which both the intrinsic rates are modified by means of time-dependent terms. In order to quantify the effect of such terms the evaluation of the relative entropy is made. The first passage time problem through suitable boundaries is studied. Moreover, some simulation results are shown in order to capture the dependence of the involved functions on the parameters. Finally, an application to tumor growth is presented and simulation results are shown.

  18. A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth.

    PubMed

    d'Onofrio, Alberto; Fasano, Antonio; Monechi, Bernardo

    2011-03-01

    We present a new extension of Gompertz law for tumour growth and anti-tumour therapy. After discussing its qualitative and analytical properties, we show, in the spirit of [16], that, like the standard Gompertz model, it is fully compatible with the two-population model of Gyllenberg and Webb, formulated in [14] in order to provide a theoretical basis to Gompertz law. Compatibility with the model proposed in [17] is also investigated. Comparisons with some experimental data confirm the practical applicability of the model. Numerical simulations about the method performance are presented.

  19. Modeling tumor growth in the presence of a therapy with an effect on rate growth and variability by means of a modified Gompertz diffusion process.

    PubMed

    Román-Román, Patricia; Román-Román, Sergio; Serrano-Pérez, Juan José; Torres-Ruiz, Francisco

    2016-10-21

    In experimental studies on tumor growth, whenever the time evolution of the relative volume of a tumor in an untreated (control) group can be fitted by a Gompertz diffusion process there is a possibility that an antiproliferative therapy, which modifies the growth rate of the process that fits the treated group, may also affect its variability. The present paper proposes several procedures for the estimation of the time function included in the infinitesimal variance of the new process, as well as the time function affecting the growth rate (which is included in the infinitesimal mean). Also, a hypothesis testing is designed to confirm or refute the need for including such a time-dependent function in the infinitesimal variance. In order to validate and compare the proposed procedures a simulation study has been carried out. In addition, a proposal is made for a strategy aimed at finding the optimal combination of procedures for each case. A real data application concerning the effects of cisplatin on a patient-derived xenograft (PDX) tumor model showcases the advantages of this model over others that have been used in the past.

  20. Gompertz kinetics model of fast chemical neurotransmission currents.

    PubMed

    Easton, Dexter M

    2005-10-01

    At a chemical synapse, transmitter molecules ejected from presynaptic terminal(s) bind reversibly with postsynaptic receptors and trigger an increase in channel conductance to specific ions. This paper describes a simple but accurate predictive model for the time course of the synaptic conductance transient, based on Gompertz kinetics. In the model, two simple exponential decay terms set the rates of development and decline of transmitter action. The first, r, triggering conductance activation, is surrogate for the decelerated rate of growth of conductance, G. The second, r', responsible for Y, deactivation of the conductance, is surrogate for the decelerated rate of decline of transmitter action. Therefore, the differential equation for the net conductance change, g, triggered by the transmitter is dg/dt=g(r-r'). The solution of that equation yields the product of G(t), representing activation, and Y(t), which defines the proportional decline (deactivation) of the current. The model fits, over their full-time course, published records of macroscopic ionic current associated with fast chemical transmission. The Gompertz model is a convenient and accurate method for routine analysis and comparison of records of synaptic current and putative transmitter time course. A Gompertz fit requiring only three independent rate constants plus initial current appears indistinguishable from a Markov fit using seven rate constants.

  1. For prediction of elder survival by a Gompertz model, number dead is preferable to number alive.

    PubMed

    Easton, Dexter M; Hirsch, Henry R

    2008-12-01

    The standard Gompertz equation for human survival fits very poorly the survival data of the very old (age 85 and above), who appear to survive better than predicted. An alternative Gompertz model based on the number of individuals who have died, rather than the number that are alive, at each age, tracks the data more accurately. The alternative model is based on the same differential equation as in the usual Gompertz model. The standard model describes the accelerated exponential decay of the number alive, whereas the alternative, heretofore unutilized model describes the decelerated exponential growth of the number dead. The alternative model is complementary to the standard and, together, the two Gompertz formulations allow accurate prediction of survival of the older as well as the younger mature members of the population.

  2. Nonselective Harvesting of a Prey-Predator Fishery with Gompertz Law of Growth

    ERIC Educational Resources Information Center

    Purohit, D.; Chaudhuri, K. S.

    2002-01-01

    This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

  3. Gompertz model with delays and treatment: mathematical analysis.

    PubMed

    Bodnar, Marek; Piotrowska, Monika Joanna; Foryś, Urszula

    2013-06-01

    In this paper we study the delayed Gompertz model, as a typical model of tumor growth, with a term describing external interference that can reflect a treatment, e.g. chemotherapy. We mainly consider two types of delayed models, the one with the delay introduced in the per capita growth rate (we call it the single delayed model) and the other with the delay introduced in the net growth rate (the double delayed model). We focus on stability and possible stability switches with increasing delay for the positive steady state. Moreover, we study a Hopf bifurcation, including stability of arising periodic solutions for a constant treatment. The analytical results are extended by numerical simulations for a pharmacokinetic treatment function.

  4. Biological implications of the Weibull and Gompertz models of aging.

    PubMed

    Ricklefs, Robert E; Scheuerlein, Alex

    2002-02-01

    Gompertz and Weibull functions imply contrasting biological causes of demographic aging. The terms describing increasing mortality with age are multiplicative and additive, respectively, which could result from an increase in the vulnerability of individuals to extrinsic causes in the Gompertz model and the predominance of intrinsic causes at older ages in the Weibull model. Experiments that manipulate extrinsic mortality can distinguish these biological models. To facilitate analyses of experimental data, we defined a single index for the rate of aging (omega) for the Weibull and Gompertz functions. Each function described the increase in aging-related mortality in simulated ages at death reasonably well. However, in contrast to the Weibull omega(W), the Gompertz omega(G) was sensitive to variation in the initial mortality rate independently of aging-related mortality. Comparisons between wild and captive populations appear to support the intrinsic-causes model for birds, but give mixed support for both models in mammals.

  5. Estimation of genetic (co)variances of Gompertz growth function parameters in pigs.

    PubMed

    Coyne, J M; Matilainen, K; Berry, D P; Sevon-Aimonen, M-L; Mäntysaari, E A; Juga, J; Serenius, T; McHugh, N

    2017-04-01

    The objective of this study was to estimate genetic (co)variances for the Gompertz growth function parameters, asymptotic mature weight (A), the ratio of mature weight to birthweight (B) and rate of maturation (k), using alternative modelling approaches. The data set consisted of 51 893 live weight records from 10 201 growing pigs. The growth of each pig was modelled using the Gompertz model employing either a two-step fixed effect or mixed model approach or a one-step mixed model approach using restricted maximum likelihood for the estimation of genetic (co)variance. Heritability estimates for the Gompertz growth function parameters, A (0.40), B (0.69) and k (0.45), were greatest for the one-step approach, compared with the two-step fixed effects approach, A (0.10), B (0.33) and k (0.13), and the two-step mixed model approach, A (0.17), B (0.32) and k (0.18). Inferred genetic correlations (i.e. correlations of estimated breeding values) between growth function parameters within models ranged from -0.78 to 0.76, and across models ranged from 0.28 to 0.73 for parameter A, 0.75 to 0.88 for parameter B and 0.09 to 0.37 for parameter k. Correlations between predicted daily sire live weights based on the Gompertz growth curve parameters' estimated breeding values from 60 to 200 days of age between all three modelled approaches were moderately to strongly correlated (0.75 to 0.95). Results from this study provide heritability estimates for biologically interpretable parameters of pig growth through the quantification of genetic (co)variances, thereby facilitating the estimation of breeding values for inclusion in breeding objectives to aid in breeding and selection decisions.

  6. The Trans-Gompertz Function: An Alternative to the Logistic Growth Function with Faster Growth.

    PubMed

    Kozusko, F; Bourdeau, M

    2015-12-01

    The growth characteristics of the recently derived Trans-Gompertz function are compared to those of the Generalized Logistic function. Both functions are defined by one shaping parameter and one rate parameter. The functions are matched at a specified point on the growth curve by equating both the first and second derivatives. Analysis shows that the matched Trans-Gompertz function will have grown at a faster rate with a larger inflection point ratio.

  7. FBST for covariance structures of generalized Gompertz models

    NASA Astrophysics Data System (ADS)

    Maranhão, Viviane Teles de Lucca; Lauretto, Marcelo De Souza; Stern, Julio Michael

    2012-10-01

    The Gompertz distribution is commonly used in biology for modeling fatigue and mortality. This paper studies a class of models proposed by Adham and Walker, featuring a Gompertz type distribution where the dependence structure is modeled by a lognormal distribution, and develops a new multivariate formulation that facilitates several numerical and computational aspects. This paper also implements the FBST, the Full Bayesian Significance Test for pertinent sharp (precise) hypotheses on the lognormal covariance structure. The FBST's e-value, ev(H), gives the epistemic value of hypothesis, H, or the value of evidence in the observed in support of H.

  8. An Evaluation of Growth Models as Predictive Tools for Estimates at Completion (EAC)

    DTIC Science & Technology

    2009-03-01

    Composite Index methods. Our study uses the Gompertz growth curve to produce three EAC Models based on contract phase: A Production Model, a...31 9. Regression Error Results ...............................................................................................33 10. Gompertz ...36 12. Gompertz Parameter Estimates, Development

  9. Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions

    NASA Astrophysics Data System (ADS)

    Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.

    In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.

  10. Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

    PubMed Central

    2010-01-01

    Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice. PMID:21029411

  11. Complementary Gompertz survival models: decreasing alive versus increasing dead.

    PubMed

    Easton, Dexter M

    2009-05-01

    The survival patterns of many animals can be classified into one of two asymmetric sigmoid forms: One group can be predicted from the standard, classical Gompertz assumption that, with age, the number of individuals alive in the population decreases exponentially at an exponentially increasing rate. The other can be predicted from the alternative Gompertz assumption that, with age, the number of individuals that have died increases exponentially at an exponentially decreasing rate. The two models have similar mathematical forms, but the curves are not the same. In contrast to the standard, the alternative form has an early rapid fall and terminates in a gradual decay of the number of live individuals. It fits "non-Gompertzian" survival plots that are not predicted by the number-alive assumption. Analyses of published data show one or the other survival mode in various animal populations, depending on sex, genetic strain, nutrition, or activity.

  12. Gompertz mortality law and scaling behavior of the Penna model.

    PubMed

    Coe, J B; Mao, Y

    2005-11-01

    The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.

  13. Gompertz mortality law and scaling behavior of the Penna model

    NASA Astrophysics Data System (ADS)

    Coe, J. B.; Mao, Y.

    2005-11-01

    The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism’s genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.

  14. A Markovian Growth Dynamics on Rooted Binary Trees Evolving According to the Gompertz Curve

    NASA Astrophysics Data System (ADS)

    Landim, C.; Portugal, R. D.; Svaiter, B. F.

    2012-08-01

    Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields (Probab. Theory Relat. Fields 79(4):509-542, 1988) model. Fix n≥1 and β>0. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate β( n- k)/ n, where k is the distance from the node to the root. Denote by Z n ( t) the number of nodes with no descendants at time t and let T n = β -1 nln( n/ln4)+(ln2)/(2 β). We prove that 2- n Z n ( T n + nτ), τ∈ℝ, converges to the Gompertz curve exp(-(ln2) e - βτ ). We also prove a central limit theorem for the martingale associated to Z n ( t).

  15. Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

    PubMed

    Frank, T D

    2002-07-01

    Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.

  16. Flexible alternatives to the Gompertz equation for describing growth with age in turkey hens.

    PubMed

    Porter, T; Kebreab, E; Darmani Kuhi, H; Lopez, S; Strathe, A B; France, J

    2010-02-01

    A total of 49 profiles of growing turkey hens from commercial flocks were used in this study. Three flexible growth functions (von Bertalanffy, Richards, and Morgan) were evaluated with regard to their ability to describe the relationship between BW and age and were compared with the Gompertz equation with its fixed point of inflection, which might result in its overestimation. For each function, 4 ways of analysis were implemented. A basic model was fitted first, followed by implementation of a first-order autoregressive correlation structure. A model that considered only mature BW varied with year and another that considered only the rate coefficient varied with different years were applied. The results showed that the fixed point of inflection of the Gompertz equation can be a limitation and that the relationship between BW and age in turkeys was best described using flexible growth functions. However, the Richards equation failed to converge when fitted to the turkey growth data; therefore, it was not considered further. Inclusion of an autoregressive process of the first order rendered a substantially improved fit to data for the 3 growth functions. The Morgan equation provided the best fit to the data set and was used for characterizing mean growth curves for the 7 yr of production. It was estimated that the maximum growth rate occurred at 3.74, 3.65, 3.99, 4.18, 4.05, 4.01, and 3.77 kg BW for production years from 1997 to 2003, respectively. It is recommended that flexible growth functions should be considered as an alternative to the simpler functions (with a fixed point of inflection) for describing the relationship between BW and age in turkeys because they were easier to fit and very often gave a closer fit to data points because of their flexibility, and therefore a smaller residual MS value, than simpler models. It can also be recommended that studies should consider adding a first-order autoregressive process when analyzing repeated measures data with

  17. Soft bounds on diffusion produce skewed distributions and Gompertz growth

    NASA Astrophysics Data System (ADS)

    Mandrà, Salvatore; Lagomarsino, Marco Cosentino; Gherardi, Marco

    2014-09-01

    Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound." At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.

  18. Soft bounds on diffusion produce skewed distributions and Gompertz growth.

    PubMed

    Mandrà, Salvatore; Lagomarsino, Marco Cosentino; Gherardi, Marco

    2014-09-01

    Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound." At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.

  19. A new Gompertz-type diffusion process with application to random growth.

    PubMed

    Gutiérrez-Jáimez, Ramón; Román, Patricia; Romero, Desirée; Serrano, Juan J; Torres, Francisco

    2007-07-01

    Stochastic models describing growth kinetics are very important for predicting many biological phenomena. In this paper, a new Gompertz-type diffusion process is introduced, by means of which bounded sigmoidal growth patterns can be modeled by time-continuous variables. The main innovation of the process is that the bound can depend on the initial value, a situation that is not provided by the models considered to date. After building the model, a comprehensive study is presented, including its main characteristics and a simulation of sample paths. With the aim of applying this model to real-life situations, and given its possibilities in forecasting via the mean function, discrete sampling based inference is developed. The likelihood equations are not directly solvable, and because of difficulties that arise with the usual numerical methods employed to solve them, an iterative procedure is proposed. The possibilities of the new process are illustrated by means of an application to real data, concretely, to growth in rabbits.

  20. The gompertz function can coherently describe microbial mineralization of growth-sustaining pesticides.

    PubMed

    Johnsen, Anders R; Binning, Philip J; Aamand, Jens; Badawi, Nora; Rosenbom, Annette E

    2013-08-06

    Mineralization of (14)C-labeled tracers is a common way of studying the environmental fate of xenobiotics, but it can be difficult to extract relevant kinetic parameters from such experiments since complex kinetic functions or several kinetic functions may be needed to adequately describe large data sets. In this study, we suggest using a two-parameter, sigmoid Gompertz function for parametrizing mineralization curves. The function was applied to a data set of 252 normalized mineralization curves that represented the potential for degradation of the herbicide MCPA in three horizons of an agricultural soil. The Gompertz function fitted most of the normalized curves, and trends in the data set could be visualized by a scatter plot of the two Gompertz parameters (rate constant and time delay). For agricultural topsoil, we also tested the effect of the MCPA concentration on the mineralization kinetics. Reduced initial concentrations lead to shortened lag-phases, probably due to reduced need for bacterial growth. The effect of substrate concentration could be predicted by simply changing the time delay of the Gompertz curves. This delay could to some extent also simulate concentration effects for 2,4-D mineralization in agricultural soil and aquifer sediment and 2,6-dichlorobenzamide mineralization in single-species, mineral medium.

  1. Genetic (co)variances and breeding value estimation of Gompertz growth curve parameters in Finnish Yorkshire boars, gilts and barrows.

    PubMed

    Koivula, M; Sevón-Aimonen, M-L; Strandén, I; Matilainen, K; Serenius, T; Stalder, K J; Mäntysaari, E A

    2008-06-01

    This paper's objectives were to estimate the genetic (co)variance components of the Gompertz growth curve parameters and to evaluate the relationship of estimated breeding values (EBV) based on average daily gain (ADG) and Gompertz growth curves. Finnish Yorkshire central test station performance data was obtained from the Faba Breeding (Vantaa, Finland). The final data set included 121,488 weight records from 10,111 pigs. Heritability estimates for the Gompertz growth parameters mature weight (alpha), logarithm of mature weight to birth weight ratio (beta) and maturation rate (kappa) were 0.44, 0.55 and 0.31, respectively. Genotypic and phenotypic correlations between the growth curve parameters were high and mainly negative. The only positive relationship was found between alpha and beta. Pearson and Spearman rank correlation coefficients between EBV for ADG and daily gain calculated from Gompertz growth curves were 0.79. The Spearman rank correlation between the sire EBV for ADG and Gompertz growth curve parameter-based ADG for all sires with at least 15 progeny was 0.86. Growth curves differ significantly between individuals and this information could be utilized for selection purposes when improving growth rate in pigs.

  2. Modelling of Scenedesmus obliquus; function of nutrients with modified Gompertz model.

    PubMed

    Celekli, Abuzer; Balci, Muharrem; Bozkurt, Hüseyin

    2008-12-01

    This study attempted to investigate variation in biovolume of Scenedesmus obliquus, in the modified Johnson medium at 20+/-2 degrees C, under 16kergcm(-2)s(-1) continuous illumination. The experiments were carried out at four nitrate (8, 12, 16, and 20mM) and four phosphate (0.1, 0.3, 0.5 and 0.7mM) concentrations at pH 7 and 8. The best response for algal growth was found at 0.3mM phosphate and 12mM nitrate at pH 7, as it was obtained from weight averaging method. Besides, optimum phosphate and nitrate concentrations significantly distinguished (p<0.01) from other concentrations according to Turkey's HSD test. Key features of the growth of S. obliquus under phosphate and nitrate influenced batch culture was successfully predicted by modified Gompertz model. Through the cultivations, specific growth rate (mu) ranged from 0.30 to 1.02 day(-1), while biovolume doubling time (td) varied from 0.68 to 2.30 days. There were important differences (p<0.05) for both mu and td among response variables. Both nutrients displayed noteworthy effect (p<0.01) on the algal biovolume.

  3. Estimating Gompertz Growth Curves from Marine Mammal Strandings in the Presence of Missing Data.

    PubMed

    Shotwell, Mary; McFee, Wayne; Slate, Elizabeth H

    2010-01-01

    Stranded bottlenose dolphins (Tursiops truncatus) off the coast of South Carolina (SC) provide data essential for population health assessment. Of the 598 bottlenose dolphin strandings in SC from 1993 to 2007, 91 were of sufficient body condition to obtain organ weights. Of these 91 animals, only 52 were brought back to the laboratory for total body weight measurements. Because it is more feasible to transport smaller animals to the laboratory setting for necropsy procedures, a selection bias is present in that data for larger animals are often missing. Regression and propensity score multiple imputation methods are utilized to account for missing data needed to compute growth. Fitted Gompertz growth curves for SC animals with and without adjustment for missing data are compared to those found from the northwestern Gulf of Mexico. South Carolina animals display a trend in lower asymptotic mean total body weights and faster growth rates compared to the Gulf of Mexico population. The differences generally increased in magnitude after imputation methods. South Carolina females were originally estimated to reach larger maximum sizes than Gulf of Mexico females, but after imputation this relationship reversed. The findings suggest selection bias should be accounted for in sampling stranded dolphins.

  4. Statistical analysis of dependent competing risks model from Gompertz distribution under progressively hybrid censoring.

    PubMed

    Shi, Yimin; Wu, Min

    2016-01-01

    Previous studies have mostly considered the competing risks to be independent even when the interpretation of the failure modes implies dependency. This paper studies the dependent competing risks model from Gompertz distribution under Type-I progressively hybrid censoring scheme. We derive the maximum likelihood estimations of the model parameters, and then the asymptotic likelihood theory and Bootstrap method are used to obtain the confidence intervals. The simulation results are provided to investigate the effects of different dependence structures on the estimations of parameters. Finally, one data set was used for illustrative purpose.

  5. Kinetic models for batch ethanol production from sweet sorghum juice under normal and high gravity fermentations: Logistic and modified Gompertz models.

    PubMed

    Phukoetphim, Niphaphat; Salakkam, Apilak; Laopaiboon, Pattana; Laopaiboon, Lakkana

    2017-02-10

    The aim of this study was to model batch ethanol production from sweet sorghum juice (SSJ), under normal gravity (NG, 160g/L of total sugar) and high gravity (HG, 240g/L of total sugar) conditions with and without nutrient supplementation (9g/L of yeast extract), by Saccharomyces cerevisiae NP 01. Growth and ethanol production increased with increasing initial sugar concentration, and the addition of yeast extract enhanced both cell growth and ethanol production. From the results, either logistic or a modified Gompertz equation could be used to describe yeast growth, depending on information required. Furthermore, the modified Gompertz model was suitable for modeling ethanol production. Both the models fitted the data very well with coefficients of determination exceeding 0.98. The results clearly showed that these models can be employed in the development of ethanol production processes using SSJ under both NG and HG conditions. The models were also shown to be applicable to other ethanol fermentation systems employing pure and mixed sugars as carbon sources.

  6. Gompertz-Laird model prediction of optimum utilization of crude protein and metabolizable energy by French guinea fowl broilers.

    PubMed

    Nahashon, S N; Aggrey, S E; Adefope, N A; Amenyenu, A; Wright, D

    2010-01-01

    This study was conducted to assess the influence of dietary CP and ME on growth parameters of the French guinea fowl, a meat-type variety. In a 2 x 3 x 3 factorial arrangement, 297 one-day-old French guinea keets (162 females and 135 males) were randomly assigned to experimental diets comprising 3,050, 3,100, and 3,150 kcal of ME/kg, each containing 21, 23, and 25% CP from hatch to 4 wk of age (WOA), and 3,100, 3150, and 3,200 kcal of ME/kg, each containing 19, 21, and 23% CP at 5 to 8 WOA. Using BW and G:F data from hatch to 8 WOA, the Gompertz-Laird growth model was employed to estimate growth patterns of the French guinea fowl. Mean differences in exponential growth rate, age of maximum growth, and asymptotic BW among dietary CP and ME levels were not significant. However, instantaneous growth rate and weight at inflection point were significantly higher (P < 0.05) in birds on the 25% CP diet than those on the 21% CP diet at hatch to 4 WOA (1.12 kg/wk and 0.79 kg vs. 1.04 kg/wk and 0.74 kg, respectively). The exponential growth rate was also higher (P < 0.05) in birds fed the 3,050 kcal of ME/kg diet with either 23 or 25% CP than those fed diets containing 3,050 kcal of ME/kg and 21% CP. Mean G:F was higher (P < 0.05) in birds fed diets containing 3,050 kcal of ME/kg and either 21 or 23% CP than those in other dietary treatments. Therefore, based on the Gompertz-Laird growth model estimates, feeding 21 and 23% CP and 3,100 kcal of ME/kg at hatch to 4 WOA and 19 and 21% CP with 3,150 kcal of ME/kg at 5 to 8 WOA can be recommended as adequate for growth for the French guinea fowl broilers.

  7. Senescence rates in patients with end-stage renal disease: a critical appraisal of the Gompertz model.

    PubMed

    Koopman, J J E; Rozing, M P; Kramer, A; de Jager, D J; Ansell, D; De Meester, J M J; Prütz, K G; Finne, P; Heaf, J G; Palsson, R; Kramar, R; Jager, K J; Dekker, F W; Westendorp, R G J

    2011-04-01

    The most frequently used model to describe the exponential increase in mortality rate over age is the Gompertz equation. Logarithmically transformed, the equation conforms to a straight line, of which the slope has been interpreted as the rate of senescence. Earlier, we proposed the derivative function of the Gompertz equation as a superior descriptor of senescence rate. Here, we tested both measures of the rate of senescence in a population of patients with end-stage renal disease. It is clinical dogma that patients on dialysis experience accelerated senescence, whereas those with a functional kidney transplant have mortality rates comparable to the general population. Therefore, we calculated the age-specific mortality rates for European patients on dialysis (n=274 221; follow-up=594 767 person-years), for European patients with a functioning kidney transplant (n=61 286; follow-up=345 024 person-years), and for the general European population. We found higher mortality rates, but a smaller slope of logarithmic mortality curve for patients on dialysis compared with both patients with a functioning kidney transplant and the general population (P<0.001). A classical interpretation of the Gompertz model would imply that the rate of senescence in patients on dialysis is lower than in patients with a functioning transplant and lower than in the general population. In contrast, the derivative function of the Gompertz equation yielded the highest senescence rates for patients on dialysis, whereas the rate was similar in patients with a functioning transplant and the general population. We conclude that the rate of senescence is better described by the derivative function of the Gompertz equation.

  8. Exponentiated exponential model (Gompertz kinetics) of Na+ and K+ conductance changes in squid giant axon.

    PubMed Central

    Easton, D M

    1978-01-01

    The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. PMID:638223

  9. Voltage-clamp predictions by gompertz kinetics model relating squid-axon Na+-gating and ionic currents.

    PubMed

    Easton, Dexter M

    2005-10-01

    Gompertz kinetics is a simple, realistic, accurate, and computationally parsimonious alternative for prediction of macroscopic changes in Na+ conductance during voltage clamp. Conductance delay and time course depend on initial amplitudes and decay rates of surrogates for the macroscopic gating currents. The model is tested by the fit to published data of other authors. The proposed physical basis for the model is that membrane potential perturbation triggers motion of charged "gating" components of the axon membrane at rapid (activating) and at slow (inactivating) rates. The resulting distortion increases and more slowly diminishes the probability that conduction channels will be open.

  10. Experimental epizootiology of Zoophthora anhuiensis (Entomophthorales) against Myzus persicae (Homoptera: Aphididae) with a description of a modified Gompertz model for aphid epizootics.

    PubMed

    Feng, Ming-Guang; Li, Hui-Ping

    2003-11-01

    Epizootiological features of Zoophthora anhuiensis, a fungal pathogen specific to aphids in southern China, were studied in six aptera colonies of Myzus persicae at 16 regimes of temperature (T = 10, 15, 20 and 25 degrees C) and relative humidity (H = 90%, 95%, 98% and 100% RH) with initially infected proportion (Ip) of 0.5 in experiment (Expt) 1 or at a fixed regime of 15 degrees C and 100% RH with a variable Ip of 0.17-1.00 in Expt 2. Mycosis-caused mortalities (Mp) varied with aphid densities (D) over time after colony initiation (t) were well fitted to a Gompertz growth model modified to include the variables T, H, Ip and D in the form of Mp = 91.72exp[-5.282exp[-(0.0095T + 0.0128H/T-0.5407D2/H)t

  11. [Approximation of Time Series of Paramecia caudatum Dynamics by Verhulst and Gompertz Models: Non-traditional Approach].

    PubMed

    Nedorezov, L V

    2015-01-01

    For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.

  12. An Embryonic Growth Pathway is Reactivated in Human Prostate Cancer

    DTIC Science & Technology

    2005-06-01

    assess growth of the four cell lines, a Gompertz prostatectomy (n = 2), and six prostate cancer (PC) speci- growth model was fitted to each line. Day... Gompertz model with men (N), in hyperplastic (benign) tissue from men without line-specific asymptote and growth rate was estimated via Gauss-New...histologically confirmed tumor with histologically con- The plots and Gompertz fits were generated in R version 1.6.25.1 (36). firmed benign tissue obtained from

  13. Predictive implications of Gompertz's law

    NASA Astrophysics Data System (ADS)

    Richmond, Peter; Roehner, Bertrand M.

    2016-04-01

    Gompertz's law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold up to age 106. At that age the death rate is about 50%. Beyond 106 there is so far no convincing statistical evidence available because the number of survivors are too small even in large nations. However, assuming that Gompertz's law continues to hold beyond 106, we conclude that the mortality rate becomes equal to 1 at age 120 (meaning that there are 1000 deaths in a population of one thousand). In other words, the upper bound of human life is near 120. The existence of this fixed-point has interesting implications. It allows us to predict the form of the relationship between death rates at age 35 and the doubling time of Gompertz's law. In order to test this prediction, we first carry out a transversal analysis for a sample of countries comprising both industrialized and developing nations. As further confirmation, we also develop a longitudinal analysis using historical data over a time period of almost two centuries. Another prediction arising from this fixed-point model, is that, above a given population threshold, the lifespan of the oldest persons is independent of the size of their national community. This prediction is also supported by empirical evidence.

  14. Modeling the Growth of Archaeon Halobacterium halobium Affected by Temperature and Light.

    PubMed

    Lu, Hao; Yuan, Wenqiao; Cheng, Jay; Rose, Robert B; Classen, John J; Simmons, Otto D

    2017-03-01

    The objective of this study was to develop sigmoidal models, including three-parameter (Quadratic, Logistic, and Gompertz) and four-parameter models (Schnute and Richards) to simulate the growth of archaeon Halobacterium halobium affected by temperature and light. The models were statistically compared by using t test and F test. In the t test, confidence bounds for parameters were used to distinguish among models. For the F test, the lack of fit of the models was compared with the prediction error. The Gompertz model was 100 % accepted by the t test and 97 % accepted by the F test when the temperature effects were considered. Results also indicated that the Gompertz model was 94 % accepted by the F test when the growth of H. halobium was studied under varying light intensities. Thus, the Gompertz model was considered the best among the models studied to describe the growth of H. halobium affected by temperature or light. In addition, the biological growth parameters, including specific growth rate, lag time, and asymptote changes under Gompertz modeling, were evaluated.

  15. [Numerical modeling of ideal cohorts of aging organisms obeying the Gompertz-Makeham law in association with the Strehler-Mildwan correlation].

    PubMed

    Golubev, A G

    2004-01-01

    The Gompertz-Makeham law (-dn/dt x l/n(t)=C+lambdae(gammat)) so as other genuine laws of Nature is strictly applicable only to ideal objects (populations and cohorts) analogously to laws of mechanics or thermodynamics, which are exactly true only for such physical abstractions as mass points or ideal gases. Therefore, a biologically meaningful interpretation of the parameters of this law is likely to be more important for understanding the aging process than devising of alternative analytical descriptions of biodemographic processes for the sake of a better fit only. Numerical modeling of ideal cohorts of aging organisms obeying the Gompertz-Makeha law makes it possible to differentiate possible real and apparent changes in mortality patterns that occur in human history and in evolution and are observed in gerontological experiments and to demonstratively show such effects as the dependency of longevity upon population size, the evolutionarily important possibility of reciprocal changes in the mean and maximal longevity, or detection of apparent changes in negatively correlated aging rate and vitality when the Makeham term is ignored, which is usual in demography. The basic difference between the Makeham term Cand Gompertz term lambdae(gammat) is suggested to be not that the former is constant, whereas the latter is age-dependent, but that the former comprises the contributions of inherently irresistible stresses to mortality, whereas the latter comprises the contributions of resistible stresses to mortality and shows how changes in the ability to resist them is translated into changes in mortality.

  16. Ever since Gompertz.

    PubMed

    Olshansky, S J; Carnes, B A

    1997-02-01

    In 1825 British actuary Benjamin Gompertz made a simple but important observation that a law of geometrical progression pervades large portions of different tables of mortality for humans. The simple formula he derived describing the exponential rise in death rates between sexual maturity and old age is commonly, referred to as the Gompertz equation-a formula that remains a valuable tool in demography and in other scientific disciplines. Gompertz's observation of a mathematical regularity in the life table led him to believe in the presence of a low of mortality that explained why common age patterns of death exist. This law of mortality has captured the attention of scientists for the past 170 years because it was the first among what are now several reliable empirical tools for describing the dying-out process of many living organisms during a significant portion of their life spans. In this paper we review the literature on Gompertz's law of mortality and discuss the importance of his observations and insights in light of research on aging that has taken place since then.

  17. Use of the recursion formula of the Gompertz survival function to evaluate life-table data.

    PubMed

    Bassukas, I D

    1996-08-29

    The recursion formula of the Gompertz function is an established method for the analysis of growth processes. In the present study the recursion formula of the Gompertz survival function 1n S(t + s) = a + b x ln S(t) is introduced for the analysis of survival data, where S(t) is the survival fraction at age 1, s is the constant age increment between two consecutive measurements of the survival fraction and a and b are parameters. With the help of this method--and provided stroboscopial measurements of rates of survival are available--the Gompertz survival function, instead of the corresponding mortality function, can be determined directly using linear regression analysis. The application of the present algorithm is demonstrated by analysing two sets of data taken from the literature (survival of Drosophila imagoes and of female centenarians) using linear regression analysis to fit survival or mortality rates to the corresponding models. In both cases the quality of fit was superior by using the algorithm presently introduced. Moreover, survival functions calculated from the fits to the mortality law only poorly predict the survival data. On the contrary, the results of the present method not only fit to the measurements, but, for both sets of data the mortality parameters calculated by the present method are essentially identical to those obtained by a corresponding application of a non-linear Marquardt-Levenberg algorithm to fit the same sets of data to the explicit form of the Gompertz survival function. Taking into consideration the advantages of using a linear fit (goodness-of-fit test and efficient statistical comparison of survival patterns) the method of the recursion formula of the Gompertz survival function is the most preferable method to fit survival data to the Gompertz function.

  18. 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…

  19. A genetic investigation of various growth models to describe growth of lambs of two contrasting breeds.

    PubMed

    Lambe, N R; Navajas, E A; Simm, G; Bünger, L

    2006-10-01

    This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from linear regression. In both breeds, all nonlinear models fitted the data well, with an average coefficient of determination (R2) of > 0.98. The linear model had a lower average R2 than any of the nonlinear models (< 0.94). The variables used to describe the best 3 models (logistic, Gompertz, and Richards) included estimated final BW (A); maximum ADG (B); age at maximum ADG (C); position of point of inflection in relation to A (D, for Richards only). The Richards and Gompertz models provided the best fit (average R2 = 0.986 to 0.989) in both breeds. Richards estimated an extra variable, allowing increased flexibility in describing individual growth patterns, but the Akaike's information criteria value (which weighs log-likelihood by number of parameters estimated) was similar to that of the Gompertz model. Variables A, B, C, and D were moderately to highly heritable in Texel lambs (h2 = 0.33 to 0.87), and genetic correlations between variables within-model ranged from -0.80 to 0.89, suggesting some flexibility to change the shape of the growth curve when selecting for different variables. In SBF lambs, only variables from the logistic and Gompertz models had moderate heritabilities (0.17 to 0.56), but with high genetic correlations between variables within each model (< -0.88 or > 0.92). Selection on growth variables seems promising (in Texel more than SBF), but high genetic correlations between variables may restrict the possibilities to change the growth curve shape. A random regression model was also fitted to the data to allow predictions of growth rates at relevant time

  20. Stochastic Modelling of Gompertzian Tumor Growth

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; Behera, A.

    2009-08-01

    We study the effect of correlated noise in the Gompertzian tumor growth model for non-zero correlation time. The steady state probability distributions and average population of tumor cells are analyzed within the Fokker-Planck formalism to investigate the importance of additive and multiplicative noise. We find that the correlation strength and correlation time have opposite effects on the steady state probability distributions. It is observed that the non-bistable Gompertzian model, driven by correlated noise exhibits a stochastic resonance and phase transition. This behaviour of the Gompertz model is unaffected with the change of correlation time and occurs as a result of multiplicative noise.

  1. Forecasting Marine Corps Enlisted Attrition Through Parametric Modeling

    DTIC Science & Technology

    2009-03-01

    OF PAGES 85 14. SUBJECT TERMS Forecasting, Attrition, Marine Corps NEAS losses, Gompertz Model, Survival Analysis 16. PRICE CODE 17. SECURITY...18 1. Parametric Proportional Hazards Models ......................................18 2. Gompertz Models...19 a. Gompertz Hazard Function....................................................19 b. Gompertz Cumulative

  2. Gompertz law and aging as exclusion effects.

    PubMed

    Hallén, Anund

    2007-10-01

    The exponential increase with age in mortality rate, the Gompertz law, indicates that the decrease in vitality and viability linked to aging depends on phenomena with exponential or logarithmic dynamics. Gompertz slope (alpha) is assumed to be a measure of aging rate, provided the studied cohort is homogeneous and in a supporting environment. The law provides no clue about the cause of aging, but may be formally correlated with various physical or mathematical functions. A possible correlation between the Ogston-Laurent exclusion equation and human aging is examined. An increase with age of an inert cross-linked insoluble protein network is assumed to result in a logarithmic decrease in water volume available to colloidal macromolecules. In this model, alpha is assumed to be a measure of the rate of accumulation of the polypeptide network.

  3. Gompertz' survivorship law as an intrinsic principle of aging.

    PubMed

    Sas, Arthur A; Snieder, Harold; Korf, Jakob

    2012-05-01

    We defend the hypothesis that life-spanning population survivorship curves, as described by Gompertz' law and composed from cross-sectional data (here mortality), reflect an intrinsic aging principle active in each subject of that population. In other words Gompertz' law reflects aging of a prototypical subject, provided minimal (or no) external causes of death (i.e. fatal infections, starvation, accidents). Our approach deviates from the traditional (exponential) Gompertz' hazard function. For instance, the here formulated Gompertz' law accurately describes old-age deceleration of both all-cause mortality and the incidence of some ageing-associated cancers, as illustrated for the Dutch population. We consider the possibility that the old-age expression and progression of cancer and other pathologies becomes suppressed, because of random (and exponential) accumulation of damage during life. Gompertz' law may trigger new concepts and models describing life-spanning physiological and pathological processes of aging. We discuss (and reject) various aging models (e.g. a predominant role of individual variations at birth; reliability theory) and point to the explanatory potential of network models and systemic regulatory models.

  4. Applying Statistical Models to Mammographic Screening Data to Understand Growth and Progression of Ductal Carcinoma in Situ

    DTIC Science & Technology

    2005-09-01

    size with time); 2. Constant rate of doubling (exponential dependence of size on time); 3. Decreasing rate of growth with size ( Gompertz model). These...Exponential 720.4 -xoeta .0 .0rpet 0.3 203- Gompertz ോ -Gompez 0.2 0.2 0.1 0.1 0 , 0 0.1 1 10 0.1 1 10 Lesion Size Lesion Size Progressive Weakening...Models 0.8 0.7 0.6- Z,0.5 5Linear . 0.4 - -Exponential 72.4 0. •0.3 - Gompertz 0.2 0.1 0 0.1 1 10 Lesion Size Task 4: Manuscript preparation We have

  5. Gompertz-Makeham life expectancies: expressions and applications.

    PubMed

    Missov, Trifon I; Lenart, Adam

    2013-12-01

    In a population of individuals, whose mortality is governed by a Gompertz-Makeham hazard, we derive closed-form solutions to the life-expectancy integral, corresponding to the cases of homogeneous and gamma-heterogeneous populations, as well as in the presence/absence of the Makeham term. Derived expressions contain special functions that aid constructing high-accuracy approximations, which can be used to study the elasticity of life expectancy with respect to model parameters. Knowledge of Gompertz-Makeham life expectancies aids constructing life-table exposures.

  6. Lifetime growth in wild meerkats: incorporating life history and environmental factors into a standard growth model.

    PubMed

    English, Sinéad; Bateman, Andrew W; Clutton-Brock, Tim H

    2012-05-01

    Lifetime records of changes in individual size or mass in wild animals are scarce and, as such, few studies have attempted to model variation in these traits across the lifespan or to assess the factors that affect them. However, quantifying lifetime growth is essential for understanding trade-offs between growth and other life history parameters, such as reproductive performance or survival. Here, we used model selection based on information theory to measure changes in body mass over the lifespan of wild meerkats, and compared the relative fits of several standard growth models (monomolecular, von Bertalanffy, Gompertz, logistic and Richards). We found that meerkats exhibit monomolecular growth, with the best model incorporating separate growth rates before and after nutritional independence, as well as effects of season and total rainfall in the previous nine months. Our study demonstrates how simple growth curves may be improved by considering life history and environmental factors, which may be particularly relevant when quantifying growth patterns in wild populations.

  7. Modelling the growth of Japanese eel Anguilla japonica in the lower reach of the Kao-Ping River, southern Taiwan: an information theory approach.

    PubMed

    Lin, Y J; Tzeng, W N

    2009-07-01

    Information theory was applied to select the best model fitting total length (L(T))-at-age data and calculate the averaged model for Japanese eel Anguilla japonica compiled from published literature and the differences in growth between sexes were examined. Five candidate growth models were the von Bertalanffy, generalized von Bertalanffy, Gompertz, logistic and power models. The von Bertalanffy growth model with sex-specific coefficients was best supported by the data and nearly overlapped the averaged growth model based on Akaike weights, indicating a similar fit to the data. The Gompertz, generalized von Bertalanffy and power growth models were also substantially supported by the data. The L(T) at age of A. japonica were larger in females than in males according to the averaged growth mode, suggesting a sexual dimorphism in growth. Model inferences based on information theory, which deal with uncertainty in model selection and robust parameter estimates, are recommended for modelling the growth of A. japonica.

  8. Effects on generalized growth models driven by a non-Poissonian dichotomic noise

    NASA Astrophysics Data System (ADS)

    Bologna, M.; Calisto, H.

    2011-10-01

    In this paper we consider a general growth model with stochastic growth rate modelled via a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its probability distribution. We consider the, as yet, unexplored case where the deterministic growth rate is perturbed by a dichotomic noise characterized by a waiting time distribution in the two state that is a power law with power 1 < μ < 2. We apply the results to two well-known growth models; Malthus-Verhulst and Gompertz.

  9. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

    PubMed Central

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

    2014-01-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

  10. A new growth curve model for biological growth: some inferential studies on the growth of Cirrhinus mrigala.

    PubMed

    Bhowmick, Amiya Ranjan; Bhattacharya, Sabyasachi

    2014-08-01

    Growth of living organisms is a fundamental biological process. It depicts the physiological development of the species related to the environment. Mathematical development of growth curve models has a long history since its birth. We propose a mathematical model to describe the evolution of relative growth rate as a function of time based on a real life experiment on a major Indian Carp Cirrhinus mrigala. We establish that the proposed model is able to describe the fish growth dynamics more accurately for our experimental data than some existing models e.g. logistic, Gompertz, exponential. Approximate expressions of the points of inflection and the time of achieving the maximum relative growth rate are derived. We study, in detail, the existence of a nonlinear least squares estimator of the model parameters and their consistency properties. Test-statistics is developed to study the equality of points of inflection and equality of the amount of time necessary to achieve the maximum relative growth rate for a species at two different locations. Using the theory of variance stabilizing transformations, we propose a new test statistic to test the effect of the decay parameter for the proposed growth law. The testing procedure is found to be more sensitive in comparison with the test based on nonlinear least squares estimates. Our proposed model provides a general framework to model growth in other disciplines as well.

  11. Nonlinear Stochastic Markov Processes and Modeling Uncertainty in Populations

    DTIC Science & Technology

    2011-07-06

    growth rate g(x) = rx ( 1− x κ ) and the general tran- sition rates g(x, t) = (a0(t) − a1(t) ln x)x of which the standard Gompertz growth rates g(x) = r...probabilistic formulation (5.4) and the stochastic formulation (5.5), which nicely illustrates our earlier theoretical results. Example 5.3 ( Gompertz ...stochastic version of the generalized Gompertz model ẋ = (a0(t)− a1(t) lnx)x, which has been extensively used in biological and medical research to describe

  12. Evidence for the Gompertz curve in the income distribution of Brazil 1978-2005

    NASA Astrophysics Data System (ADS)

    Moura, N. J., Jr.; Ribeiro, M. B.

    2009-01-01

    This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)], where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution P(x) = βx-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.

  13. 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.

  14. Reaction-diffusion model for the growth of avascular tumor

    NASA Astrophysics Data System (ADS)

    Ferreira, S. C.; Martins, M. L.; Vilela, M. J.

    2002-02-01

    A nutrient-limited model for avascular cancer growth including cell proliferation, motility, and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determining factor in generating papillary tumor morphology.

  15. Modeling the growth of Enterococcus faecium in bologna sausage.

    PubMed Central

    Zanoni, B; Garzaroli, C; Anselmi, S; Rondinini, G

    1993-01-01

    A study to set up mathematical models which allow the prediction of Enterococcus faecium growth in bologna sausage (mortadella) was carried out. Growth curves were obtained at different temperatures (5, 6, 12, 15, 25, 32, 35, 37, 42, 46, 50, 52, and 55 degrees C). The Gompertz and logistic models, modified by Zwietering, were found to fit with the representation of experimental curves. The variations of the parameters A (i.e., the asymptotic value reached by the relative population during the stationary growth phase), mu m (i.e., the maximum specific growth rate during the exponential growth phase), and lambda (i.e., the lag time) with temperature were then modeled. The variation of A with temperature can be described by an empirical polynomial model, whereas the variation of mu m and lambda can be described by the Ratkowsky model modified by Zwietering and the Adair model, respectively. Data processing of these models has shown that the minimum growth temperature for E. faecium is 0.1 degrees C, the maximum growth temperature is 53.4 degrees C, and the optimal growth temperature is 42 to 45 degrees C. PMID:8250562

  16. 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.

  17. Least-squares fitting Gompertz curve

    NASA Astrophysics Data System (ADS)

    Jukic, Dragan; Kralik, Gordana; Scitovski, Rudolf

    2004-08-01

    In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,...,m, m≥3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.

  18. Evaluation of growth models for follicle development and ovulation in Lusitano mares.

    PubMed

    Mata, F

    2012-12-01

    Several growth models are commonly used in the biological sciences, to model the follicle growth occurring in the estrous cycle. The aim of this project was to find the model that best fit the follicular size growth data for Lusitano mares. Retrospective data collected from reproduction book records of n=84 mares and n=124 cycles was used to find the series to be fitted to the models. The exponential, Gompertz, logistic, von Bertalanffy, Richards and Weibull models were used, and the most parsimonious and best fit was achieved with the logistic model (r(2)=0.999). The logistic model fits the Lusitano mare's follicle size growth data very well and its parameters were also shown to have a credible biological interpretation.

  19. Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

    NASA Astrophysics Data System (ADS)

    McAneney, H.; O'Rourke, S. F. C.

    2007-02-01

    The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these 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 (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

  20. Strehler-Mildvan correlation is a degenerate manifold of Gompertz fit.

    PubMed

    Tarkhov, Andrei E; Menshikov, Leonid I; Fedichev, Peter O

    2017-03-07

    correlation may show up as a consequence of the fitting degeneracy, its appearance is not limited to homogeneous cohorts. In fact, the problem persists even beyond the simple Gompertz mortality law. We show that the same degeneracy occurs exactly in the same way, if a more advanced Gompertz-Makeham aging model is employed to improve the modeling. We explain how SM type of relation between the demographic parameters may still be observed even in extremely large cohorts with immense statistical power, such as in human census datasets, provided that systematic historical changes are weak in nature and lead to a gradual change in the mean lifespan.

  1. The Gompertz-Pareto income distribution

    NASA Astrophysics Data System (ADS)

    Chami Figueira, F.; Moura, N. J.; Ribeiro, M. B.

    2011-02-01

    This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country, and the Pareto power law, which describes its tiny richest part. Equations for the Lorenz curve, Gini coefficient and the percentage share of the Gompertzian part relative to the total income are all written in this distribution. We show that only three parameters, determined by linear data fitting, are required for its complete characterization. Consistency checks are carried out using income data of Brazil from 1981 to 2007 and they lead to the conclusion that the GPD is consistent and provides a coherent and simple analytical tool to describe personal income distribution data.

  2. 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

  3. Mathematical modelling of the growth of human fetus anatomical structures.

    PubMed

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

    2016-07-08

    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.

  4. 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.

  5. Growth Kinetics of Listeria monocytogenes in Broth and Beef Frankfurters– Determination of Lag Phase Duration and Exponential Growth Rate under Isothermal Conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The objective of this research was to develop a new kinetic model to describe the isothermal growth of microorganisms. The new model was tested with Listeria monocytogenes in broth and frankfurters, and compared with two commonly used models - Baranyi and modified Gompertz models. Bias factor (BF)...

  6. 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.

  7. 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.

  8. Evaluation of primary models to describe the growth of Pichia anomala and study of temperature, NaCl, and pH effects on its biological parameters by response surface methodology.

    PubMed

    Arroyo, F N; Durán Quintana, M C; Garrido Fernández, A

    2005-03-01

    Tolerance of Pichia anomala, a strain of yeast associated with olive fermentation, to salt, temperature, and pH was studied in yeast-malt-peptone-glucose medium using a nonfactorial central composite experimental design with three repetitions in the center to account for pure error. Modified Gompertz, logistic, Richards-Stannard, and Baranyi-Roberts models were used to determine maximum specific growth rate (micro(max)) and lag phase period (lambda) from the growth curves (primary models). All models produced a good fit (significant at P < 0.05), but the graphical and statistical analyses of the data indicated that the modified Gompertz and Richards-Stannard models were the most appropriate. The biological parameters obtained with the diverse models were fitted to a response surface secondary model. A significant decrease in micro(max) was observed as temperature decreased and salt increased. A significant increase in lambda was observed as temperature (linear and quadratic effects) and pH decreased and as salt content increased. Effects of interactions were complex and depended on models. Validation revealed acceptable errors and bias in micro(max) and lambda values obtained in independent experiments. Validation growth curves were best reproduced by using the values of micro(max) and lambda predicted by the response surface from the modified Gompertz and Richards-Stannard models. Results from this study can be applied to table olive fermentation or storage and for production of table olives as refrigerated commercial products without the use of preservatives or pasteurization.

  9. Makeham's addition to the Gompertz law re-evaluated.

    PubMed

    Hallén, Anund

    2009-08-01

    The Makeham parameter, a constant mortality rate independent of aging added to the Gompertz law of human mortality, is proposed to be a measure of the impact on mortality rate by extrinsic causes of mortality, with the effect of aging removed. A small intrinsic contribution to mortality, assumed to depend on the components involved in cellular function, is linked to the initial mortality rate of the Gompertz law. To avoid biased results and conclusions, the impact of extrinsic mortality should be eliminated from the Gompertz parameters.

  10. Accuracy of growth model parameters: effects of frequency and duration of data collection, and missing information.

    PubMed

    Aggrey, Samuel E

    2008-01-01

    This study was done to compare the accuracy of prediction of growth parameters using the Gompertz model when (1) data was collected infrequently, (2) data collection was truncated, and (3) data was missing. Initial growth rate and rate of decay were reduced by half when the model was fitted to data collected biweekly compared to data collected weekly. This reduction led to an increase in age of maximum growth and subsequently over-predicted the asymptotic body weight. When only part of the growth duration was used for prediction, both the initial growth rate and rate of decay were reduced. The degree of data truncation also affected sexual dimorphism of the parameters estimated. Using pre-asymptotic data for growth parameter prediction does not allow the intrinsic efficiency of growth to be determined accurately. However, using growth data with body weights missing at different phases of the growth curve does not seem to significantly affect the predicted growth parameters. Speculative or diagnostic conclusions on intrinsic growth should be done with data collected at short intervals to avoid potential inaccuracies in the prediction of initial growth rate, exponential decay rate, age of maximum growth and asymptotic weight.

  11. 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.

  12. Modelling urban growth patterns

    NASA Astrophysics Data System (ADS)

    Makse, Hernán A.; Havlin, Shlomo; Stanley, H. Eugene

    1995-10-01

    CITIES grow in a way that might be expected to resemble the growth of two-dimensional aggregates of particles, and this has led to recent attempts1á¤-3 to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion-limited aggregation4,5 (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies1. The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming á¤~development unitsᤙ (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the clusterᤙs branches. Here we show that an alternative model, in which development units are correlated rather than being added to the cluster at random, is better able to reproduce the observed morphology of cities and the area distribution of sub-clusters (á¤~towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model6á¤-8 in the presence of a density gradient9, is motivated by the fact that in urban areas development attracts further development. The model offers the possibility of predicting the global properties (such as scaling behaviour) of urban morphologies.

  13. Evolutionary theory of ageing and the problem of correlated Gompertz parameters.

    PubMed

    Burger, Oskar; Missov, Trifon I

    2016-11-07

    The Gompertz mortality model is often used to evaluate evolutionary theories of ageing, such as the Medawar-Williams' hypothesis that high extrinsic mortality leads to faster ageing. However, fits of the Gompertz mortality model to data often find the opposite result that mortality is negatively correlated with the rate of ageing. This negative correlation has been independently discovered in several taxa and is known in actuarial studies of ageing as the Strehler-Mildvan correlation. We examine the role of mortality selection in determining late-life variation in susceptibility to death, which has been suggested to be the cause of this negative correlation. We demonstrate that fixed-frailty models that account for heterogeneity in frailty do not remove the correlation and that the correlation is an inherent statistical property of the Gompertz distribution. Linking actuarial and biological rates of ageing will continue to be a pressing challenge, but the Strehler-Mildvan correlation itself should not be used to diagnose any biological, physiological, or evolutionary process. These findings resolve some key tensions between theory and data that affect evolutionary and biological studies of ageing and mortality. Tests of evolutionary theories of ageing should include direct measures of physiological performance or condition.

  14. Generalized exponential function and discrete growth models

    NASA Astrophysics Data System (ADS)

    Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino

    2009-07-01

    Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.

  15. A robust estimation of the exponent function in the Gompertz law

    NASA Astrophysics Data System (ADS)

    Ibarra-Junquera, V.; Monsivais, M. P.; Rosu, H. C.; López-Sandoval, R.

    2006-08-01

    The estimation of the solution of a system of two differential equations introduced by Norton et al. [Predicting the course of Gompertzian growth, Nature 264 (1976) 542-544] that is equivalent to the famous Gompertz growth law is performed by means of the recent adaptive scheme of Besançon and collaborators [High gain observer based state and parameter estimation in nonlinear systems, paper 204, the sixth IFAC Symposium, Stuttgart Symposium on Nonlinear Control Systems (NOLCOS), 2004, available at ]. Results of computer simulations illustrate the robustness of the approach.

  16. Flexible and fixed mathematical models describing growth patterns of chukar partridges

    NASA Astrophysics Data System (ADS)

    Aygün, Ali; Narinç, Doǧan

    2016-04-01

    In animal science, the nonlinear regression models for growth curve analysis ofgrowth patterns are separated into two groups called fixed and flexible according to their point of inflection. The aims of this study were to compare fixed and flexible growth functions and to determine the best fit model for the growth data of chukar partridges. With this aim, the growth data of partridges were modeled with widely used models, such as Gompertz, Logistic, Von Bertalanffy as well as the flexible functions, such as, Richards, Janoschek, Levakovich. So as to evaluate growth functions, the R2 (coefficient of determination), adjusted R2 (adjusted coefficient of determination), MSE (mean square error), AIC (Akaike's information criterion) and BIC (Bayesian information criterion) goodness of fit criteria were used. It has been determined that the best fit model from the point of chukar partridge growth data according to mentioned goodness of fit criteria is Janoschek function which has a flexible structure. The Janoschek model is not only important because it has a higher number of parameters with biological meaning than the other functions (the mature weight and initial weight parameters), but also because it was not previously used in the modeling of the chukar partridge growth.

  17. Mathematical models for growth in alligator (Alligator mississippiensis) embryos developing at different incubation temperatures.

    PubMed

    Bardsley, W G; Ackerman, R A; Bukhari, N A; Deeming, D C; Ferguson, M W

    1995-08-01

    A variety of model-based (growth models) and model-free (cubic splines, exponentials) equations were fitted using weighted-nonlinear least squares regression to embryonic growth data from Alligator mississippiensis eggs incubated at 30 and 33 degrees C. Goodness of fit was estimated using a chi 2 on the sum of squared, weighted residuals, and run and sign tests on the residuals. One of the growth models used (Preece & Baines, 1978) was found to be superior to the classical growth models (exponential, monomolecular, logistic, Gompertz, von Bertalanffy) and gave an adequate fit to all longitudinal measures taken from the embryonic body and embryonic mass. However, measurements taken from the head could not be fitted by growth models but were adequately fitted by weighted least squares cubic splines. Data for the stage of development were best fitted by a sum of 2 exponentials with a transition point. Comparison of the maximum growth rates and parameter values, indicated that the growth data at 30 degrees C could be scaled to 33 degrees C to multiplying the time by a scaling factor of 1.2. This is equivalent to a Q10 of about 1.86 or, after solving the Arrhenius equation, an E++ of 46.9 kJmol-1. This may be interpreted as indicating a common rate-limiting step in development at the 2 temperatures.

  18. 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), aw (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.

  19. Predictive modeling of Pseudomonas fluorescens growth under different temperature and pH values.

    PubMed

    Gonçalves, Letícia Dias Dos Anjos; Piccoli, Roberta Hilsdorf; Peres, Alexandre de Paula; Saúde, André Vital

    Meat is one of the most perishable foods owing to its nutrient availability, high water activity, and pH around 5.6. These properties are highly conducive for microbial growth. Fresh meat, when exposed to oxygen, is subjected to the action of aerobic psychrotrophic, proteolytic, and lipolytic spoilage microorganisms, such as Pseudomonas spp. The spoilage results in the appearance of slime and off-flavor in food. In order to predict the growth of Pseudomonas fluorescens in fresh meat at different pH values, stored under refrigeration, and temperature abuse, microbial mathematical modeling was applied. The primary Baranyi and Roberts and the modified Gompertz models were fitted to the experimental data to obtain the growth parameters. The Ratkowsky extended model was used to determine the effect of pH and temperature on the growth parameter μmax. The program DMFit 3.0 was used for model adjustment and fitting. The experimental data showed good fit for both the models tested, and the primary and secondary models based on the Baranyi and Roberts models showed better validation. Thus, these models can be applied to predict the growth of P. fluorescens under the conditions tested.

  20. Dynamic mathematical model to predict microbial growth and inactivation during food processing.

    PubMed Central

    Van Impe, J F; Nicolaï, B M; Martens, T; De Baerdemaeker, J; Vandewalle, J

    1992-01-01

    Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods. PMID:1444404

  1. Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice.

    PubMed

    Hartung, Niklas; Mollard, Séverine; Barbolosi, Dominique; Benabdallah, Assia; Chapuisat, Guillemette; Henry, Gerard; Giacometti, Sarah; Iliadis, Athanassios; Ciccolini, Joseph; Faivre, Christian; Hubert, Florence

    2014-11-15

    Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading

  2. 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.

  3. A heterogeneous population model for the analysis of bacterial growth kinetics.

    PubMed

    McKellar, R C

    1997-05-20

    A two-compartment, heterogeneous population model (HPM) was derived using the simulation software SB ModelMaker to describe the growth of Listeria monocytogenes in bacteriological media at 5-35 degrees C. The model assumed that, at time t = 0, the inoculum was distributed between two distinct compartments, Non-Growing and Growing, and that growth could be described by four parameters: initial total cell population (N0), final maximum cell population (Nmax), maximum specific growth rate (mu(max)), and initial cell population in the Growing compartment (G0). The model was fitted to the data by optimizing the four parameters, and lag phase duration (lambda) was calculated. The resulting values of mu(max) and lambda were similar to those determined using the modified Gompertz equation. A new parameter, w0, was defined which relates to the proportion of the initial cell population capable of growth, and is a measure of the initial physiological state of the cells. A modified model in which mu(max) was replaced with a temperature function, and w0 replaced G0, was used to predict the effect of temperature on the growth of L. monocytogenes. The results of this study raise questions concerning the current definition of the lag phase.

  4. Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process.

    PubMed

    Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Román-Román, Sergio; Torres-Ruiz, Francisco

    2015-01-07

    A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process. This paper proposes a methodology to estimate the time-dependent functions representing the effect of a therapy when one of the functions is known or can be previously estimated. This is the case of therapies that are jointly applied, when experimental data are available from either an untreated control group or from groups treated with single and combined therapies. Moreover, this procedure allows us to establish the nature (or, at least, the prevalent effect) of a single therapy in vivo. To accomplish this, we suggest a criterion based on the Kullback-Leibler divergence (or relative entropy). Some simulation studies are performed and an application to real data is presented.

  5. 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.

  6. How could the Gompertz-Makeham law evolve.

    PubMed

    Golubev, A

    2009-05-07

    In line with the origin of life from the chemical world, biological mortality kinetics is suggested to originate from chemical decomposition kinetics described by the Arrhenius equation k = A*exp(-E/RT). Another chemical legacy of living bodies is that, by using the appropriate properties of their constituent molecules, they incorporate all their potencies, including adverse ones. In early evolution, acquiring an ability to use new molecules to increase disintegration barrier E might be associated with new adverse interactions, yielding products that might accumulate in organisms and compromise their viability. Thus, the main variable of the Arrhenius equation changed from T in chemistry to E in biology; mortality turned to rise exponentially as E declined with increasing age; and survivorship patterns turned to feature slow initial and fast late descent making the bulk of each finite cohort to expire within a short final period of its lifespan. Numerical modelling shows that such acquisition of new functions associated with faster functional decline may increase the efficiency of investing resources into progeny, in line with the antagonistic pleiotropy theory of ageing. Any evolved time trajectories of functional changes were translated into changes in mortality through exponent according to the generalised Gompertz-Makeham law mu = C(t)+Lambda*exp[-E(t)], which is reduced to the conventional form when E(t) = E0-gammat and C is constant. The proposed model explains the origin of the linear mid-age functional decline followed by its deceleration at later ages and the positive correlation between the initial vitality and the rate of ageing.

  7. Justifying the Gompertz curve of mortality via the generalized Polya process of shocks.

    PubMed

    Cha, Ji Hwan; Finkelstein, Maxim

    2016-06-01

    A new probabilistic model of aging that can be applied to organisms is suggested and analyzed. Organisms are subject to shocks that follow the generalized Polya process (GPP), which has been recently introduced and characterized in the literature. Distinct from the nonhomogeneous Poisson process that has been widely used in applications, the important feature of this process is the dependence of its future behavior on the number of previous events (shocks). The corresponding survival and the mortality rate functions are derived and analyzed. The general approach is used for justification of the Gompertz law of human mortality.

  8. Lattice models of biological growth

    SciTech Connect

    Young, D.A.; Corey, E.M. )

    1990-06-15

    We show that very simple iterative rules for the growth of cells on a two-dimensional lattice can simulate biological-growth phenomena realistically. We discuss random cellular automata models for the growth of fern gametophytes, branching fungi, and leaves, and for shape transformations useful in the study of biological variation and evolution. Although there are interesting analogies between biological and physical growth processes, we stress the uniqueness of biological automata behavior. The computer growth algorithms that successfully mimic observed growth behavior may be helpful in determining the underlying biochemical mechanisms of growth regulation.

  9. Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis

    PubMed Central

    Hadjiandreou, Marios M.; Rizki, Gizem; Achilleos, Achilleas; Strati, Katerina; Mitsis, Georgios D.

    2015-01-01

    Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results. PMID:26649886

  10. Microbial growth curves: what the models tell us and what they cannot.

    PubMed

    Peleg, Micha; Corradini, Maria G

    2011-12-01

    Most of the models of microbial growth in food are Empirical algebraic, of which the Gompertz model is the most notable, Rate equations, mostly variants of the Verhulst's logistic model, or Population Dynamics models, which can be deterministic and continuous or stochastic and discrete. The models of the first two kinds only address net growth and hence cannot account for cell mortality that can occur at any phase of the growth. Almost invariably, several alternative models of all three types can describe the same set of experimental growth data. This lack of uniqueness is by itself a reason to question any mechanistic interpretation of growth parameters obtained by curve fitting alone. As argued, all the variants of the Verhulst's model, including the Baranyi-Roberts model, are empirical phenomenological models in a rate equation form. None provides any mechanistic insight or has inherent advantage over the others. In principle, models of all three kinds can predict non-isothermal growth patterns from isothermal data. Thus a modeler should choose the simplest and most convenient model for this purpose. There is no reason to assume that the dependence of the "maximum specific growth rate" on temperature, pH, water activity, or other factors follows the original or modified versions of the Arrhenius model, as the success of Ratkowsky's square root model testifies. Most sigmoid isothermal growth curves require three adjustable parameters for their mathematical description and growth curves showing a peak at least four. Although frequently observed, there is no theoretical reason that these growth parameters should always rise and fall in unison in response to changes in external conditions. Thus quantifying the effect of an environmental factor on microbial growth require that all the growth parameters are addressed, not just the "maximum specific growth rate." Different methods to determine the "lag time" often yield different values, demonstrating that it is a

  11. Modeling Exponential Population Growth

    ERIC Educational Resources Information Center

    McCormick, Bonnie

    2009-01-01

    The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social…

  12. 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.

  13. Modeling microbial growth and dynamics.

    PubMed

    Esser, Daniel S; Leveau, Johan H J; Meyer, Katrin M

    2015-11-01

    Modeling has become an important tool for widening our understanding of microbial growth in the context of applied microbiology and related to such processes as safe food production, wastewater treatment, bioremediation, or microbe-mediated mining. Various modeling techniques, such as primary, secondary and tertiary mathematical models, phenomenological models, mechanistic or kinetic models, reactive transport models, Bayesian network models, artificial neural networks, as well as agent-, individual-, and particle-based models have been applied to model microbial growth and activity in many applied fields. In this mini-review, we summarize the basic concepts of these models using examples and applications from food safety and wastewater treatment systems. We further review recent developments in other applied fields focusing on models that explicitly include spatial relationships. Using these examples, we point out the conceptual similarities across fields of application and encourage the combined use of different modeling techniques in hybrid models as well as their cross-disciplinary exchange. For instance, pattern-oriented modeling has its origin in ecology but may be employed to parameterize microbial growth models when experimental data are scarce. Models could also be used as virtual laboratories to optimize experimental design analogous to the virtual ecologist approach. Future microbial growth models will likely become more complex to benefit from the rich toolbox that is now available to microbial growth modelers.

  14. Modeling tin whisker growth.

    SciTech Connect

    Weinberger, Christopher Robert

    2013-08-01

    Tin, lead, and lead-tin solders are the most commonly used solders due to their low melting temperatures. However, due to the toxicity problems, lead must now be removed from solder materials. This has lead to the re-emergence of the issue of tin whisker growth. Tin whiskers are a microelectronic packaging issue because they can lead to shorts if they grow to sufficient length. However, the cause of tin whisker growth is still not well understood and there is lack of robust methods to determine when and if whiskering will be a problem. This report summarizes some of the leading theories on whisker growth and attempts to provide some ideas towards establishing the role microstructure plays in whisker growth.

  15. 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,…

  16. 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…

  17. Growth and Modeling of Staphylococcus aureus in Flour Products under Isothermal and Nonisothermal Conditions.

    PubMed

    Cao, Hui; Wang, Tingting; Yuan, Min; Yu, Jingsong; Xu, Fei

    2017-03-01

    This study was conducted to investigate the growth of Staphylococcus aureus in traditional Chinese flour products under isothermal (10, 15, 20, 25, 30, and 37°C) and nonisothermal (10 to 20, 20 to 30, and 25 to 37°C) conditions. Then, models for the growth of S. aureus in flour products as a function of storage temperature, pH, and water activity (aw) were developed, and the goodness of fit of models was evaluated using the determination coefficient (R(2)), root mean square error (RMSE), bias factor (Bf), and accuracy factor (Af). Based on the above information, S. aureus growth in steamed bread under nonisothermal conditions was predicted from experiments performed under isothermal conditions. It was shown that different combinations of temperature and aw in flour products have a strong influence on the growth of S. aureus . The modified Gompertz model was found to be more suitable for describing the growth data of S. aureus in flour products, with an R(2) of >0.99 and an RMSE of <0.37. The newly developed secondary models were validated, and for the specific growth rate and the lag time, the R(2) values were 0.96 and 0.97, Af was 1.12 and 1.06, and Bf was 1.13 and 1.05, respectively. The predicted nonisothermal growth curves of S. aureus were in agreement with the reported experimental ones, with RMSE <0.29, Af value 1.02 to 1.09, and Bf value 0.92 to 0.99. These results indicated that the predictive models provided useful information for the establishment of safety standards and a risk assessment for S. aureus in flour products.

  18. Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences

    NASA Astrophysics Data System (ADS)

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

    2006-05-01

    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.

  19. Psychological Models of Educational Growth.

    ERIC Educational Resources Information Center

    Nucci, Larry P.; Walberg, Herbert J.

    A discussion of models of intellectual development and their application to education identifies the two major groups of such models and examines recent attempts to combine them. The two types of theories are described as the psychometric models, which see intellectual growth as the incremental amassing and associating of discrete ideas, and the…

  20. Mesoscopic model for tumor growth.

    PubMed

    Izquierdo-Kulich, Elena; Nieto-Villar, José Manuel

    2007-10-01

    In this work, we propose a mesoscopic model for tumor growth to improve our understanding of the origin of the heterogeneity of tumor cells. In this sense, this stochastic formalism allows us to not only to reproduce but also explain the experimental results presented by Brú. A significant aspect found by the model is related to the predicted values for beta growth exponent, which capture a basic characteristic of the critical surface growth dynamics. According to the model, the value for growth exponent is between 0,25 and 0,5, which includes the value proposed by Kadar-Parisi-Zhang universality class (0,33) and the value proposed by Brú (0,375) related to the molecular beam epitaxy (MBE) universality class. This result suggests that the tumor dynamics are too complex to be associated to a particular universality class.

  1. 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

  2. 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.

  3. 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.

  4. Growth curve prediction from optical density data.

    PubMed

    Mytilinaios, I; Salih, M; Schofield, H K; Lambert, R J W

    2012-03-15

    A fundamental aspect of predictive microbiology is the shape of the microbial growth curve and many models are used to fit microbial count data, the modified Gompertz and Baranyi equation being two of the most widely used. Rapid, automated methods such as turbidimetry have been widely used to obtain growth parameters, but do not directly give the microbial growth curve. Optical density (OD) data can be used to obtain the specific growth rate and if used in conjunction with the known initial inocula, the maximum population data and knowledge of the microbial number at a predefined OD at a known time then all the information required for the reconstruction of a standard growth curve can be obtained. Using multiple initial inocula the times to detection (TTD) at a given standard OD were obtained from which the specific growth rate was calculated. The modified logistic, modified Gompertz, 3-phase linear, Baranyi and the classical logistic model (with or without lag) were fitted to the TTD data. In all cases the modified logistic and modified Gompertz failed to reproduce the observed linear plots of the log initial inocula against TTD using the known parameters (initial inoculum, MPD and growth rate). The 3 phase linear model (3PLM), Baranyi and classical logistic models fitted the observed data and were able to reproduce elements of the OD incubation-time curves. Using a calibration curve relating OD and microbial numbers, the Baranyi equation was able to reproduce OD data obtained for Listeria monocytogenes at 37 and 30°C as well as data on the effect of pH (range 7.05 to 3.46) at 30°C. The Baranyi model was found to be the most capable primary model of those examined (in the absence of lag it defaults to the classic logistic model). The results suggested that the modified logistic and the modified Gompertz models should not be used as Primary models for TTD data as they cannot reproduce the observed data.

  5. Fingering in Stochastic Growth Models

    PubMed Central

    Aristotelous, Andreas C.; Durrett, Richard

    2015-01-01

    Motivated by the widespread use of hybrid-discrete cellular automata in modeling cancer, two simple growth models are studied on the two dimensional lattice that incorporate a nutrient, assumed to be oxygen. In the first model the oxygen concentration u(x, t) is computed based on the geometry of the growing blob, while in the second one u(x, t) satisfies a reaction-diffusion equation. A threshold θ value exists such that cells give birth at rate β(u(x, t) − θ)+ and die at rate δ(θ − u(x, t)+. In the first model, a phase transition was found between growth as a solid blob and “fingering” at a threshold θc = 0.5, while in the second case fingering always occurs, i.e., θc = 0. PMID:26430353

  6. Growth characteristics and development of a predictive model for Bacillus cereus in fresh wet noodles with added ethanol and thiamine.

    PubMed

    Kim, Bo-Yeon; Lee, Ji-Young; Ha, Sang-Do

    2011-04-01

    Response surface methodology was used to determine growth characteristics and to develop a predictive model to describe specific growth rates of Bacillus cereus in wet noodles containing a combination of ethanol (0 to 2% [vol/wt]) and vitamin B(1) (0 to 2 g/liter). B. cereus F4810/72, which produces an emetic toxin, was used in this study. The noodles containing B. cereus were incubated at 10°C. The growth curves were fitted to the modified Gompertz equation using nonlinear regression, and the growth rate values from the curves were used to establish the predictive model using a response surface methodology quadratic polynomial equation as a function of concentrations of ethanol and vitamin B(1). The model was shown to fit the data very well (r(2) = 0.9505 to 0.9991) and could be used to accurately predict growth rates. The quadratic polynomial model was validated, and the predicted growth rate values were in good agreement with the experimental values. The polynomial model was found to be an appropriate secondary model for growth rate (GR) and lag time (LT) based on the correlation of determination (r(2) = 0.9899 for GR, 0.9782 for LT), bias factor (B(f) = 1.006 for GR, 0.992 for LT), and accuracy factor (A(f) = 1.024 for GR, 1.011 for LT). Thus, this model holds great promise for use in predicting the growth of B. cereus in fresh wet noodles using only the bacterial concentration, an important contribution to the manufacturing of safe products.

  7. 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

  8. Gompertz - A program for evaluation and comparison of survival curves.

    PubMed

    Klemera, P; Doubal, S

    2000-07-01

    Principles, properties and use of a program for evaluation of survival curves are described. Parameters of Gompertzian mortality curves are computed from survival data of two populations by help of nonlinear regression. The differences in parameters of both curves are evaluated statistically. This method evaluates effectively even survival data of very small populations. The results are presented in numeric, verbal and graphic forms. Finally, reading of the results is offered to distinguish changes corresponding to altered aging rate from changes caused by influences not affecting the basic mechanism of aging. Program GOMPERTZ in the form of Microsoft Excel workbook equipped with Visual Basic procedures is offered free through e-mail (klemera@faf.cuni.cz).

  9. Growth kinetics of Listeria monocytogenes in broth and beef frankfurters--determination of lag phase duration and exponential growth rate under isothermal conditions.

    PubMed

    Huang, L

    2008-06-01

    The objective of this study was to develop a new kinetic model to describe the isothermal growth of microorganisms. The new model was tested with Listeria monocytogenes in tryptic soy broth and frankfurters, and compared with 2 commonly used models-Baranyi and modified Gompertz models. Bias factor (BF), accuracy factor (AF), and root mean square errors (RMSE) were used to evaluate the 3 models. Either in broth or in frankfurter samples, there were no significant differences in BF (approximately 1.0) and AF (1.02 to 1.04) among the 3 models. In broth, the mean RMSE of the new model was very close to that of the Baranyi model, but significantly lower than that of the modified Gompertz model. However, in frankfurters, there were no significant differences in the mean RMSE values among the 3 models. These results suggest that these models are equally capable of describing isothermal bacterial growth curves. Almost identical to the Baranyi model in the exponential and stationary phases, the new model has a more identifiable lag phase and also suggests that the bacteria population would increase exponentially until the population approaches to within 1 to 2 logs from the stationary phase. In general, there is no significant difference in the means of the lag phase duration and specific growth rate between the new and Baranyi models, but both are significantly lower than those determined from the modified Gompertz models. The model developed in this study is directly derived from the isothermal growth characteristics and is more accurate in describing the kinetics of bacterial growth in foods.

  10. 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.

  11. 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…

  12. A new application of Gompertz function in photohemolysis: the effect of temperature on red blood cell hemolysis photosensitized by protoporphyrin IX.

    PubMed

    Al-Akhras, M

    2006-08-01

    Photosensitization by protoporphyrin IX (PpIX) is accelerated at different irradiation temperatures, different dark incubation temperatures (Tinc) and different irradiation times. The applicability of Gompertz function to the fractional photohemolysis ratio, a and the rate of fractional photohemolysis, b is found to be the most appropriate model to fit the experimental data with minimum parameters and minimum errors. The reduction in Gompertz parameters, the fractional ratio values of a, and increase in the fractional rate values b, for 20 microM PpIX irradiated with black light at low irradiation temperature 5 degrees C and higher Tinc 37 degrees C was noticed. The parameter a has higher values at lower irradiation time and lower irradiation temperatures which indicates a longer photohemolysis process and longer t 50. Values of the parameter b were found to be strongly temperature-dependent, and always increase with increasing irradiation time and Tinc with lower values at lower irradiation time and lower Tinc. There are no significant changes in the lysis of RBCs process at irradiation temperatures equal to or higher than 35 degrees C. Similarly, no significant change on t50 at higher irradiation time at Tinc 24 and 37 degrees C. In conclusion, Gompertz analysis technique adapts to study the photohemolysis process at different conditions as a best-fit model.

  13. 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

  14. Latent Growth Modeling for Logistic Response Functions

    ERIC Educational Resources Information Center

    Choi, Jaehwa; Harring, Jeffrey R.; Hancock, Gregory R.

    2009-01-01

    Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

  15. Modelling the growth of feather crystals

    SciTech Connect

    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.

  16. A Growth Model for Multilevel Ordinal Data

    ERIC Educational Resources Information Center

    Segawa, Eisuke

    2005-01-01

    Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

  17. 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)

  18. 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.

  19. Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

    NASA Astrophysics Data System (ADS)

    Cabella, Brenno Caetano Troca; Ribeiro, Fabiano; Martinez, Alexandre Souto

    2012-02-01

    We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.

  20. A MODEL OF GROWTH AND GROWTH CONTROL IN MATHEMATICAL TERMS

    PubMed Central

    Weiss, Paul; Kavanau, J. Lee

    1957-01-01

    A practicable model of the growth process, which gives better definition to the problem of growth and growth regulation and greater precision to related experimental work than do earlier models, is developed on the basis of the following assumptions: "Growth" is the net balance of mass produced and retained over mass destroyed and otherwise lost, implying continual metabolic degradation and replacement. Terminal size represents stationary equilibrium between incremental and decremental components. The mass of an organic system consists of two functionally different components,—generative and differentiated. Generative mass increases by the catalytic action of key compounds ("templates") characteristic of each cell type. Each cell also produces specific freely diffusible compounds antagonistic to these templates ("antitemplates"). Growth regulation occurs automatically by a negative "feedback" in which increasing numbers of antitemplates progressively block the corresponding templates. Differential equations expressing these interrelationships are formulated, integrated, and the solutions evaluated for the case of chick growth. These specific solutions lead to descriptions of the normal growth of a biological system which are in good agreement with known facts, and to predictions of the course of automatic growth regulations after experimental or pathological disturbances which reproduce adequately biological observations in this domain. PMID:13463267

  1. 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.

  2. Testing mechanistic models of growth in insects

    PubMed Central

    Maino, James L.; Kearney, Michael R.

    2015-01-01

    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. PMID:26609084

  3. A continuous growth model for plant tissue

    NASA Astrophysics Data System (ADS)

    Bozorg, Behruz; Krupinski, Pawel; Jönsson, Henrik

    2016-12-01

    Morphogenesis in plants and animals involves large irreversible deformations. In plants, the response of the cell wall material to internal and external forces is determined by its mechanical properties. An appropriate model for plant tissue growth must include key features such as anisotropic and heterogeneous elasticity and cell dependent evaluation of mechanical variables such as turgor pressure, stress and strain. In addition, a growth model needs to cope with cell divisions as a necessary part of the growth process. Here we develop such a growth model, which is capable of employing not only mechanical signals but also morphogen signals for regulating growth. The model is based on a continuous equation for updating the resting configuration of the tissue. Simultaneously, material properties can be updated at a different time scale. We test the stability of our model by measuring convergence of growth results for a tissue under the same mechanical and material conditions but with different spatial discretization. The model is able to maintain a strain field in the tissue during re-meshing, which is of particular importance for modeling cell division. We confirm the accuracy of our estimations in two and three-dimensional simulations, and show that residual stresses are less prominent if strain or stress is included as input signal to growth. The approach results in a model implementation that can be used to compare different growth hypotheses, while keeping residual stresses and other mechanical variables updated and available for feeding back to the growth and material properties.

  4. Assessment of models for anaerobic biodegradation of a model bioplastic: Poly(hydroxybutyrate-co-hydroxyvalerate).

    PubMed

    Ryan, Cecily A; Billington, Sarah L; Criddle, Craig S

    2017-03-01

    Kinetic models of anaerobic digestion (AD) are widely applied to soluble and particulate substrates, but have not been systematically evaluated for bioplastics. Here, five models are evaluated to determine their suitability for modeling of anaerobic biodegradation of the bioplastic poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV): (1) first-order kinetics with and without a lag phase, (2) two-step first-order, (3) Monod (4) Contois, and (5) Gompertz. Three models that couple biomass growth with substrate hydrolysis (Monod, Contois, and Gompertz) gave the best overall fits for the data (R(2)>0.98), with reasonable estimates of ultimate CH4 production. The particle size limits of these models were then evaluated. Below a particle size of 0.8mm, rates of hydrolysis and acetogenesis exceeded rates of methanogenesis with accumulation of intermediates leading to a temporary inhibition of CH4 production. Based on model fit and simplicity, the Gompertz model is recommended for applications in which particle size is greater than 0.8mm.

  5. A novel measurement method of microorganism growth by tunable diode laser-absorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Xiang, Jindong; Shao, Jie; Ying, Chaofu; Wang, Liming; Guo, Jie

    2015-05-01

    The objective of this work was to attain essential parameters by using a Gompertz model that employed a new approach of wavelength modulation spectroscopy (WMS) to describe the microorganism growth. The measurement method of WMS introduces noninvasive technique instead of complicated invasive microorganism operation analysis and quickly obtains the accurate real-time measurement results. By using the WMS measurement, the specific growth curve of microorganism growth clearly displayed every three minute, which has characteristics of high sensitivity, high spectral resolution, fast time response and overcomes the randomness and error operation of traditional analysis methods. The measurement value of BF and AF in the range of 1.008 to 1.043 and the lower MSE showed that Gompertz model can fit the data well and be capable of describing bacteria growth rate and lag time. The results of experiment data suggested that the specific growth rate of microorganism depends on the temperature. With the increase of temperature ranging from 25 °C to 42 °C , the lag time of bacteria growth has been shortened. And the suitable temperature of bacteria growth is about 37 °C . Judging from the growth rate of microorganisms, we can identify the microbial species, not only to improve the precision and efficiency, but also to provides a rapidly sensitive way for microbial detection. The lag time of microorganism growth also provides a great application prospect for shelf life of the food safety.

  6. Modeling tissue growth within nonwoven scaffolds pores.

    PubMed

    Edwards, Sharon L; Church, Jeffrey S; Alexander, David L J; Russell, Stephen J; Ingham, Eileen; Ramshaw, John A M; Werkmeister, Jerome A

    2011-02-01

    In this study we present a novel approach for predicting tissue growth within the pores of fibrous tissue engineering scaffolds. Thin nonwoven polyethylene terephthalate scaffolds were prepared to characterize tissue growth within scaffold pores, by mouse NR6 fibroblast cells. On the basis of measurements of tissue lengths at fiber crossovers and along fiber segments, mathematical models were determined during the proliferative phase of cell growth. Tissue growth at fiber crossovers decreased with increasing interfiber angle, with exponential relationships determined on day 6 and 10 of culture. Analysis of tissue growth along fiber segments determined two growth profiles, one with enhanced growth as a result of increased tissue lengths near the fiber crossover, achieved in the latter stage of culture. Derived mathematical models were used in the development of a software program to visualize predicted tissue growth within a pore. This study identifies key pore parameters that contribute toward tissue growth, and suggests models for predicting this growth, based on fibroblast cells. Such models may be used in aiding scaffold design, for optimum pore infiltration during the tissue engineering process.

  7. Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs.

    PubMed

    Kebreab, E; Schulin-Zeuthen, M; Lopez, S; Soler, J; Dias, R S; de Lange, C F M; France, J

    2007-10-01

    Success of pig production depends on maximizing return over feed costs and addressing potential nutrient pollution to the environment. Mathematical modeling has been used to describe many important aspects of inputs and outputs of pork production. This study was undertaken to compare 4 mathematical functions for the best fit in terms of describing specific data sets on pig growth and, in a separate experiment, to compare these 4 functions for describing of P utilization for growth. Two data sets with growth data were used to conduct growth analysis and another data set was used for P efficiency analysis. All data sets were constructed from independent trials that measured BW, age, and intake. Four growth functions representing diminishing returns (monomolecular), sigmoidal with a fixed point of inflection (Gompertz), and sigmoidal with a variable point of inflection (Richards and von Bertalanffy) were used. Meta-analysis of the data was conducted to identify the most appropriate functions for growth and P utilization. Based on Bayesian information criteria, the Richards equation described the BW vs. age data best. The additional parameter of the Richards equation was necessary because the data required a lower point of inflection (138 d) than the Gompertz, with a fixed point of inflexion at 1/e times the final BW (189 d), could accommodate. Lack of flexibility in the Gompertz equation was a limitation to accurate prediction. The monomolecular equation was best at determining efficiencies of P utilization for BW gain compared with the sigmoidal functions. The parameter estimate for the rate constant in all functions decreased as available P intake increased. Average efficiencies during different stages of growth were calculated and offer insight into targeting stages where high feed (nutrient) input is required and when adjustments are needed to accommodate the loss of efficiency and the reduction of potential pollution problems. It is recommended that the Richards

  8. Design issues for population growth models

    PubMed Central

    López Fidalgo, J.; Ortiz Rodríguez, I.M.

    2010-01-01

    We briefly review and discuss design issues for population growth and decline models. We then use a flexible growth and decline model as an illustrative example and apply optimal design theory to find optimal sampling times for estimating model parameters, specific parameters and interesting functions of the model parameters for the model with two real applications. Robustness properties of the optimal designs are investigated when nominal values or the model is mis-specified, and also under a different optimality criterion. To facilitate use of optimal design ideas in practice, we also introduce a website for generating a variety of optimal designs for popular models from different disciplines. PMID:21647244

  9. 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.

  10. A multivariate Bayesian model for embryonic growth.

    PubMed

    Willemsen, Sten P; Eilers, Paul H C; Steegers-Theunissen, Régine P M; Lesaffre, Emmanuel

    2015-04-15

    Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth.

  11. Evaluation of mathematical models to describe testicular growth in Blackbelly ram lambs.

    PubMed

    Jiménez-Severiano, H; Reynoso, M L; Román-Ponce, S I; Robledo, V M

    2010-10-15

    The primary objective was to compare various mathematical models to describe scrotal circumference (SC) and paired testis volume development in Blackbelly ram lambs. The study was conducted in the state of Querétaro, México (20° 43' N, 100° 15' W). Spring-born Blackbelly ram lambs (n = 41) were housed outdoors and fed alfalfa hay and concentrate. Body weight, SC, and testis length, diameter, and volume were recorded every 2 wk from 24 to 172 d of age (June 18 to November 3). The following mathematical functions were used to model SC-age and testis volume-age relationship: Von Bertalanffy, Brody, Gompertz, Logistic, and Richards. The suitability of the models was evaluated based on parameter values and standard errors, residual mean square, the coefficient of determination (R(2)), and the average prediction error (APE). All models, except for Brody's, had good fit to SC (R(2) > 0.98) and testis volume (R(2) > 0.95), and produced similar growth curves in the range of ages studied. The logistic model predicted SC at maturity quite well, 33.6 ± 0.6 cm as compared with 33.9 ± 0.5 cm observed in adult animals; all models had APE's smaller than ± 7% between 56 and 168 d of age. The Bertalanffy model predicted testis volume at maturity quite well, 513 ± 22 cm(3) as compared with 488 ± 20 cm(3) calculated for adult animals. The logistic model had a good fit to testis volume during the period of study, but underestimated the volume at maturity by 28%. All models, except for Brody's, had APE's smaller than ± 14% between 98 and 168 d of age. The logistic and Bertalanffy models predicted the inflection point for SC at 83 and 59 d of age, and testis volume at 116 and 109 d of age, respectively. In conclusion, all models, except for Brody's, had good fit to actual SC and testis volume data in the range of age evaluated, whereas the logistic and Bertalanffy's models made the best predictions for adult SC and testis volume, respectively.

  12. Image based modeling of tumor growth.

    PubMed

    Meghdadi, N; Soltani, M; Niroomand-Oscuii, H; Ghalichi, F

    2016-09-01

    Tumors are a main cause of morbidity and mortality worldwide. Despite the efforts of the clinical and research communities, little has been achieved in the past decades in terms of improving the treatment of aggressive tumors. Understanding the underlying mechanism of tumor growth and evaluating the effects of different therapies are valuable steps in predicting the survival time and improving the patients' quality of life. Several studies have been devoted to tumor growth modeling at different levels to improve the clinical outcome by predicting the results of specific treatments. Recent studies have proposed patient-specific models using clinical data usually obtained from clinical images and evaluating the effects of various therapies. The aim of this review is to highlight the imaging role in tumor growth modeling and provide a worthwhile reference for biomedical and mathematical researchers with respect to tumor modeling using the clinical data to develop personalized models of tumor growth and evaluating the effect of different therapies.

  13. A Practitioner's Guide to Growth Models

    ERIC Educational Resources Information Center

    Castellano, Katherine E.; Ho, Andrew D.

    2013-01-01

    This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…

  14. Cluster growth modeling of plateau erosion

    NASA Technical Reports Server (NTRS)

    Stark, Colin P.

    1994-01-01

    The pattern of erosion of a plateau along an escarpment may be modeled usng cluster growth techniques, recently popularized in models of drainage network evolution. If erosion on the scarp takes place in discrete events at rates subject to local substrate strength, the whole range of behavior is described by a combination of three cluster growth mechanisms: invasion percolation, Eden growth and diffusion-limited aggregation (DLA). These model the relative importance of preexisting substrate strength, background weathering, and seepage weathering and erosion respectively. The rate of seepage processes is determined by the efflux of groundwater at the plateau margin, which in turn is determined by the pressure field in the plateau aquifer. If this process acted alone, it would produce erosion patterns in the form of Laplacian fractals, with groundwater recharge from a distant source, or Poissionian fractals, with groundwater recharge uniform over the plateau. DLA is used to mimic the Laplacian or Poissonian potential field and the corresponding seepage growth process. The scaling structure of clusters grown by pure DLA, invasion percolation, or Eden growth is well known; this study presents a model which combines all three growth mechanisms for the first time. Mixed growth processes create clusters with different scaling properties and morphologies over distinct length scale ranges, and this is demonstrable in natural examples of plateau erosion.

  15. [The issue of feasibility of a general theory of aging I. Generalized Gompertz-Makeham Law].

    PubMed

    Golubev, A G

    2009-01-01

    Aging and longevity are interrelated so intimately that they should be treated with a unified theory. The longevity of every single cohort of living beings is determined by the rate of their dying-out. In most cases, mortality rates increase in accelerated fashions to reach values making the bulk of each finite cohort completely exhausted within a relatively narrow time interval shifted to the end of its resulting lifespan. Among simple functions with biologically interpretable parameters, the best fit to this pattern is demonstrated by the Gompertz-Makeham Law (GML): mu = C + lambda x e(gamma x t). A generalized form of GML mu = C(t) + lambda x e(-E(t)) is suggested and interpreted as a law of the dependency of mortality upon vitality rather than on age. It is reduced to the conventional GML when E depends linearly on t, that the age is an observable correlate of unobservable vitality. C(t) captures the inherently irresistible causes of death. The generalized GML can accommodate any mode of age-dependent functional decline, which should be placed into the exponent index to be translated into changes in mortality rate, and is compatible with any sort of cohort heterogeneity, which may be captured by substituting of GML parameters with relevant distributions or by combining of several generalized GML models. The generalized GML is suggested to result from the origin of life from the chemical world, which was associated with the transition of the role of the main variable in the Arrhenius equation k = A x exp[-Ea/(R x T)] for the dependency of chemical disintegration on temperature from T to Ea upon the transition from molecular to multimolecular prebiotic entities. Thus, the generalized GML is not a result of biological evolution but is a sort of chemical legacy of biology, which makes an important condition for life to evolve.

  16. Developmental Stages in Dynamic Plant Growth Models

    NASA Astrophysics Data System (ADS)

    Maclean, Heather; Dochain, Denis; Waters, Geoff; Stasiak, Michael; Dixon, Mike; Van Der Straeten, Dominique

    2011-09-01

    During the growth of red beet plants in a closed environment plant growth chamber, a change in metabolism was observed (decreasing photosynthetic quotient) which was not predicted by a previously developed simple dynamic model of photosynthesis and respiration reactions. The incorporation of developmental stages into the model allowed for the representation of this change in metabolism without adding unnecessary complexity. Developmental stages were implemented by dividing the model into two successive sub-models with independent yields. The transition between the phases was detected based on online measurements. Results showed an accurate prediction of carbon dioxide and oxygen fluxes.

  17. Contour Instabilities in Early Tumor Growth Models

    NASA Astrophysics Data System (ADS)

    Ben Amar, M.; Chatelain, C.; Ciarletta, P.

    2011-04-01

    Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.

  18. 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…

  19. Modeling plant growth and development.

    PubMed

    Prusinkiewicz, Przemyslaw

    2004-02-01

    Computational plant models or 'virtual plants' are increasingly seen as a useful tool for comprehending complex relationships between gene function, plant physiology, plant development, and the resulting plant form. The theory of L-systems, which was introduced by Lindemayer in 1968, has led to a well-established methodology for simulating the branching architecture of plants. Many current architectural models provide insights into the mechanisms of plant development by incorporating physiological processes, such as the transport and allocation of carbon. Other models aim at elucidating the geometry of plant organs, including flower petals and apical meristems, and are beginning to address the relationship between patterns of gene expression and the resulting plant form.

  20. Growth model of Escherichia coli O157:H7 at various storage temperatures on kale treated by thermosonication combined with slightly acidic electrolyzed water.

    PubMed

    Mansur, Ahmad Rois; Wang, Jun; Park, Myeong-Su; Oh, Deog-Hwan

    2014-01-01

    This study was conducted to investigate the disinfection efficacy of hurdle treatments (thermosonication plus slightly acidic electrolyzed water [SAcEW]) and to develop a model for describing the effect of storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) on the growth of Escherichia coli O157:H7 on fresh-cut kale treated with or without (control) thermosonication combined with SAcEW. The hurdle treatments of thermosonication plus SAcEW had strong bactericidal effects against E. coli O157:H7 on kale, with approximately 3.3-log reductions. A modified Gompertz model was used to describe growth parameters such as specific growth rate (SGR) and lag time (LT) as a function of storage temperature, with high coefficients of determination (R(2) > 0.98). SGR increased and LT declined with rising temperatures in all samples. A significant difference was found between the SGR values obtained from treated and untreated samples. Secondary models were established for SGR and LT to evaluate the effects of storage temperature on the growth kinetics of E. coli O157:H7 in treated and untreated kale. Statistical evaluation was carried out to validate the performance of the developed models, based on the additional experimental data not used for the model development. The validation step indicated that the overall predictions were inside the acceptable prediction zone and had lower standard errors, indicating that this new growth model can be used to assess the risk of E. coli O157:H7 contamination on kale.

  1. 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

    2017-02-08

    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.

  2. 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.

  3. An Investigation of Time Series Growth Curves as a Predictor of Diminishing Manufacturing Sources of Electronic Components.

    DTIC Science & Technology

    1981-09-01

    research- ers such a Pearl and Gompertz (27:111-115). However, in the search to develop forecasting methods, researchers noticed "a similarity between the...expressed in general terms as y = 1/(a + bcX), where a, b, and c are parameter values and x is time. Another frequently used growth curve is the Gompertz ...curve (27:113-115). The equation for the Gompertz is y a Le-l:e-kx where L is an upper limit to the growth of the y-variable, b and k are parameter

  4. Thermal models pertaining to continental growth

    NASA Technical Reports Server (NTRS)

    Morgan, Paul; Ashwal, Lew

    1988-01-01

    Thermal models are important to understanding continental growth as the genesis, stabilization, and possible recycling of continental crust are closely related to the tectonic processes of the earth which are driven primarily by heat. The thermal energy budget of the earth was slowly decreasing since core formation, and thus the energy driving the terrestrial tectonic engine was decreasing. This fundamental observation was used to develop a logic tree defining the options for continental growth throughout earth history.

  5. Modeling Stromatolite Growth Under Oscillatory Flows

    NASA Astrophysics Data System (ADS)

    Patel, H. J.; Gong, J.; Tice, M. M.

    2014-12-01

    Stromatolite growth models based on diffusion limited aggregation (DLA) has been fairly successful at producing features commonly recognized in stromatolitic structures in the rock record. These models generally require slow mixing of solutes at time scales comparable to the growth of organisms and largely ignore fluid erosions. Recent research on microbial mats suggests that fluid flow might have a dominant control on the formation, deformation and erosion of surface microbial structures, raising the possibility that different styles of fluid flow may influence the morphology of stromatolites. Many stromatolites formed in relatively high energy, shallow water environments under oscillatory currents driven by wind-induced waves. In order to investigate the potential role of oscillatory flows in shaping stromatolites, we are constructing a numerical model of stromatolite growth parameterized by flume experiments with cyanobacterial biofilms. The model explicitly incorporates reaction-diffusion processes, surface deformation and erosion, biomass growth, sedimentation and mineral precipitation. A Lattice-Boltzmann numerical scheme was applied to the reaction-diffusion equations in order to boost computational efficiency. A basic finite element method was employed to compute surface deformation and erosion. Growth of biomass, sedimentation and carbonate precipitation was based on a modified discrete cellular automata scheme. This model will be used to test an alternative hypothesis for the formation of stromatolites in higher energy, shallow and oscillatory flow environments.

  6. Plant Growth Modelling and Applications: The Increasing Importance of Plant Architecture in Growth Models

    PubMed Central

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

    2008-01-01

    Background 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. Scope 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

  7. Multiple mild heat-shocks decrease the Gompertz component of mortality in Caenorhabditis elegans.

    PubMed

    Wu, Deqing; Cypser, James R; Yashin, Anatoli I; Johnson, Thomas E

    2009-09-01

    Exposure to mild heat-stress (heat-shock) can significantly increase the life expectancy of the nematode Caenorhabditis elegans. A single heat-shock early in life extends longevity by 20% or more and affects life-long mortality by decreasing initial mortality only; the rate of increase in subsequent mortality (Gompertz component) is unchanged. Repeated mild heat-shocks throughout life have a larger effect on life span than does a single heat-shock early in life. Here, we ask how multiple heat-shocks affect the mortality trajectory in nematodes and find increases of life expectancy of close to 50% and of maximum longevity as well. We examined mortality using large numbers of animals and found that multiple heat-shocks not only decrease initial mortality, but also slow the Gompertz rate of increase in mortality. Thus, multiple heat-shocks have anti-aging hormetic effects and represent an effective approach for modulating aging.

  8. 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

  9. Assessment of MARMOT Grain Growth Model

    SciTech Connect

    Fromm, B.; Zhang, Y.; Schwen, D.; Brown, D.; Pokharel, R.

    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 UO2. To assure a rigorous comparison, the 2D and 3D initial experimental microstructures of UO2 samples were characterized using non-destructive Synchrotron x-ray. The same samples were then annealed at 2273K for grain 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.

  10. A Dynamic Systems Model of Cognitive and Language Growth.

    ERIC Educational Resources Information Center

    van Geert, Paul

    1991-01-01

    A conceptual framework of cognitive growth is sketched and a mathematical model of cognitive growth is presented with the conclusion that the most plausible model is a model of logistic growth with delayed feedback. The model is transformed into a dynamic systems model based on the logistic-growth equation. (SLD)

  11. 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

  12. 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.

  13. 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.

  14. Theoretical model of crystal growth shaping process

    NASA Astrophysics Data System (ADS)

    Tatarchenko, V. A.; Uspenski, V. S.; Tatarchenko, E. V.; Nabot, J. Ph.; Duffar, T.; Roux, B.

    1997-10-01

    A theoretical investigation of the crystal growth shaping process is carried out on the basis of the dynamic stability concept. The capillary dynamic stability of shaped crystal growth processes for various forms of the liquid menisci is analyzed using the mathematical model of the phenomena in the axisymmetric case. The catching boundary condition of the capillary boundary problem is considered and the limits of its application for shaped crystal growth modeling are discussed. The static stability of a liquid free surface is taken into account by means of the Jacobi equation analysis. The result is that a large number of menisci having drop-like shapes are statically unstable. A few new non-traditional liquid meniscus shapes (e.g., bubbles and related shapes) are proposed for the case of a catching boundary condition.

  15. 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.

  16. A tumor growth model with deformable ECM.

    PubMed

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

    2014-11-26

    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.

  17. A tumor growth model with deformable ECM

    PubMed Central

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

    2015-01-01

    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. PMID:25427284

  18. 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…

  19. Mathematical modelling of avascular-tumour growth.

    PubMed

    Ward, J P; King, J R

    1997-03-01

    A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes resulting from cell birth and death generate a velocity field within the spheroid. Numerical solutions of the model reveal that after a period of time the variables settle to a constant profile propagating at a fixed speed. The travelling-wave limit is formulated and analytical solutions are found for a particular case. Numerical results for more general parameters compare well with these analytical solutions. Asymptotic techniques are applied to the physically relevant case of a small death rate, revealing two phases of growth retardation from the initial exponential growth, the first of which is due to nutrient-diffusion limitations and the second to contraction during necrosis. In this limit, maximal and "linear' phase growth speeds can be evaluated in terms of the model parameters.

  20. Ruminant models of prenatal growth restriction.

    PubMed

    Anthony, R V; Scheaffer, A N; Wright, C D; Regnault, T R H

    2003-01-01

    Intrauterine growth restriction (IUGR) is a significant health issue that not only affects infant mortality and morbidity, but may also predispose individuals to coronary heart disease, diabetes, hypertension and stroke as adults. The majority of IUGR pregnancies in humans are characterized by asymmetric fetal growth, resulting from inadequate nutrient transfer to the fetus. Furthermore, most of these pregnancies involve functional placental insufficiency, and may also show altered umbilical velocimetry. As the severity of IUGR increases, the fetus becomes increasingly hypoxic, hypoglycaemic and acidotic. In addition, placental transfer or utilization of some amino acids is known to be altered in IUGR pregnancies. Although a great deal has been learned from clinical studies of human IUGR, appropriate animal models are required to define completely the mechanisms involved in the development of IUGR. The pregnant sheep is a long-standing model for placental-fetal interactions, and fetal growth restriction can be induced in pregnant sheep by maternal nutrient restriction, maternal nutrient excess, administration of glucocorticoid, utero-placental embolization, carunclectomy and maternal hyperthermia. Although all of these sheep models are capable of inducing fetal growth restriction, the degree of restriction is variable. This review compares these sheep models of IUGR with the characteristics of human IUGR.

  1. Unrestricted Mixture Models for Class Identification in Growth Mixture Modeling

    ERIC Educational Resources Information Center

    Liu, Min; Hancock, Gregory R.

    2014-01-01

    Growth mixture modeling has gained much attention in applied and methodological social science research recently, but the selection of the number of latent classes for such models remains a challenging issue, especially when the assumption of proper model specification is violated. The current simulation study compared the performance of a linear…

  2. Interaction Effects in Growth Modeling: A Full Model.

    ERIC Educational Resources Information Center

    Wen, Zhonglin; Marsh, Herbert W.; Hau, Kit-Tai

    2002-01-01

    Points out two concerns with recent research by F. Li and others (2000) and T. Duncan and others (1999) that extended the structural equation model of latent interactions developed by K. Joreskog and F. Yang (1996) to latent growth modeling. Used mathematical derivation and a comparison of alternative models fitted to simulated data to develop a…

  3. Combined effects of chlorine and thiamine dilauryl sulfate on reduction of Listeria monocytogenes in chicken breast and development of predictive growth models.

    PubMed

    Oh, Se-Ra; Park, Shin Young; Ha, Sang-Do

    2014-06-01

    The inhibitory effect of chlorine (50, 100, and 200 mL/kg) and thiamine dilauryl sulfate (TDS: 100, 500, and 1,000 mg/kg) on Listeria monocytogenes in chicken breast was investigated. Also, predictive growth models as a function of chlorine and TDS concentration, and storage temperature (4, 10, and 15°C) were developed using a polynomial model. Listeria monocytogenes counts were significantly (P < 0.05) different in samples treated with sterile distilled water and combinations of chlorine and TDS. The maximum reduction effect was 0.5 log cfu/g by combined treatment of 200 mL/kg chlorine and 1,000 mg/kg TDS. The largest synergistic effect was 0.38 log cfu/g by combined treatment of 100 mL/kg chlorine and 1,000 mg/kg TDS. The primary models that were developed to obtain the specific growth rates (SGR) and lag time (LT) had good fitness (R(2) > 0.91) determined by the reparameterized Gompertz equation. The secondary polynomial models were calculated by nonlinear regression analysis. In the validation of the developed models, the bias factor (Bf) and accuracy factor (Af) for SGR were 0.54 and 1.84, respectively, whereas those for LT were 0.97 and 1.04, respectively. In quality analysis, chlorine and TDS did not change the color or texture of chicken breast meat during storage at 4°C for 7 d. Thus, our findings indicate that a combined treatment of 100 mL/kg chlorine and 1,000 mg/kg TDS appears to an effective method into reduce L. monocytogenes in broiler carcasses with no negative effects on color and textural quality. The predictive models were in good agreement with the validation and may be used to predict L. monocytogenes growth in chicken breast.

  4. 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.

  5. Some novel growth functions and their application with reference to growth in ostrich.

    PubMed

    Faridi, A; López, S; Ammar, H; Salwa, K S; Golian, A; Thornley, J H M; France, J

    2015-06-01

    Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative β-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (Wf). The results from the first comparison showed that the functions generally gave acceptable values of R2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AICc). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into Wf gave the best fit, resulting in smaller AIC and AIC values compared with those in the other 2 approaches. On the basis of AICc, best fit was achieved with CBP, followed by gMM, Lomolino, and

  6. A simple model for black hole growth

    NASA Astrophysics Data System (ADS)

    Schawinski, Kevin; Weigel, Anna K. K.; Caplar, Neven; Wong, Ivy

    2017-01-01

    We present a simple phenomenological model for black hole growth in the z~0 universe. We show that nuclear activity can be described by two separate, mass-independent Eddington Ratio Distribution Functions (ERDFs) operating in blue and red galaxies, respectively. Our forward-modeling approach constrains these two ERDFs by comparing to the observed X-ray and radio luminosity functions. Alternative ERDFs with mass-dependence, such as those expected from AGN-driven mass-quenching of galaxies, are ruled out. We discuss the implications of this model and outline potential applications

  7. 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

  8. 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.

  9. Discrete growth models on deterministic fractal substrate

    NASA Astrophysics Data System (ADS)

    Tang, Gang; Xun, Zhipeng; Wen, Rongji; Han, Kui; Xia, Hui; Hao, Dapeng; Zhou, Wei; Yang, Xiquan; Chen, Yuling

    2010-11-01

    The growth of the modified Family model and the Etching model on the Sierpinski carpet is studied by means of numerical simulations. The evolving interface of the aggregates is described by the well-established Family-Vicsek dynamic scaling approach. The results of the modified Family model prove the universality of the fractional Langevin equation introduced by Lee and Kim [S.B. Lee, J.M. Kim, Phys. Rev. E 80 (2009) 021101]. The Etching model also shows good scaling behavior. We conjecture that the systematic deviations of the data found in the ballistic deposition [C.M. Horowitz, F. Romá, E.V. Albano, Phys. Rev. E 78 (2008) 061118] may be due to the finite-size effects of the Ballistic Deposition model.

  10. Modeling Interaction Effects in Latent Growth Curve Models.

    ERIC Educational Resources Information Center

    Li, Fuzhong; Duncan, Terry E.; Acock, Alan

    2000-01-01

    Presents an extension of the method of estimating interaction effects among latent variables to latent growth curve models developed by K. Joreskog and F. Yang (1996). Illustrates the procedure and discusses results in terms of practical and statistical problems associated with interaction analyses in latent curve models and structural equation…

  11. Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach.

    PubMed

    Bhowmick, Amiya Ranjan; Chattopadhyay, Gaurangadeb; Bhattacharya, Sabyasachi

    2014-01-01

    Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.

  12. 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.

  13. 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.

  14. 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

  15. Stochastic roots of growth phenomena

    NASA Astrophysics Data System (ADS)

    De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.

    2014-05-01

    We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.

  16. Alternative growth functions for predicting body, carcass, and breast weight in ducks: Lomolino equation and extreme value function.

    PubMed

    Faridi, A; Murawska, D; Golian, A; Mottaghitalab, M; Gitoee, A; Lopez, S; France, J

    2014-04-01

    In this study, 2 alternative growth functions, the Lomolino and the extreme value function (EVF), are introduced and their ability to predict body, carcass, and breast weight in ducks evaluated. A comparative study was carried out of these equations with standard growth functions: Gompertz, exponential, Richards, and generalized Michaelis-Menten. Goodness of fit of the functions was evaluated using R(2), mean square error, Akaike information criterion, and Bayesian information criterion, whereas bias factor, accuracy factor, Durbin-Watson statistic, and number of runs of sign were the criteria used for analysis of residuals. Results showed that predictive performance of all functions was acceptable, though the Richards and exponential equations failed to converge in a few cases for both male and female ducks. Based on goodness-of-fit statistics, the Richards, Gompertz, and EVF were the best equations whereas the worst fits to the data were obtained with the exponential. Analysis of residuals indicated that, for the different traits investigated, the least biased and the most accurate equations were the Gompertz, EVF, Richards, and generalized Michaelis-Menten, whereas the exponential was the most biased and least accurate. Based on the Durbin-Watson statistic, all models generally behaved well and only the exponential showed evidence of autocorrelation for all 3 traits investigated. Results showed that with all functions, estimated final weights of males were higher than females for the body, carcass, and breast weight profiles. The alternative functions introduced here have desirable advantages including flexibility and a low number of parameters. However, because this is probably the first study to apply these functions to predict growth patterns in poultry or other animals, further analysis of these new models is suggested.

  17. A physiological model of softwood cambial growth.

    PubMed

    Hölttä, Teemu; Mäkinen, Harri; Nöjd, Pekka; Mäkelä, Annikki; Nikinmaa, Eero

    2010-10-01

    Cambial growth was modelled as a function of detailed levelled physiological processes for cell enlargement and water and sugar transport to the cambium. Cambial growth was described at the cell level where local sugar concentration and turgor pressure induce irreversible cell expansion and cell wall synthesis. It was demonstrated how transpiration and photosynthesis rates, metabolic and physiological processes and structural features of a tree mediate their effects directly on the local water and sugar status and influence cambial growth. Large trees were predicted to be less sensitive to changes in the transient water and sugar status, compared with smaller ones, as they have more water and sugar storage and were, therefore, less coupled to short-term changes in the environment. Modelling the cambial dynamics at the individual cell level turned out to be a complex task as the radial short-distance transport of water and sugars and control signals determining cell division and cessation of cell enlargement and cell wall synthesis had to be described simultaneously.

  18. SOA multiday growth: Model artifact or reality?

    NASA Astrophysics Data System (ADS)

    Lee-Taylor, J. M.; Madronich, S.; Aumont, B.; Hodzic, A.; Camredon, M.; Valorso, R.

    2013-12-01

    Simulations of SOA gas-particle partitioning with the explicit gas-phase chemical mechanism generator GECKO-A show significant SOA mass growth continuing for several days, even as the initial air parcel is diluted into the regional atmosphere. This result is a robust feature of our model and occurs with both anthropogenic and biogenic precursors. The growth originates from continuing oxidation of gas-phase precursors which persist in equilibrium with the particle phase. This result implies that sources of aerosol precursors could influence the chemical and radiative characteristics of the atmosphere over a wider region than previously imagined, and that SOA measurements near precursor sources may routinely underestimate this influence. It highlights the need to better understand the sink terms in the SOA budget.

  19. Network growth models and genetic regulatory networks

    NASA Astrophysics Data System (ADS)

    Foster, D. V.; Kauffman, S. A.; Socolar, J. E. S.

    2006-03-01

    We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with the innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as the parameters are varied, including the broadening of the in-degree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.

  20. Network growth models and genetic regulatory networks

    NASA Astrophysics Data System (ADS)

    Socolar, Joshua; Foster, David; Kauffman, Stuart

    2006-03-01

    We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.

  1. 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…

  2. Estimating Reliability with Discrete Growth Models.

    DTIC Science & Technology

    1988-03-01

    Chandler, Jr. Captain, United States Army B.S., United States .Military Academy, 1978 Submitted in partial fulfillment of the requirements for the...WITH ftE:wr DISCRETE GROWTH MODELS j 5,8 by James D. Chandler, Jr. March 1988 Thesis Advisor: W. M. Woods Approved for public release; distribution is...8217\\.~ 3 tDir rhuton \\ oIb t’~0 Reputt F) A.pproved tor public reka’ie: distribuiieii is ’ilitilnfed. r-’n~~)’:’~~ ~rr \\~.~er ~5 Mornltrin; or

  3. A non-autonomous stochastic predator-prey model.

    PubMed

    Buonocore, Aniello; Caputo, Luigia; Pirozzi, Enrica; Nobile, Amelia G

    2014-04-01

    The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities. The asymptotic behavior of the predator-prey stochastic model is also analyzed.

  4. Quantitative Modeling of Growth and Dispersal in Population Models.

    DTIC Science & Technology

    1986-01-01

    partial differential equations. Applications to dispersal and nonlinear growth/predation models arc dnsity- depresented . Computational iresults using...depend only on size x. The ideas we present here can be readily modified to treat theoretically and computationally the more general case where g and m

  5. Comparison of Models for Estimating Individual Growth Curves.

    ERIC Educational Resources Information Center

    Burchinal, Margaret R.

    Growth curve models are a useful tool for developmentalists because they can estimate an attribute's developmental function by providing a mathematical description of growth on an attribute over time. However, selection of a growth curve model appropriate for estimating individual developmental functions is problematic. The ideal model is the one…

  6. Enhancement and modeling of microparticle-added Rhizopus oryzae lactic acid production.

    PubMed

    Coban, Hasan Bugra; Demirci, Ali

    2016-02-01

    Lactic acid has a wide industrial application area and can be produced by fungal strains. However, excessive bulk growth form of fungi during the fermentations is a major problem, which limits the fermentation performance. Microparticles are excellent tools to prevent bulk fungal growth and provide homogenized fermentation broth to increase uniformity and the prediction performance of the models. Therefore, in this study, addition of aluminum oxide and talcum microparticles into fermentations was evaluated to enhance the production of lactic acid by Rhizopus oryzae. The results showed that the bulk fungal growth was prevented and the lactic acid concentration increased from 6.02 to 13.88 and 24.01 g/L, when 15 g/L of aluminum oxide or 10 g/L of talcum was used, respectively, in the shake-flask fermentations. Additionally, substrate concentration, pH, and agitation were optimized in the bioreactors using response surface methodology, and optimum values were determined as 126 g/L of glucose, 6.22 pH, and 387 rpm, respectively. Under these conditions, lactic acid production further increased to 75.1 ± 1.5 g/L with 10 g/L of talcum addition. Also, lactic acid production and glucose consumption in the batch fermentation were successfully modeled with modified Gompertz model and modified logistic model. RMSE and MAE values for lactic acid production were calculated as 2.279 and 1.498 for the modified Gompertz model; 3.6 and 4.056 for the modified logistic model. Additionally, modified logistic model predicted glucose consumption with -2.088 MAE and 2.868 RMSE, whereas these values were calculated as 2.035 and 3.946 for the modified Gompertz model.

  7. A competition model for wormhole growth

    NASA Astrophysics Data System (ADS)

    Cabeza Diaz de Cerio, Yoar; Carrera, Jesus; Hidalgo, Juan J.

    2016-04-01

    Flow preferential pathways generated by dissolution are commonly known as wormholes. Wormhole generation and evolution are topics of interest not only for karst aquifer studies but also for fields as CO2 storage and oil industry among others. The objective of this work is to show that given an initial perturbation, the development of the dissolution pattern can be considered deterministic. This means that the evolution of the effective hydraulic conductivity can be predicted. To this end we use a wormhole growth model in which wormholes compete for the available water. In the competition model the wormholes grow proportionally to the flow rate through them. The wormhole flow rate is a function of the wormholes lengths and distances between them. We derive empirical expressions for the flow rates from steady state flow synthetic models with different geometries. Finally, we perform series of simulations using this competition model, applying random initial perturbations and different number of wormholes for each set of simulations and we study the evolution of the dissolution pattern. We find that the resulting wormhole patterns are in good agreement with others generated with much more complex models.

  8. Regime Switching in the Latent Growth Curve Mixture Model

    ERIC Educational Resources Information Center

    Dolan, Conor V.; Schmittmann, Verena D.; Lubke, Gitta H.; Neale, Michael C.

    2005-01-01

    A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing…

  9. Continuum models for epitaxial growth with elasticity

    NASA Astrophysics Data System (ADS)

    Xiang, Yang

    In heteroepitaxial growth, the mismatch between the lattice constants in the film and the substrate causes misfit strain in the film, making a flat surface unstable to small perturbations. This morphological instability is called Asaro-Tiller-Grinfeld (ATG) instability, which can drive the film to self-organize into nanostructures such as quantum wires or quantum dots. At low temperature, the surface consists of steps and facets, when the misfit strain causes step bunching, traditional continuum models for ATG instability does not apply directly. In the first part of this thesis, we derive a PDE model for step bunching by taking the continuum limit of the discrete models proposed by Tersoff et al and Duport et al. We study the linear instability of a uniform step train with small perturbations and compare our results with those of discrete models and continuum models for traditional ATG instability. We numerically study the nonlinear evolution of this instability and compare our results with those of discrete models. We also study the equilibrium shapes of step bunches and explain their coalescence. In the second part of this thesis, we derive a nonlinear approximate PDE for the ATG instability. In the ATG instability, the misfit strain is coupled with surface morphology and an elasticity problem must be solved numerically. Linear approximation is made in some cases such as when computing the equilibrium island shapes. Using the exact solution for a cycloid surface obtained by Chiu and Gao, we find that our nonlinear approximation has a wider range of applicability than linear approximation. Numerical simulation using our nonlinear PDE model predicts formation of a cusp-like surface morphology from initially small perturbations of flat surfaces, which agrees well with the result obtained by Spencer and Meiron by solving the elasticity problem numerically.

  10. Modeling and Optimization for Epitaxial Growth: Transport and Growth Studies

    DTIC Science & Technology

    1999-01-01

    Epsilon-1 microprocessor and controlled automatically in–situ. For example, PID controllers and MFCs regulate the thermocouple temperatures and inlet flow...thermocouples are regulated by PID controllers . The set-up of the reactor apparatus may partially explain the smaller variation in actual growth rates. Recall

  11. 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,…

  12. Modeling LX-17 Detonation Growth and Decay Using the Ignition and Growth Model

    NASA Astrophysics Data System (ADS)

    Tarver, Craig M.; Chidester, Steven K.

    2009-12-01

    The previously established Ignition and Growth reactive flow model for the detonating triaminotrinitrobenzene (TATB) based plastic bonded explosive LX-17 is applied to recent experimental detonation propagation/failure experiments using unconfined, Lucite confined, and copper confined cylinders. The model also simulates two corner turning experiments in which steel and Lucite act as boundary materials. Finally, the model is used to calculate a one-inch diameter "Hockey Puck" test in which the booster explosive is HMX-based rather than TATB-based. Since the LX-17 Ignition and Growth model parameters are normalized to a great deal of one-, two- and three-dimensional detonation propagation data, they accurately predict all of this new experimental detonation velocity and arrival time data.

  13. Incorporating Student Mobility in Achievement Growth Modeling: A Cross-Classified Multiple Membership Growth Curve Model

    ERIC Educational Resources Information Center

    Grady, Matthew W.; Beretvas, S. Natasha

    2010-01-01

    Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve…

  14. Growth model for arbuscular mycorrhizal fungi.

    PubMed

    Schnepf, A; Roose, T; Schweiger, P

    2008-07-06

    In order to quantify the contribution of arbuscular mycorrhizal (AM) fungi to plant phosphorus nutrition, the development and extent of the external fungal mycelium and its nutrient uptake capacity are of particular importance. We develop and analyse a model of the growth of AM fungi associated with plant roots, suitable for describing mechanistically the effects of the fungi on solute uptake by plants. The model describes the development and distribution of the fungal mycelium in soil in terms of the creation and death of hyphae, tip-tip and tip-hypha anastomosis, and the nature of the root-fungus interface. It is calibrated and corroborated using published experimental data for hyphal length densities at different distances away from root surfaces. A good agreement between measured and simulated values was found for three fungal species with different morphologies: Scutellospora calospora (Nicol. & Gerd.) Walker & Sanders; Glomus sp.; and Acaulospora laevis Gerdemann & Trappe associated with Trifolium subterraneum L. The model and findings are expected to contribute to the quantification of the role of AM fungi in plant mineral nutrition and the interpretation of different foraging strategies among fungal species.

  15. Disseminated thrombosis-induced growth plate necrosis in rat: a unique model for growth plate arrest.

    PubMed

    Nyska, Meir; Shabat, Shay; Long, Philip H; Howard, Charles; Ezov, Nathan; Levin-Harrus, Tal; Mittelman, Moshe; Redlich, Meir; Yedgar, Saul; Nyska, Abraham

    2005-01-01

    Exposure of rats to 2-butoxyethanol (BE) produces early hemolytic anemia and disseminated thrombosis. This leads to infarctions in multiple organs, including bones and cartilage. BE, administered for different durations of exposure in two separate experiments, produced metaphyseal vascular thrombosis, growth plate infarction, and partial or complete physeal growth arrest. This reproducible model may serve as a useful tool in the study of some conditions that manifest growth plate damage. The suitability of this model for investigating the pathogenesis of growth plate necrosis and as a model for potential therapy for various human growth plate disorders are discussed.

  16. Modelling the unsteady growth state population balance for a nonlinear growth model in an MSMPR crystallizer

    SciTech Connect

    Carver, C.; Chipman, N.A.; Carleson, T.E.

    1994-03-01

    The precipitation of zirconium and other metal species as hydroxides (hydrous oxides) from simulated nuclear waste process solutions has been investigated as a potential method to reduce radioactive waste volumes. The reaction of ammonium hexaflourozirconate was used to simulate these waste streams. Studies were conducted to investigate the unsteady state response of crystallization in mixed suspension, mixed product removal (MSMPR) crystallizer. Size distributions below 40 {mu}m from laboratory batch and MSMPR data indicate size-dependent growth may be occurring because they may fit the Abegg, Stevens and Larson (ASL) model. However, these distributions also may fit a transient growth model based on the Method of Lines numerical solution to the unsteady state population balance equation. The development of the Method of Lines solution as well as experimental agreement with both models were studied.

  17. 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

  18. Reactive burn models and ignition & growth concept

    SciTech Connect

    Menikoff, Ralph S; Shaw, Milton S

    2010-01-01

    Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition and Growth concept, introduced by Lee and Tarver in 1980, as the basis for reactive burn models. A homogeneized burn rate needs to account for three mesoscale physical effects (i) the density of burnt hot spots, which depends on the lead shock strength; (ii) the growth of the burn fronts triggered by hot spots, which depends on the local deflagration speed; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent hot spots. These effects can be combined and the burn model defined by specifying the reaction progress variable {lambda}(t) as a function of a dimensionless reaction length {tau}{sub hs}(t)/{ell}{sub hs}, rather than by xpecifying an explicit burn rate. The length scale {ell}{sub hs} is the average distance between hot spots, which is proportional to [N{sub hs}(P{sub s})]{sup -1/3}, where N{sub hs} is the number density of hot spots activated by the lead shock. The reaction length {tau}{sub hs}(t) = {line_integral}{sub 0}{sup t} D(P(t'))dt' is the distance the burn front propagates from a single hot spot, where D is the deflagration speed and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. They have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments.

  19. Growth rate modeling for selective tungsten LPCVD

    NASA Astrophysics Data System (ADS)

    Wolf, H.; Streiter, R.; Schulz, S. E.; Gessner, T.

    1995-10-01

    Selective chemical vapor deposition of tungsten plugs on sputtered tungsten was performed in a single-wafer cold-wall reactor using silane (SiH 4) and tungsten hexafluoride (WF 6). Extensive SEM measurements of film thickness were carried out to study the dependence of growth rates on various process conditions, wafer loading, and via dimensions. The results have been interpreted by numerical calculations based on a simulation model which is also presented. Both continuum fluid dynamics and the ballistic line-of-sight approach are used for transport modeling. The reaction rate is described by an empirical rate expression using coefficients fitted from experimental data. In the range 0.2 < p( SiH 4) /p( WF 6) < 0.75 , the reaction order was determined as 1.55 and -0.55 with respect to SiH 4 and WF 6, respectively. For higher partial pressure ratios the second-order rate dependence on p(SiH 4) and the minus first-order dependence on p(WF 6) were confirmed.

  20. Bayesian MCMC inference for the Gompertz distribution based on progressive first-failure censoring data

    NASA Astrophysics Data System (ADS)

    Soliman, Ahmed A.; Al Sobhi, Mashail M.

    2015-02-01

    This article deals with the problem of estimating parameters of the Gompertz distribution (GD) based on progressive first-failure censored data using Bayesian and non-Bayesian approaches. The two-sample prediction problem is considered to derive Bayesian prediction bounds for both future order statistics and future record values based on progressive first failure censored informative samples from GD. The sampling schemes such as, first-failure censoring, progressive type II censoring, type II censoring and complete sample can be obtained as special cases of the progressive first-failure censored scheme. Markov chain Monte Carlo (MCMC) method with Gibbs sampling procedure is used to compute the Bayes estimates and also to construct the corresponding credible intervals of the parameters. A simulation study has been conducted in order to compare the proposed Bayes estimators with the maximum likelihood estimators MLE. Finally, some numerical computations with real data set are presented for illustrating all the proposed inferential procedures.

  1. 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.

  2. 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

  3. [Postnatal growth patterns in eight species of herons and egrets (Ciconiiformes: Ardeidae)].

    PubMed

    Avila, Dennis Denis

    2011-06-01

    Avian postnatal growth has received considerable attention and its ecological implications have been deeply analyzed. In this current paper, I describe the patterns of culmen and tarsus growth, as well as of weight gain patterns in eight species of herons and egrets (Aves: Ardeidae) found in the Birama Swamp in Eastern Cuba. Between 1998 and 2006,714 nestlings of the following species were measured every two days: Butorides virescens, Bubulcus ibis, Egretta thula, E. tricolor, E. caerulea, E. rufescens, Ardea alba and Nycticorax nycticorax. Logistic and Gompertz equations were adjusted to data using non-lineal regression models with adult values as the asymptote. For each species, the following were determined and recorded: growth rate, age at inflexion, instantaneous growth rates at each age interval, and time taken to reach 90% of adult size. Reported hatchling sizes were similar in other localities, with a variation coefficient ranging between 10-19%. At hatch, each species exhibited differing sizes relative to adult values. In all cases, Gompertz equations were best fitted to explain more variance and lesser residuals. Rates of weight change and tarsus growth were alometrically related to the log of adult weight. Two main growth processes were identified: a physical extension in dimensions of each measurement reflecting inter-specific morphometric differences, and a lineal increase of the growth period from Green Heron to Great Egret. The Black-crowned Night Heron, Cattle Egret and Reddish Egret exhibited some unique measurement characteristics in comparison to the remaining members of the family. All results support the hypothesis that hypermorphosis, as the main evolutionary process in the microevolution of Ardeidae, is caused by a delayed final moment of growth.

  4. 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,…

  5. 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,…

  6. Suitability Analysis of Continuous-Use Reliability Growth Projection Models

    DTIC Science & Technology

    2015-03-26

    so a strict exponential distribu- tion was used to stay within their assumptions. In reality, however, reliability growth models often must be used...Suitability Analysis of Continuous-Use Reliability Growth Projection Models THESIS MARCH 2015 Benjamin R. Mayo, Captain, USAF AFIT-ENS-MS-15-M-120... GROWTH PROJECTION MODELS THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force

  7. 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

  8. Predictive growth model of LID: light intensification model

    NASA Astrophysics Data System (ADS)

    Tan, ChingSeong; Patel, D.; Wang, X.; Schlitz, D.; Dehkordi, P. S.; Menoni, C. S.; Chong, E. K. P.

    2013-11-01

    General precursors and growth model of Laser Induced Damage (LID) have been the focus of research in fused silica material, such as polishing residues, fractures, and contaminations. Assuming the absorption due to trapped material and mechanical strength is the same across the surfaces, various studies have shown that the LID could be minimized by reducing the light field intensification of the layers upon the laser strikes. By revisiting the definition of non-ionising radiation damage, this paper presents the modelling work and simulation of light intensification of laser induced damage condition. Our contribution is to predict the LID growth that take into various factors, specifically on the light intensification problem. The light intensification problem is a function of the inter-layer or intra-layer micro-optical properties, such as transmittance and absorption coefficient of the material at micro- or sub-micro-meter range. The proposed model will first estimate the light propagation that convoluted with the multiply scattering light and subsequently the field intensification within the nodule dimension. This will allow us to evaluate the geometrical factor of the nodule effect over the intensification. The result show that the light intensification is higher whenever the backscattering and multiple scattering components are higher due to its interference with the incoming wave within its coherency.

  9. An autocatalytic kinetic model for describing microbial growth during fermentation.

    PubMed

    Ibarz, Albert; Augusto, Pedro E D

    2015-01-01

    The mathematical modelling of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stability and safety. This work develops and proposes a new semi-empirical mathematical model, based on an autocatalytic kinetic, to describe the microbial growth through its biomass concentration. The proposed model was successfully validated using 15 microbial growth patterns, covering the three most important types of microorganisms in food and biotechnological processing (bacteria, yeasts and moulds). Its main advantages and limitations are discussed, as well as the interpretation of its parameters. It is shown that the new model can be used to describe the behaviour of microbial growth.

  10. 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

  11. 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.

  12. Spiral Growth in Plants: Models and Simulations

    ERIC Educational Resources Information Center

    Allen, Bradford D.

    2004-01-01

    The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

  13. 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…

  14. Trans-theta logistics: a new family of population growth sigmoid functions.

    PubMed

    Kozusko, F; Bourdeau, M

    2011-12-01

    Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.

  15. 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.

  16. Growth and development of chicks of two species of partridge: the grey partridge (Perdix perdix) and the chukar (Alectoris chukar).

    PubMed

    Pis, Tomasz

    2012-01-01

    1. In two partridge species, the grey partridge (Perdix perdix) and chukar (Alectoris chukar), from hatching up to 120 d, the growth rate and development of body mass, wing, tarsus, and bill length were measured and fitted by Gompertz equations. 2. As a typical precocial species, partridges hatched with relatively well developed legs and bills, and wing growth followed a gradual development of thermoregulation. 3. Gompertz growth constants for body mass growth were 0·039 and 0·038 for grey partridges and chukars, respectively. 4. The allometric relationship between tarsus length and body mass followed a geometric similarity (1/3 power) in both grey partridges and chukars.

  17. The model muddle: in search of tumor growth laws.

    PubMed

    Gerlee, Philip

    2013-04-15

    In this article, we will trace the historical development of tumor growth laws, which in a quantitative fashion describe the increase in tumor mass/volume over time. These models are usually formulated in terms of differential equations that relate the growth rate of the tumor to its current state and range from the simple one-parameter exponential growth model to more advanced models that contain a large number of parameters. Understanding the assumptions and consequences of such models is important, as they often underpin more complex models of tumor growth. The conclusion of this brief survey is that although much improvement has occurred over the last century, more effort and new models are required if we are to understand the intricacies of tumor growth.

  18. 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.

  19. 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.

  20. Centrality Fingerprints for Power Grid Network Growth Models

    NASA Astrophysics Data System (ADS)

    Gurfinkel, Aleks Jacob; Silva, Daniel A.; Rikvold, Per Arne

    In our previous work, we have shown that many of the properties of the Florida power grid are reproduced by deterministic network growth models based on the minimization of energy dissipation Ediss. As there is no a priori best Ediss minimizing growth model, we here present a tool, called the "centrality fingerprint," for probing the behavior of different growth models. The centrality fingerprints are comparisons of the current flow into/out of the network with the values of various centrality measures calculated at every step of the growth process. Finally, we discuss applications to the Maryland power grid.

  1. A Mathematical Model Coupling Tumor Growth and Angiogenesis

    PubMed Central

    Gomez, Hector

    2016-01-01

    We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments. PMID:26891163

  2. 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.

  3. 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.

  4. 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.

  5. Stochastic growth logistic model with aftereffect for batch fermentation process

    SciTech Connect

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

    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.

  6. 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.

  7. 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…

  8. 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.

  9. Microalgae bulk growth model with application to industrial scale systems.

    PubMed

    Quinn, Jason; de Winter, Lenneke; Bradley, Thomas

    2011-04-01

    The scalability of microalgae growth systems is a primary research topic in anticipation of the commercialization of microalgae-based biofuels. To date, there is little published data on the productivity of microalgae in growth systems that are scalable to commercially viable footprints. To inform the development of more detailed assessments of industrial-scale microalgae biofuel processes, this paper presents the construction and validation of a model of microalgae biomass and lipid accumulation in an outdoor, industrial-scale photobioreactor. The model incorporates a time-resolved simulation of microalgae growth and lipid accumulation based on solar irradiation, species specific characteristics, and photobioreactor geometry. The model is validated with 9 weeks of growth data from an industrially-scaled outdoor photobioreactor. Discussion focuses on the sensitivity of the model input parameters, a comparison of predicted microalgae productivity to the literature, and an analysis of the implications of this more detailed growth model on microalgae biofuels lifecycle assessment studies.

  10. Application of a statistical bootstrapping technique to calculate growth rate variance for modelling psychrotrophic pathogen growth.

    PubMed

    Schaffner, D W

    1994-12-01

    The inherent variability or 'variance' of growth rate measurements is critical to the development of accurate predictive models in food microbiology. A large number of measurements are typically needed to estimate variance. To make these measurements requires a significant investment of time and effort. If a single growth rate determination is based on a series of independent measurements, then a statistical bootstrapping technique can be used to simulate multiple growth rate measurements from a single set of experiments. Growth rate variances were calculated for three large datasets (Listeria monocytogenes, Listeria innocua, and Yersinia enterocolitica) from our laboratory using this technique. This analysis revealed that the population of growth rate measurements at any given condition are not normally distributed, but instead follow a distribution that is between normal and Poisson. The relationship between growth rate and temperature was modeled by response surface models using generalized linear regression. It was found that the assumed distribution (i.e. normal, Poisson, gamma or inverse normal) of the growth rates influenced the prediction of each of the models used. This research demonstrates the importance of variance and assumptions about the statistical distribution of growth rates on the results of predictive microbiological models.

  11. A modeling study of GaN growth by MOVPE

    SciTech Connect

    Safvi, S.A.; Kuech, T.F.; Redwing, J.M.; Tischler, M.A.

    1996-11-01

    A model for the growth of gallium nitride in a vertical metalorganic vapor phase epitaxy reactor is presented. For a mixture of non-dilute gases, the flow temperature and concentration profiles are predicted. The results show that the growth of GaN epilayers is through an intermediate adduct of TMG and ammonia. Growth rates are predicted based on simple reaction mechanisms and compared with those obtained experimentally. Loss of adduct species due to polymerization leads to lowering in growth rate. An attempt to quantify loss of reacting species is made based on experimentally observed growth rates.

  12. Gompertzian growth and decay: a powerful descriptive tool for neuroscience.

    PubMed

    Easton, Dexter M

    2005-10-15

    First-order kinetics is based on simple exponential decay, usually expressed in base e (Naperian) notation. "Nonexponential" processes, for example, S-shaped functions, are frequently modeled as sums of that elemental construct, and the number of rate constants increases with the number of such terms. A powerful descriptive alternative to sums of simple exponentials is the Gompertz function. In Gompertz kinetics, the rate coefficient of an exponential process is assumed to change exponentially with the independent variable. Nonexponential processes are easily modeled, more efficiently and more accurately than is possible with standard kinetics. Application of Gompertz kinetics to neuroscience research topics ranging from cognitive to molecular is presented to illustrate the power of the model: distribution of nerve fiber diameters, conditioning-testing responses of excitable nerve, psychophysical estimates of taste intensity magnitude, time course of synaptic current, and behavior of membrane conductance during voltage clamp of squid axon.

  13. When growth models are not universal: evidence from marine invertebrates.

    PubMed

    Hirst, Andrew G; Forster, Jack

    2013-10-07

    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.

  14. 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

  15. Genetic parameter estimates of growth curve and reproduction traits in Japanese quail.

    PubMed

    Narinc, Dogan; Karaman, Emre; Aksoy, Tulin; Firat, Mehmet Ziya

    2014-01-01

    The goal of selection studies in broilers is to obtain genetically superior chicks in terms of major economic traits, which are mainly growth rate, meat yield, and feed conversion ratio. Multiple selection schedules for growth and reproduction are used in selection programs within commercial broiler dam lines. Modern genetic improvement methods have not been applied in experimental quail lines. The current research was conducted to estimate heritabilities and genetic correlations for growth and reproduction traits in a Japanese quail flock. The Gompertz equation was used to determine growth curve parameters. The Gibbs sampling under a multi-trait animal model was applied to estimate the heritabilities and genetic correlations for these traits. A total of 948 quail were used with complete pedigree information to estimate the genetic parameters. Heritability estimates of BW, absolute and relative growth rates at 5 wk of age (AGR and RGR), β0 and β2 parameters, and age at point of inflection (IPT) of Gompertz growth curve, total egg number (EN) from the day of first lay to 24 wk of age were moderate to high, with values ranging from 0.25 to 0.40. A low heritability (0.07) for fertility (FR) and a strong genetic correlation (0.83) between FR and EN were estimated in our study. Body weight exhibited negative genetic correlation with EN, FR, RGR, and IPT. This genetic antagonism among the mentioned traits may be overcome using modern poultry breeding methods such as selection using multi-trait best linear unbiased prediction and crossbreeding.

  16. "Growth Models" Gaining in Accountability Debate

    ERIC Educational Resources Information Center

    Hoff, David J.

    2007-01-01

    In the debate over the future of the No Child Left Behind Act, policymakers, educators, and researchers seem to agree on one thing: The federal law's accountability system should be rewritten so it rewards or sanctions schools on the basis of students' academic growth. The U.S. Department of Education recently reaffirmed the Bush administration's…

  17. Charter School Innovations: A Teacher Growth Model

    ERIC Educational Resources Information Center

    Radoslovich, Julie; Roberts, Shelley; Plaza, Andres

    2014-01-01

    Committed to being a charter school with a professional learning community that empowers teachers, New Mexico's South Valley Academy (SVA) staff transformed its state evaluation process into a practitioner action research process (Anderson, Herr, & Nihlen, 2007). While teachers self-diagnose growth needs and play active roles in improving…

  18. Modeling growth curves to track growing obesity

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Our purpose was to examine the relationship between total physical activity (PA) and PA at various intensity levels with insulin resistance at increasing waist circumference and skinfold thickness levels. Being able to describe growth appropriately and succinctly is important in many nutrition and p...

  19. Direct Observation of Aggregative Nanoparticle Growth: Kinetic Modeling of the Size Distribution and Growth Rate

    SciTech Connect

    Woehl, Taylor J.; Park, Chiwoo; Evans, James E.; Arslan, Ilke; Ristenpart, William D.; Browning, Nigel D.

    2014-01-08

    Direct observations of solution-phase nanoparticle growth using in situ liquid transmission electron microscopy (TEM) have demonstrated the importance of “non-classical” growth mechanisms, such as aggregation and coalescence, on the growth and final morphology of nanocrystals at the atomic and single nanoparticle scales. To date, groups have quantitatively interpreted the mean growth rate of nanoparticles in terms of the Lifshitz-Slyozov-Wagner (LSW) model for Ostwald ripening, but less attention has been paid to modeling the corresponding particle size distribution. Here we use in situ fluid stage scanning TEM to demonstrate that silver nanoparticles grow by a length-scale dependent mechanism, where individual nanoparticles grow by monomer attachment but ensemble-scale growth is dominated by aggregation. Although our observed mean nanoparticle growth rate is consistent with the LSW model, we show that the corresponding particle size distribution is broader and more symmetric than predicted by LSW. Following direct observations of aggregation, we interpret the ensemble-scale growth using Smoluchowski kinetics and demonstrate that the Smoluchowski model quantitatively captures the mean growth rate and particle size distribution.

  20. Initial Status in Growth Curve Modeling for Randomized Trials

    PubMed Central

    Chou, Chih-Ping; Chi, Felicia; Weisner, Constance; Pentz, MaryAnn; Hser, Yih-Ing

    2010-01-01

    The growth curve modeling (GCM) technique has been widely adopted in longitudinal studies to investigate progression over time. The simplest growth profile involves two growth factors, initial status (intercept) and growth trajectory (slope). Conventionally, all repeated measures of outcome are included as components of the growth profile, and the first measure is used to reflect the initial status. Selection of the initial status, however, can greatly influence study findings, especially for randomized trials. In this article, we propose an alternative GCM approach involving only post-intervention measures in the growth profile and treating the first wave after intervention as the initial status. We discuss and empirically illustrate how choices of initial status may influence study conclusions in addressing research questions in randomized trials using two longitudinal studies. Data from two randomized trials are used to illustrate that the alternative GCM approach proposed in this article offers better model fitting and more meaningful results. PMID:21572585

  1. 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.

  2. 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.

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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 ...

  4. Modelling the Growth of Swine Flu

    ERIC Educational Resources Information Center

    Thomson, Ian

    2010-01-01

    The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

  5. A Nonlinear Viscous Model for Sn-Whisker Growth

    NASA Astrophysics Data System (ADS)

    Yang, Fuqian

    2016-12-01

    Based on the mechanism of the grain boundary fluid flow, a nonlinear viscous model for the growth of Sn-whiskers is proposed. This model consists of two units, one with a stress exponent of one and one with a stress exponent of n -1. By letting one of the constants be zero in the model, the constitutive relationship reduces to a linear flow relation or a power-law relation, representing the flow behavior of various metals. Closed-form solutions for the growth behavior of a whisker are derived, which can be used to predict the whisker growth and the stress evolution.

  6. Dissipative-particle-dynamics model of biofilm growth

    SciTech Connect

    Xu, Zhijie; Meakin, Paul; Tartakovsky, Alexandre M.; Scheibe, Timothy D.

    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.

  7. Plant Growth Models Using Artificial Neural Networks

    NASA Technical Reports Server (NTRS)

    Bubenheim, David

    1997-01-01

    In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.

  8. Crop growth dynamics modeling using time-series satellite imagery

    NASA Astrophysics Data System (ADS)

    Zhao, Yu

    2014-11-01

    In modern agriculture, remote sensing technology plays an essential role in monitoring crop growth and crop yield prediction. To monitor crop growth and predict crop yield, accurate and timely crop growth information is significant, in particularly for large scale farming. As the high cost and low data availability of high-resolution satellite images such as RapidEye, we focus on the time-series low resolution satellite imagery. In this research, NDVI curve, which was retrieved from satellite images of MODIS 8-days 250m surface reflectance, was applied to monitor soybean's yield. Conventional model and vegetation index for yield prediction has problems on describing the growth basic processes affecting yield component formation. In our research, a novel method is developed to well model the Crop Growth Dynamics (CGD) and generate CGD index to describe the soybean's yield component formation. We analyze the standard growth stage of soybean and to model the growth process, we have two key calculate process. The first is normalization of the NDVI-curve coordinate and division of the crop growth based on the standard development stages using EAT (Effective accumulated temperature).The second is modeling the biological growth on each development stage through analyzing the factors of yield component formation. The evaluation was performed through the soybean yield prediction using the CGD Index in the growth stage when the whole dataset for modeling is available and we got precision of 88.5% which is about 10% higher than the conventional method. The validation results showed that prediction accuracy using our CGD modeling is satisfied and can be applied in practice of large scale soybean yield monitoring.

  9. 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…

  10. Knowledge Growth: Applied Models of General and Individual Knowledge Evolution

    ERIC Educational Resources Information Center

    Silkina, Galina Iu.; Bakanova, Svetlana A.

    2016-01-01

    The article considers the mathematical models of the growth and accumulation of scientific and applied knowledge since it is seen as the main potential and key competence of modern companies. The problem is examined on two levels--the growth and evolution of objective knowledge and knowledge evolution of a particular individual. Both processes are…

  11. Crop Growth Modeling in the Wind Erosion Prediction System

    Technology Transfer Automated Retrieval System (TEKTRAN)

    On land used for the production of food and fiber, the amount of growing crop and crop residue remaining on the field during no growth periods often determine whether the field is susceptible to the erosion of the soil by wind. The crop growth sub-model component of the Wind Erosion Prediction Syste...

  12. The Aponeurotic Tension Model of Craniofacial Growth in Man

    PubMed Central

    Standerwick, Richard G; Roberts, W. Eugene

    2009-01-01

    Craniofacial growth is a scientific crossroad for the fundamental mechanisms of musculoskeletal physiology. Better understanding of growth and development will provide new insights into repair, regeneration and adaptation to applied loads. Traditional craniofacial growth concepts are insufficient to explain the dynamics of airway/vocal tract development, cranial rotation, basicranial flexion and the role of the cranial base in expression of facial proportions. A testable hypothesis is needed to explore the physiological pressure propelling midface growth and the role of neural factors in expression of musculoskeletal adaptation after the cessation of anterior cranial base growth. A novel model for craniofacial growth is proposed for: 1. brain growth and craniofacial adaptation up to the age of 20; 2. explaining growth force vectors; 3. defining the role of muscle plasticity as a conduit for craniofacial growth forces; and 4. describing the effect of cranial rotation in the expression of facial form. Growth of the viscerocranium is believed to be influenced by the superficial musculoaponeurotic systems (SMAS) of the head through residual tension in the occipitofrontalis muscle as a result of cephalad brain growth and cranial rotation. The coordinated effects of the regional SMAS develop a craniofacial musculoaponeurotic system (CFMAS), which is believed to affect maxillary and mandibular development. PMID:19572022

  13. The aponeurotic tension model of craniofacial growth in man.

    PubMed

    Standerwick, Richard G; Roberts, W Eugene

    2009-05-22

    Craniofacial growth is a scientific crossroad for the fundamental mechanisms of musculoskeletal physiology. Better understanding of growth and development will provide new insights into repair, regeneration and adaptation to applied loads. Traditional craniofacial growth concepts are insufficient to explain the dynamics of airway/vocal tract development, cranial rotation, basicranial flexion and the role of the cranial base in expression of facial proportions. A testable hypothesis is needed to explore the physiological pressure propelling midface growth and the role of neural factors in expression of musculoskeletal adaptation after the cessation of anterior cranial base growth. A novel model for craniofacial growth is proposed for: 1. brain growth and craniofacial adaptation up to the age of 20; 2. explaining growth force vectors; 3. defining the role of muscle plasticity as a conduit for craniofacial growth forces; and 4. describing the effect of cranial rotation in the expression of facial form.Growth of the viscerocranium is believed to be influenced by the superficial musculoaponeurotic systems (SMAS) of the head through residual tension in the occipitofrontalis muscle as a result of cephalad brain growth and cranial rotation. The coordinated effects of the regional SMAS develop a craniofacial musculoaponeurotic system (CFMAS), which is believed to affect maxillary and mandibular development.

  14. 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.

  15. Computational Morphodynamics: A modeling framework to understand plant growth

    PubMed Central

    Chickarmane, Vijay; Roeder, Adrienne H.K.; Tarr, Paul T.; Cunha, Alexandre; Tobin, Cory; Meyerowitz, Elliot M.

    2014-01-01

    Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions providing further insight into the processes in question, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental issues: (1.) models should span and integrate single cell behavior with tissue development and (2.) the necessity to understand the feedback between mechanics of growth and chemical or molecular signaling. We review different approaches to model plant growth and discuss a variety of model types that can be implemented, with the aim of demonstrating how this methodology can be used, to explore the morphodynamics of plant development. PMID:20192756

  16. 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.

  17. 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

  18. A Gompertzian model with random effects to cervical cancer growth

    SciTech Connect

    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.

  19. Gompertzian stochastic model with delay effect to cervical cancer growth

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

    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.

  20. A Gompertzian model with random effects to cervical cancer growth

    NASA Astrophysics Data System (ADS)

    Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

    2015-05-01

    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.

  1. Gompertzian stochastic model with delay effect to cervical cancer growth

    SciTech Connect

    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.

  2. 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.

  3. Modeling the response of peach fruit growth to water stress.

    PubMed

    Génard, M; Huguet, J G

    1996-04-01

    We applied a semi-mechanistic model of fresh matter accumulation to peach fruit during the stage of rapid mesocarp development. The model, which is based on simple hypotheses of fluid flows into and out of the fruit, assumes that solution flow into the fruit increases with fruit weight and transpiration per unit weight, and decreases with the maximum daily shrinkage of the trunk, which was used as an indicator of water stress. Fruit transpiration was assumed to increase with fruit size and with radiation. Fruit respiration was considered to be related to fruit growth and to temperature. The model simulates variability in growth among fruits according to climatic conditions, degree of water stress and weight of the fruit at the beginning of the simulation. We used data obtained from well-watered and water-stressed trees grown in containers to estimate model parameters and to test the model. There was close agreement between the simulated and measured values. A sensitivity analysis showed that initial fruit weight partly determined the variation in growth among fruits. The analysis also indicated that there was an optimal irradiance for fruit growth and that the effect of high global radiation on growth varied according to the stage of fruit development. Water stress, which was the most important factor influencing fruit growth, rapidly depressed growth, particularly when applied late in the season.

  4. 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.

  5. A Model for the Growth of Self-Concept

    ERIC Educational Resources Information Center

    Guest, Gerald R.; Thomson, Eric W.

    1972-01-01

    Teachers must play a more consciously active role in fostering healthy self esteem in children. To make such action more likely to occur successfully, a model is presented to conceptualize the dynamics of growth in positive self concept. (Author)

  6. The phase-field model in tumor growth

    NASA Astrophysics Data System (ADS)

    Travasso, Rui D. M.; Castro, Mario; Oliveira, Joana C. R. E.

    2011-01-01

    Tumor growth is becoming a central problem in biophysics both from its social and medical interest and, more fundamentally, because it is a remarkable example of an emergent complex system. Focusing on the description of the spatial and dynamical features of tumor growth, in this paper we review recent tumor modeling approaches using a technique borrowed from materials science: the phase-field models. These models allow us, with a large degree of generality, to identify the paramount mechanisms causing the uncontrolled growth of tumor cells as well as to propose new guidelines for experimentation both in simulation and in the laboratory. We finish by discussing open directions of research in phase-field modeling of tumor growth to catalyze the interest of physicists and mathematicians in this emergent field.

  7. Growth/no growth models for Zygosaccharomyces rouxii associated with acidic, sweet intermediate moisture food products.

    PubMed

    Marvig, C L; Kristiansen, R M; Nielsen, D S

    2015-01-02

    The most notorious spoilage organism of sweet intermediate moisture foods (IMFs) is Zygosaccharomyces rouxii, which can grow at low water activity, low pH and in the presence of organic acids. Together with an increased consumer demand for preservative free and healthier food products with less sugar and fat and a traditionally long self-life of sweet IMFs, the presence of Z. rouxii in the raw materials for IMFs has made assessment of the microbiological stability a significant hurdle in product development. Therefore, knowledge on growth/no growth boundaries of Z. rouxii in sweet IMFs is important to ensure microbiological stability and aid product development. Several models have been developed for fat based, sweet IMFs. However, fruit/sugar based IMFs, such as fruit based chocolate fillings and jams, have lower pH and aw than what is accounted for in previously developed models. In the present study growth/no growth models for acidified sweet IMFs were developed with the variables aw (0.65-0.80), pH (2.5-4.0), ethanol (0-14.5% (w/w) in water phase) and time (0-90 days). Two different strains of Z. rouxii previously found to show pronounced resistance to the investigated variables were included in model development, to account for strain differences. For both strains data sets with and without the presence of sorbic acid (250 ppm on product basis) were built. Incorporation of time as an exploratory variable in the models gave the possibility to predict the growth/no growth boundaries at each time between 0 and 90 days without decreasing the predictive power of the models. The influence of ethanol and aw on the growth/no growth boundary of Z. rouxii was most pronounced in the first 30 days and 60 days of incubation, respectively. The effect of pH was almost negligible in the range of 2.5-4.0. The presence of low levels of sorbic acid (250 ppm) eliminated growth of both strains at all conditions tested. The two strains tested have previously been shown to have

  8. 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…

  9. Mediation Analysis in a Latent Growth Curve Modeling Framework

    ERIC Educational Resources Information Center

    von Soest, Tilmann; Hagtvet, Knut A.

    2011-01-01

    This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and…

  10. Latent Growth Curves within Developmental Structural Equation Models.

    ERIC Educational Resources Information Center

    McArdle, J. J.; Epstein, David

    1987-01-01

    Uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. The model describes a latent growth curve model that permits the estimation of parameters representing individual and group dynamics. (Author/RH)

  11. Growth of Cognitive Abilities: Dynamic Models and Scaling.

    ERIC Educational Resources Information Center

    Eckstein, Shulamith Graus

    2000-01-01

    Extends dynamic model of cognitive growth proposed by van Geert in three directions: (1) added a term to consider exposure to material to be learned; (2) developed method to apply model to cross-sectional studies; and (3) developed procedure to scale cognitive abilities tests with items of varying difficulty. Tests model with 2- to 15-year-olds'…

  12. Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method

    NASA Astrophysics Data System (ADS)

    Chang, Albert Ling Sheng; Maisin, Navies

    Cocoa pod growth modelling are useful in crop management, pest and disease management and yield forecasting. Recently, the Beta Growth Function has been used to determine the pod growth model due to its unique for the plant organ growth which is zero growth rate at both the start and end of a precisely defined growth period. Specific pod size (7cm to 10cm in length) is useful in cocoa pod borer (CPB) management for pod sleeving or pesticide spraying. The Beta Growth Function is well-fitted to the pods growth data of four different cocoa clones under non-linear function with time (t) as its independent variable which measured pod length and diameter weekly started at 8 weeks after fertilization occur until pods ripen. However, the same pod length among the clones did not indicate the same pod age since the morphological characteristics for cocoa pods vary among the clones. Depending on pod size for all the clones as guideline in CPB management did not give information on pod age, therefore it is important to study the pod age at specific pod sizes on different clones. Hence, Newton Raphson method is used to solve the non-linear equation of the Beta Growth Function of four different group of cocoa pod at specific pod size.

  13. Escherichia coli growth under modeled reduced gravity

    NASA Technical Reports Server (NTRS)

    Baker, Paul W.; Meyer, Michelle L.; Leff, Laura G.

    2004-01-01

    Bacteria exhibit varying responses to modeled reduced gravity that can be simulated by clino-rotation. When Escherichia coli was subjected to different rotation speeds during clino-rotation, significant differences between modeled reduced gravity and normal gravity controls were observed only at higher speeds (30-50 rpm). There was no apparent affect of removing samples on the results obtained. When E. coli was grown in minimal medium (at 40 rpm), cell size was not affected by modeled reduced gravity and there were few differences in cell numbers. However, in higher nutrient conditions (i.e., dilute nutrient broth), total cell numbers were higher and cells were smaller under reduced gravity compared to normal gravity controls. Overall, the responses to modeled reduced gravity varied with nutrient conditions; larger surface to volume ratios may help compensate for the zone of nutrient depletion around the cells under modeled reduced gravity.

  14. The Role of Growth Hormone and Insulin-Like Growth Factor 1 in Human Breast Cancer Growth in a Mouse Xenograft Model

    DTIC Science & Technology

    1998-10-01

    The purpose of this research is to determine the role of human growth hormone (hGH) and insulin-like growth factor 1(IGF-1) in the development of an...progression of tumor growth in the animal model. In addition, growth hormone may be semi-inhibitory to growth for tumors dependent upon estrogen

  15. The Role of Growth Hormone and Insulin-Like Growth Factor-1 in Human Breast Cancer Growth in a Mouse Xenograft Model

    DTIC Science & Technology

    1999-10-01

    The purpose of this research is to determine the role of human growth hormone (hGH) and insulin-like growth factor 1 (IGF- 1) in the development of...the progression of tumor growth in the animal model. In addition growth hormone may be semi-inhibitory to growth for tumors dependent upon estrogen

  16. Growth model of binary alloy nanopowders for thermal plasma synthesis

    SciTech Connect

    Shigeta, Masaya; Watanabe, Takayuki

    2010-08-15

    A new model is developed for numerical analysis of the entire growth process of binary alloy nanopowders in thermal plasma synthesis. The model can express any nanopowder profile in the particle size-composition distribution (PSCD). Moreover, its numerical solution algorithm is arithmetic and straightforward so that the model is easy to use. By virtue of these features, the model effectively simulates the collective and simultaneous combined process of binary homogeneous nucleation, binary heterogeneous cocondensation, and coagulation among nanoparticles. The effect of the freezing point depression due to nanoscale particle diameters is also considered in the model. In this study, the metal-silicon systems are particularly chosen as representative binary systems involving cocondensation processes. In consequence, the numerical calculation with the present model reveals the growth mechanisms of the Mo-Si and Ti-Si nanopowders by exhibiting their PSCD evolutions. The difference of the materials' saturation pressures strongly affects the growth behaviors and mature states of the binary alloy nanopowder.

  17. Modeling of thin-film GaAs growth

    NASA Technical Reports Server (NTRS)

    Heinbockel, J. H.

    1982-01-01

    A model of crystal growth is discussed that takes into account the processes of nucleation on the growing surface and also considers the processes of surface migration and desorption of adatoms. The solid on solid (SOS) model of crystal growth is represented by a rectangular array of integers where each integer represents the number of adatoms in a column perpendicular to some reference frame. The adatoms can represent atoms or molecules that are being stacked. This SOS method is used to simulate epitaxial growth of crystals. Output of the computer program developed can be graphic or quantitative.

  18. A monomer-trimer model supports intermittent glucagon fibril growth

    PubMed Central

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

    2015-01-01

    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. PMID:25758791

  19. 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.

  20. The Study on Business Growth Process Management Entropy Model

    NASA Astrophysics Data System (ADS)

    Jing, Duan

    Enterprise's growth is a dynamic process. The factors of enterprise development are changing all the time. For this reason, it is difficult to study management entropy growth-oriented enterprises from static view. Its characteristic is the business enterprise growth stage, and puts forward a kind of measuring and calculating model based on enterprise management entropy for business scale, the enterprise ability and development speed. According to entropy measured by the model, enterprise can adopt revolution measure in the moment of truth. It can make the enterprise avoid crisis and take the road of sustainable development.

  1. Another brick in the cell wall: biosynthesis dependent growth model.

    PubMed

    Barbacci, Adelin; Lahaye, Marc; Magnenet, Vincent

    2013-01-01

    Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper.

  2. 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

  3. Development, Selection, and Validation of Tumor Growth Models

    NASA Astrophysics Data System (ADS)

    Shahmoradi, Amir; Lima, Ernesto; Oden, J. Tinsley

    In recent years, a multitude of different mathematical approaches have been taken to develop multiscale models of solid tumor growth. Prime successful examples include the lattice-based, agent-based (off-lattice), and phase-field approaches, or a hybrid of these models applied to multiple scales of tumor, from subcellular to tissue level. Of overriding importance is the predictive power of these models, particularly in the presence of uncertainties. This presentation describes our attempt at developing lattice-based, agent-based and phase-field models of tumor growth and assessing their predictive power through new adaptive algorithms for model selection and model validation embodied in the Occam Plausibility Algorithm (OPAL), that brings together model calibration, determination of sensitivities of outputs to parameter variances, and calculation of model plausibilities for model selection. Institute for Computational Engineering and Sciences.

  4. The deviation of growth model for transparent conductive graphene

    PubMed Central

    2014-01-01

    An approximate growth model was employed to predict the time required to grow a graphene film by chemical vapor deposition (CVD). Monolayer graphene films were synthesized on Cu foil at various hydrogen flow rates from 10 to 50 sccm. The sheet resistance of the graphene film was 310Ω/□ and the optical transmittance was 97.7%. The Raman intensity ratio of the G-peak to the 2D peak of the graphene film was as high as ~4 when the hydrogen flow rate was 30 sccm. The fitting curve obtained by the deviation equation of growth model closely matches the data. We believe that under the same conditions and with the same setup, the presented growth model can help manufacturers and academics to predict graphene growth time more accurately. PMID:25364316

  5. Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data

    NASA Astrophysics Data System (ADS)

    Peel, Austin; Ishak, Mustapha; Troxel, M. A.

    2012-12-01

    We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation of the solution, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Λ, the time evolution of the density contrast as well as kinematic quantities of interest can be tracked through the matter- and Λ-dominated cosmic eras up to the present and into the future. In class I, we consider a localized cosmic structure representing an overdensity neighboring a central void, surrounded by an almost Friedmann-Lemaître-Robertson-Walker background, while for class II, the exact perturbations exist globally. In various models of class I and class II, the growth rate is found to be stronger in the matter-dominated era than that of the standard lambda-cold dark matter (ΛCDM) cosmology, and it is suppressed at later times due to the presence of the cosmological constant. We find that there are Szekeres models able to provide a growth history similar to that of ΛCDM while requiring less matter content and nonzero spatial curvature, which speaks to the importance of including the effects of large-scale inhomogeneities in analyzing the growth of large-scale structure. Using data for the growth factor f from redshift space distortions and the Lyman-α forest, we obtain best fit parameters for class II models and compare their ability to match observations with ΛCDM. We find that there is negligible difference between best fit Szekeres models with no priors and those for ΛCDM, both including and excluding Lyman-α data. We also find that the standard growth index γ parametrization cannot be applied in a simple way to the growth in Szekeres models, so

  6. Modelling the effect of fluctuating herbicide concentrations on algae growth.

    PubMed

    Copin, Pierre-Jean; Coutu, Sylvain; Chèvre, Nathalie

    2015-03-01

    Herbicide concentrations fluctuate widely in watercourses after crop applications and rain events. The level of concentrations in pulses can exceed the water chronic quality criteria. In the present study, we proposed modelling the effects of successive pulse exposure on algae. The deterministic model proposed is based on two parameters: (i) the typical growth rate of the algae, obtained by monitoring growth rates of several successive batch cultures in growth media, characterizing both the growth of the control and during the recovery periods; (ii) the growth rate of the algae exposed to pulses, determined from a dose-response curve obtained with a standard toxicity test. We focused on the herbicide isoproturon and on the freshwater alga Scenedesmus vacuolatus, and we validated the model prediction based on effect measured during five sequential pulse exposures in laboratory. The comparison between the laboratory and the modelled effects illustrated that the results yielded were consistent, making the model suitable for effect prediction of the herbicide photosystem II inhibitor isoproturon on the alga S. vacuolatus. More generally, modelling showed that both pulse duration and level of concentration play a crucial role. The application of the model to a real case demonstrated that both the highest peaks and the low peaks with a long duration affect principally the cell density inhibition of the alga S. vacuolatus. It is therefore essential to detect these characteristic pulses when monitoring of herbicide concentrations are conducted in rivers.

  7. 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

  8. Modeling Dynamic Height and Crown Growth in Trees

    NASA Astrophysics Data System (ADS)

    Franklin, O.; Fransson, P.; Brännström, Å.

    2015-12-01

    Previously we have shown how principles based on productivity maximization (e.g. maximization of net primary production, net growth maximization, or functional balance) can explain allocation responses to resources, such as nutrients and light (Franklin et al., 2012). However, the success of these approaches depend on how well they align with the ultimate driver of plant behavior, fitness, or life time reproductive success. Consequently, they may not fully explain how allocation changes during the life cycle of trees where not only growth but also survival and reproduction are important. In addition, maximizing instantaneous productivity does not account for path dependence of tree growth. For example, maximizing productivity during early growth in shade may delay emergence in the forest canopy and reduce lifetime fitness compared to a more height oriented strategy. Here we present an approach to model how growth of stem diameter and leaf area in relation to stem height dynamically responds to light conditions in a way that maximizes life-time fitness (rather than instantaneous growth). The model is able to predict growth of trees growing in different types of forests, including trees emerging under a closed canopy and seedlings planted in a clear-cut area. It can also predict the response to sudden changes in the light environment, due to disturbances or harvesting. We envisage two main applications of the model, (i) Modeling effects of forest management, including thinning and planting (ii) Elucidating height growth strategies in trees and how they can be represented in vegetation models. ReferenceFranklin O, Johansson J, Dewar RC, Dieckmann U, McMurtrie RE, Brännström Å, Dybzinski R. 2012. Modeling carbon allocation in trees: a search for principles. Tree Physiology 32(6): 648-666.

  9. Modelling mould growth under suboptimal environmental conditions and inoculum size.

    PubMed

    Garcia, Daiana; Ramos, Antonio J; Sanchis, Vicente; Marín, Sonia

    2010-10-01

    Predictive models can be a tool to develop strategies to prevent mould development and consequently mycotoxin production. The aims of this work were to assess the impact of a) high/low levels of inoculum and b) optimal/suboptimal environmental conditions on fungal responses based on both kinetic and probabilistic models. Different levels of spore suspensions of Aspergillus carbonarius and Penicillium expansum were prepared and inoculated centrally with a needlepoint load on malt extract agar (MEA) with 50 replicates. While optimum conditions led to a colony diameter increase which followed Baranyi's function, suboptimal conditions led to different grow functions. In general, growth rate (mu) and lag phase (lambda) were normally distributed. Specifically, the growth rate (mu) showed similar distributions under optimal growth conditions, regardless of the inoculum level, while suboptimal a(w) and temperature conditions led to higher kurtosis distributions, mainly when the inoculum levels were low. Regarding lambda, more skewed distributions were observed, mainly when the inoculum levels were low. Probability models were not much affected by the inoculum size. Lower probabilities of growth were in general predicted under marginal conditions at a given time for both strains. The slopes of the probability curves were smaller under suboptimal growth conditions due to wider distributions. Results showed that a low inoculum level and suboptimal conditions lead to high variability of the estimated growth parameters and growth probability.

  10. Small Business Training Models for Community Growth.

    ERIC Educational Resources Information Center

    Jellison, Holly M., Ed.

    Nine successful community college programs for small business management training are described in this report in terms of their college and economic context, purpose, offerings, delivery modes, operating and marketing strategies, community outreach, support services, faculty and staff, evaluation, and future directions. The model programs are…

  11. Modeling the effect of insulin-like growth factor-1 on human cell growth.

    PubMed

    Phillips, Gemma M A; Shorten, Paul R; Wake, Graeme C; Guan, Jian

    2015-01-01

    Insulin-like growth factor-1 (IGF-1) plays a key role in human growth and development. The interactions of IGF-1 with IGF-1 receptors and IGF-1 binding proteins (IGFBPs) regulate IGF-1 function. Recent research suggests that a metabolite of IGF-1, cyclo-glycyl-proline (cGP), has a role in regulating IGF-1 homeostasis. A component of this interaction is believed to be the competitive binding of IGF-1 and cGP to IGFBPs. In this paper we describe a mathematical model of the interaction between IGF-1 and cGP on human cell growth. The model can be used to understand the interaction between IGF-1, IGFBPs, cGP and IGF-1 receptors along with the kinetics of cell growth. An explicit model of the known interactions between IGF-1, cGP, IGFBPs, IGF-1 receptors explained a large portion of the variance in cell growth (R(2) = 0.83). An implicit model of the interactions between IGF-1, cGP, IGFBPs, IGF-1 receptors that included a hypothesized feedback of cGP on IGF-1 receptors explained nonlinear features of interaction between IGF-1 and cGP not described by the explicit model (R(2) = 0.84). The model also explained the effect of IGFBP antibody on the interaction between cGP and IGF-1 (R(2) = 0.78). This demonstrates that the competitive binding of IGF-1 and cGP to IGFBPs plays a large role in the interaction between IGF-1 and cGP, but that other factors potentially play a role in the interaction between cGP and IGF-1. These models can be used to predict the complex interaction between IGF-1 and cGP on human cell growth and form a basis for further research in this field.

  12. 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.

  13. Exponential order statistic models of software reliability growth

    NASA Technical Reports Server (NTRS)

    Miller, D. R.

    1986-01-01

    Failure times of a software reliability 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.

  14. Computational modeling of hypertensive growth in the human carotid artery

    PubMed Central

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

    2014-01-01

    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. PMID:25342868

  15. Minimal Model for Genome Evolution and Growth

    NASA Astrophysics Data System (ADS)

    Hsieh, Li-Ching; Luo, Liaofu; Ji, Fengmin; Lee, H. C.

    2003-01-01

    Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random mutation but primarily grows by random segmental duplication. That genomes grew mostly by duplication is consistent with the observation that repeat sequences in all genomes are widespread and intragenomic and intergenomic homologous genes are preponderant across all life forms.

  16. Modeling global organic aerosol formation and growth

    NASA Astrophysics Data System (ADS)

    Tsimpidi, Alexandra; Karydis, Vlasios; Pandis, Spyros; Lelieveld, Jos

    2014-05-01

    A computationally efficient framework for the description of organic aerosol (OA)-gas partitioning and chemical aging has been developed and implemented into the EMAC atmospheric chemistry-climate model. This model simulates the formation of primary (POA) and secondary organic aerosols (SOA) from semi-volatile (SVOC), intermediate-volatile (IVOC) and volatile organic compounds (VOC). POA are divided in two groups with saturation concentrations at 298 K 0.1, 10, 1000, 100000 µg m-3: OA from fossil fuel combustion and biomass burning. The first 2 surrogate species from each group represent the SVOC while the other surrogate species represent the IVOC. Photochemical reactions that change the volatility of the organics in the gas phase are taken into account. The oxidation products from each group of precursors (SVOC, IVOC, and VOC) are lumped into an additional set of oxidized surrogate species (S-SOA, I-SOA, and V-SOA, respectively) in order to track their source of origin. This model is used to i) estimate the relative contributions of SOA and POA to total OA, ii) determine how SOA concentrations are affected by biogenic and anthropogenic emissions, and iii) evaluate the effect of photochemical aging and long-range transport on OA budget over specific regions.

  17. Mathematical Modeling of Tumor Cell Growth and Immune System Interactions

    NASA Astrophysics Data System (ADS)

    Rihan, Fathalla A.; Safan, Muntaser; Abdeen, Mohamed A.; Abdel-Rahman, Duaa H.

    In this paper, we provide a family of ordinary and delay differential equations to describe the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells, and the rate of influx of IL2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor-dormancy.

  18. 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.

  19. Testing the Testing: Validity of a State Growth Model

    ERIC Educational Resources Information Center

    Brown, Kim Trask

    2008-01-01

    Possible threats to the validity of North Carolina's accountability model used to predict academic growth were investigated in two ways: the state's regression equations were replicated but updated to utilize current testing data and not that from years past as in the state's current model; and the updated equations were expanded to include…

  20. Practical Formulations of the Latent Growth Item Response Model

    ERIC Educational Resources Information Center

    McGuire, Leah Walker

    2010-01-01

    Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with…

  1. 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…

  2. A Cautionary Note on Modeling Growth Trends in Longitudinal Data

    ERIC Educational Resources Information Center

    Kuljanin, Goran; Braun, Michael T.; DeShon, Richard P.

    2011-01-01

    Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a…

  3. Nonlinear and Quasi-Simplex Patterns in Latent Growth Models

    ERIC Educational Resources Information Center

    Bianconcini, Silvia

    2012-01-01

    In the SEM literature, simplex and latent growth models have always been considered competing approaches for the analysis of longitudinal data, even if they are strongly connected and both of specific importance. General dynamic models, which simultaneously estimate autoregressive structures and latent curves, have been recently proposed in the…

  4. Phase field modeling of grain growth in porous polycrystalline solids

    NASA Astrophysics Data System (ADS)

    Ahmed, Karim E.

    The concurrent evolution of grain size and porosity in porous polycrystalline solids is a technically important problem. All the physical properties of such materials depend strongly on pore fraction and pore and grain sizes and distributions. Theoretical models for the pore-grain boundary interactions during grain growth usually employ restrictive, unrealistic assumptions on the pore and grain shapes and motions to render the problem tractable. However, these assumptions limit the models to be only of qualitative nature and hence cannot be used for predictions. This has motivated us to develop a novel phase field model to investigate the process of grain growth in porous polycrystalline solids. Based on a dynamical system of coupled Cahn-Hilliard and All en-Cahn equations, the model couples the curvature-driven grain boundary motion and the migration of pores via surface diffusion. As such, the model accounts for all possible interactions between the pore and grain boundary, which highly influence the grain growth kinetics. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. The model was used to investigate the effect of porosity on the kinetics of grain growth in UO2 and CeO2 in 2D and 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four- grain junctions were found to transform to edge pores (pores on two-grain junction) before complete separation. The simulations demonstrated that inhomogeneous distribution of pores and pore breakaway lead to abnormal grain growth. The simulations also showed that grain growth kinetics in these materials changes from boundary-controlled to pore-controlled as the amount of porosity increases. The kinetic growth

  5. 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.

  6. 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.

  7. 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.

  8. Growth mechanism of carbon nanotubes: a nano Czochralski model

    PubMed Central

    2012-01-01

    Carbon nanotubes (CNTs) have been under intense investigations during the past two decades due to their unique physical and chemical properties; however, there is still no commonly accepted growth mechanism to describe the growth behavior of CNTs. Here, we propose a nano Czochralski (CZ) model which regards the catalytic growth of a CNT as a CZ process taking place on the nano scale. The main idea is that, during the CNT growth, each catalyst particle acts as a nano crucible to nucleate and maintain the CNT growth, and the extruding CNT rotates relative to the nano crucible, leading to a chirality-dependent growth rate. In this case, the structural quality gradually changes along the CNT due to the dynamic generation-reconstruction-diffusion of defects during the CNT growth. The nano CZ mechanism may also apply to the catalytic growth of many other one-dimensional (1D) nanostructures (including various nanotubes and nanowires), thus further efforts will be stimulated in the quality and property control, as well as application explorations of these 1D nanomaterials. PMID:22747835

  9. Potts-model grain growth simulations: Parallel algorithms and applications

    SciTech Connect

    Wright, S.A.; Plimpton, S.J.; Swiler, T.P.

    1997-08-01

    Microstructural morphology and grain boundary properties often control the service properties of engineered materials. This report uses the Potts-model to simulate the development of microstructures in realistic materials. Three areas of microstructural morphology simulations were studied. They include the development of massively parallel algorithms for Potts-model grain grow simulations, modeling of mass transport via diffusion in these simulated microstructures, and the development of a gradient-dependent Hamiltonian to simulate columnar grain growth. Potts grain growth models for massively parallel supercomputers were developed for the conventional Potts-model in both two and three dimensions. Simulations using these parallel codes showed self similar grain growth and no finite size effects for previously unapproachable large scale problems. In addition, new enhancements to the conventional Metropolis algorithm used in the Potts-model were developed to accelerate the calculations. These techniques enable both the sequential and parallel algorithms to run faster and use essentially an infinite number of grain orientation values to avoid non-physical grain coalescence events. Mass transport phenomena in polycrystalline materials were studied in two dimensions using numerical diffusion techniques on microstructures generated using the Potts-model. The results of the mass transport modeling showed excellent quantitative agreement with one dimensional diffusion problems, however the results also suggest that transient multi-dimension diffusion effects cannot be parameterized as the product of the grain boundary diffusion coefficient and the grain boundary width. Instead, both properties are required. Gradient-dependent grain growth mechanisms were included in the Potts-model by adding an extra term to the Hamiltonian. Under normal grain growth, the primary driving term is the curvature of the grain boundary, which is included in the standard Potts-model Hamiltonian.

  10. Differential Growth Trajectories for Achievement Among Children Retained in First Grade: A Growth Mixture Model

    PubMed Central

    Chen, Qi; Hughes, Jan N.; Kwok, Oi-Man

    2013-01-01

    The authors investigated the differential effect of retention on the development of academic achievement from grade one to five on children retained in first grade over six years. Growth Mixture Model (GMM) analyses supported the existence of two distinct trajectory groups of retained children for both reading and math among 125 ethnically and linguistically diverse retained children. For each achievement domain, a low intercept/higher growth group (Class 1) and a high intercept/slower growth group (Class 2) were identified. Furthermore, Class 1 children were found to score lower on several measures of learning related skills (LRS) variables and were characterized by having poorer self-regulation and less prosocial behaviors, compared to the other group. Findings suggest that some children appear to benefit more from retention, in terms of higher reading and math growth, than others. Study findings have implications for selecting children into retention intervention and early intervention. PMID:24771882

  11. Biologically-motivated system identification: application to microbial growth modeling.

    PubMed

    Yan, Jinyao; Deller, J R

    2014-01-01

    This paper presents a new method for identification of system models that are linear in parametric structure, but arbitrarily nonlinear in signal operations. The strategy blends traditional system identification methods with three modeling strategies that are not commonly employed in signal processing: linear-time-invariant-in-parameters models, set-based parameter identification, and evolutionary selection of the model structure. This paper reports recent advances in the theoretical foundation of the methods, then focuses on the operation and performance of the approach, particularly the evolutionary model determination. The method is applied to the modeling of microbial growth by Monod Kinetics.

  12. A Model for Tetragonal Lysozyme Crystal Nucleation and Growth

    NASA Technical Reports Server (NTRS)

    Pusey, Marc L.; Curreri, Peter A. (Technical Monitor)

    2002-01-01

    Macromolecular crystallization is a complex process, involving a system that typically has 5 or more components (macromolecule, water, buffer + counter ion, and precipitant). Whereas small molecules have only a few contacts in the crystal lattice, macromolecules generally have 10's or even 100's of contacts between molecules. These can range from hydrogen bonds (direct or water-mediated), through van der Waals, hydrophobic, salt bridges, and ion-mediated contacts. The latter interactions are stronger and require some specificity in the molecular alignment, while the others are weaker, more prevalent, and more promiscuous, i.e., can be readily broken and reformed between other sites. Formation of a consistent, ordered, 3D structure may be difficult or impossible in the absence of any or presence of too many strong interactions. Further complicating the process is the inherent structural asymmetry of monomeric (single chain) macromolecules. The process of crystal nucleation and growth involves the ordered assembly of growth units into a defined 3D lattice. We suggest that for many macromolecules, particularly those that are monomeric, this involves a preliminary solution-phase assembly process into a growth unit having some symmetry prior to addition to the lattice, recapitulating the initial stages of the nucleation process. If this model is correct then fluids and crystal growth models assuming a strictly monodisperse nutrient solution need to be revised. This model has been developed from experimental evidence based upon face growth rate, AFM, and fluorescence energy transfer data for the nucleation and growth of tetragonal lysozyme crystals.

  13. Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models

    NASA Astrophysics Data System (ADS)

    Pestana, Dinis D.; Aleixo, Sandra M.; Rocha, J. Leonel

    Classical central limit theorems, culminating in the theory of infinite divisibility, accurately describe the behaviour of stochastic phenomena with asymptotically negligible components. The classical theory fails when a single component may assume an extreme protagonism. The early developments of the speculation theory didn't incorporate the pioneer work of Pareto on heavy tailed models, and the proper setup to conciliate regularity and abrupt changes, in a wide range of natural phenomena, is Karamata's concept of regular variation and the role it plays in the theory of domains of attraction, [8], and Resnick's tail equivalence leading to the importance of generalized Pareto distribution is the scope of extreme value theory, [13]. Waliszewski and Konarski discussed the applicability of the Gompertz curve and its fractal behaviour for instance in modeling healthy and neoplasic cells tissue growth, [15]. Gompertz function is the Gumbel extreme value model, whose broad domain of attraction contains intermediate tail weight laws with a wide range of behaviour. Aleixo et al. investigated fractality associated with Beta (p,q) models, [1], [2], [10] and [11]. In this work, we introduce a new family of probability density functions tied to the classical beta family, the Beta*(p,q) models, some of which are generalized Pareto, that span the possible regular variation of tails. We extend the investigation to other extreme stable models, namely Fréchet's and Weibull's types in the General Extreme Value (GEV) model.

  14. Power of Latent Growth Modeling for Detecting Linear Growth: Number of Measurements and Comparison with Other Analytic Approaches

    ERIC Educational Resources Information Center

    Fan, Xitao; Fan, Xiaotao

    2005-01-01

    The authors investigated 2 issues concerning the power of latent growth modeling (LGM) in detecting linear growth: the effect of the number of repeated measurements on LGM's power in detecting linear growth and the comparison between LGM and some other approaches in terms of power for detecting linear growth. A Monte Carlo simulation design was…

  15. 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

  16. Modeling microbial populations with the original and modified versions of the continuous and discrete logistic equations.

    PubMed

    Peleg, M

    1997-08-01

    The life histories of microbial populations, under favorable and adverse conditions, exhibit a variety of growth, decay, and fluctuation patterns. They have been described by numerous mathematical models that varies considerably in structure and number of constants. The continuous logistic equation alone and combined with itself or with its mirror image, the Fermi function, can produce many of the observed growth patterns. They include those that are traditionally described by the Gompertz equation and peaked curves, with the peak being symmetric or asymmetric narrow or wide. The shape of survival and dose response curves appears to be determined by the distribution of the resistance's to the lethal agent among the individual organisms. Thus, exponential decay and Fermian or Gompertz-type curves can be considered manifestations of skewed to the right, symmetric, and skewed to the left distributions, respectively. Because of the mathematical constraints and determinism, the original discrete logistic equation can rarely be an adequate model of real microbial populations. However, by making its proportionality constant a normal-random variate it can simulate realistic histories of fluctuating microbial populations, including scenarios of aperiodic population explosions of varying intensities of the kind found in food-poisoning episodes.

  17. A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits

    PubMed Central

    Blasco, Agustín; Piles, Miriam; Varona, Luis

    2003-01-01

    Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear. PMID:12605849

  18. Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics

    PubMed Central

    Molina, Ignacio; Theodoropoulos, Constantinos

    2014-01-01

    A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to

  19. Modeling bacterial population growth from stochastic single-cell dynamics.

    PubMed

    Alonso, Antonio A; Molina, Ignacio; Theodoropoulos, Constantinos

    2014-09-01

    A few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to

  20. SEM++: A particle model of cellular growth, signaling and migration

    NASA Astrophysics Data System (ADS)

    Milde, Florian; Tauriello, Gerardo; Haberkern, Hannah; Koumoutsakos, Petros

    2014-06-01

    We present a discrete particle method to model biological processes from the sub-cellular to the inter-cellular level. Particles interact through a parametrized force field to model cell mechanical properties, cytoskeleton remodeling, growth and proliferation as well as signaling between cells. We discuss the guiding design principles for the selection of the force field and the validation of the particle model using experimental data. The proposed method is integrated into a multiscale particle framework for the simulation of biological systems.

  1. 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.

  2. 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.

  3. 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

  4. Modeling Intrinsic Heterogeneity and Growth of Cancer Cells

    PubMed Central

    Greene, James M.; Levy, Doron; Fung, King L.; Silva de Souza, Paloma; Gottesman, Michael M.; Lavi, Orit

    2014-01-01

    Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multi-drug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level. PMID:25457229

  5. Modeling intrinsic heterogeneity and growth of cancer cells.

    PubMed

    Greene, James M; Levy, Doron; Fung, King Leung; Souza, Paloma S; Gottesman, Michael M; Lavi, Orit

    2015-02-21

    Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multidrug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level.

  6. Kinetic model of particle-inhibited grain growth

    NASA Astrophysics Data System (ADS)

    Thompson, Gary Scott

    The effects of second phase particles on matrix grain growth kinetics were investigated using Al2O3-SiC as a model system. In particular, the validity of the conclusion drawn from a previous kinetic analysis that the kinetics of particle-inhibited grain growth in Al2 O3-SiC samples with an intermediate volume fraction of second phase could be well quantified by a modified-Zener model was investigated. A critical analysis of assumptions made during the previous kinetic analysis revealed oversimplifications which affect the validity of the conclusion. Specifically, the degree of interaction between particles and grain boundaries was assumed to be independent of the mean second phase particle size and size distribution. In contrast, current measurements indicate that the degree of interaction in Al2O3-SiC is dependent on these parameters. An improved kinetic model for particle-inhibited grain growth in Al 2O3-SiC was developed using a modified-Zener approach. The comparison of model predictions with experimental grain growth data indicated that significant discrepancies (as much as 4--5 orders of magnitude) existed. Based on this, it was concluded that particles had a much more significant effect on grain growth kinetics than that caused by a simple reduction of the boundary driving force due to the removal of boundary area. Consequently, it was also concluded that the conclusion drawn from the earlier kinetic analysis regarding the validity of a modified-Zener model was incorrect. Discrepancies between model and experiment were found to be the result of a significant decrease in experimental growth rate constant not predicted by the model. Possible physical mechanisms for such a decrease were investigated. The investigation of a small amount of SiO2 on grain growth in Al2O3 indicated that the decrease was not the result of a decrease in grain boundary mobility due to impurity contamination by particles. By process of elimination and based on previous observations

  7. Kinetic model for microbial growth and desulphurisation with Enterobacter sp.

    PubMed

    Liu, Long; Guo, Zhiguo; Lu, Jianjiang; Xu, Xiaolin

    2015-02-01

    Biodesulphurisation was investigated by using Enterobacter sp. D4, which can selectively desulphurise and convert dibenzothiophene into 2-hydroxybiphenyl (2-HBP). The experimental values of growth, substrate consumption and product generation were obtained at 95 % confidence level of the fitted values using three models: Hinshelwood equation, Luedeking-Piret and Luedeking-Piret-like equations. The average error values between experimental values and fitted values were less than 10 %. These kinetic models describe all the experimental data with good statistical parameters. The production of 2-HBP in Enterobacter sp. was by "coupled growth".

  8. Deterministic versus stochastic aspects of superexponential population growth models

    NASA Astrophysics Data System (ADS)

    Grosjean, Nicolas; Huillet, Thierry

    2016-08-01

    Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.

  9. Fatigue crack growth with single overload - Measurement and modeling

    NASA Technical Reports Server (NTRS)

    Davidson, D. L.; Hudak, S. J., Jr.; Dexter, R. J.

    1987-01-01

    This paper compares experiments with an analytical model of fatigue crack growth under variable amplitude. The stereoimaging technique was used to measure displacements near the tips of fatigue cracks undergoing simple variations in load amplitude-single overloads and overload/underload combinations. Measured displacements were used to compute strains, and stresses were determined from the strains. Local values of crack driving force (Delta-K effective) were determined using both locally measured opening loads and crack tip opening displacements. Experimental results were compared with simulations made for the same load variation conditions using Newman's FAST-2 model. Residual stresses caused by overloads, crack opening loads, and growth retardation periods were compared.

  10. Modeling of a compost biofilter incorporating microbial growth

    SciTech Connect

    Morgenroth, E.; Schroeder, E.D.; Chang, D.P.Y.; Scow, K.M.

    1995-11-01

    Biofiltration of air streams is gaining acceptance as an air pollution control technology. Biofilters are advantageous because of low operating costs and low energy requirements. Biofilters are advantageous for the removal of biodegradable pollutants at low concentrations. In this paper steady state and dynamic models for biofilters are presented. Analytical steady state models are useful for design purposes. The effects of changing operating conditions on removal efficiency and elimination capacity can be predicted. Dynamic models give a better representation of processes in a biofilter. A dynamic biofilter model incorporating microbial growth was developed. The dynamic model accounts for higher organism density at the inlet due to higher substrate concentrations.

  11. MODELING GROWTH OF AU-CU NANOCRYSTALLIINE COATINGS

    SciTech Connect

    Jankowski, A F

    2005-09-22

    The electrodeposition process parameters of current density, pulse duration, and cell potential affect both the structure and composition of the foils. The mechanism for nucleation and growth as determined from current transients yield relationships for nucleus density and nucleation rate. To develop an understanding of the role of the process parameters on grain size--as a design structural parameter to control strength, for example, a formulation is presented to model the affects of the deposition energetics on grain size and morphology. An activation energy for the deposition process is modeled that reveals different growth mechanisms, wherein nucleation and diffusion effects are each dominant as dependent upon pulse duration. A diffusion coefficient common for each of the pulsed growth modes demarcates an observed transition in growth from smooth to rough surfaces. Empirical relationships are developed that relate the parameters of the deposition process to the morphology and grain size at the nanoscale. Regimes for nanocrystalline growth include a short and long pulse mode, each with distinct activation energies. The long pulse has the additional contribution of bulk-like diffusion whereas the short pulse is limited to surface diffusion and nucleation. For either pulse condition, a transition from a rough (or nodular) growth to a smooth surface results with an increase in the kinetics of diffusion.

  12. Platelet leukocyte gel facilitates bone substitute growth and autologous bone growth in a goat model.

    PubMed

    Everts, Peter A M; Delawi, Diyar; Mahoney, Christine Brown; van Erp, Albert; Overdevest, Eddy P; van Zundert, André; Knape, Johannes T A; Dhert, Wouter J A

    2010-02-01

    The aim of this study is to evaluate multiple conditions on the formation of bone growth in a goat model. We prepared from a unit of whole blood, platelet-leukocyte gel (PLG) to stimulate bone formation, based on the release of platelet growth factors. Two 3-compartment cages containing autologous bone, calcium phosphate, and trabecular metal were implanted onto goat spinal transverse processes. One cage was treated with PLG, prepared according to a standardized protocol. An untreated cage served as a control. To monitor bone formation overtime, fluorochrome markers were administered at 2, 3, and 5 weeks. Animals were sacrificed at 9 weeks after implantation. Bone growth in these 3-compartments cages was examined by histology and histomorphometry of nondecalcified sections using traditional light and epifluorescent microscopy. Compared to the control samples, bone growth in the PLG-treated autologous bone and calcium phosphate samples was significantly more. Fairly little bone growth was seen in PLG treated or untreated trabecular metal scaffolds. The results obtained from this goat model suggest a potential role for the application of autologous PLG during surgeries in which autologous bone grafts or calcium phosphate scaffolds are used.

  13. Photorealistic Modeling of the Growth of Filamentous Specimens

    NASA Astrophysics Data System (ADS)

    Sedlář, Jiří; Flusser, Jan; Sedlářová, Michaela

    2007-12-01

    We present a new method for modeling the development of settled specimens with filamentous growth patterns, such as fungi and oomycetes. In phytopathology, the growth parameters of such microorganisms are frequently examined. Their development is documented repeatedly, in a defined time sequence, leaving the growth pattern incomplete. This restriction can be overcome by reconstructing the missing images from the images acquired at consecutive observation sessions. Image warping is a convenient tool for such purposes. In the proposed method, the parameters of the geometric transformation are estimated by means of the growth tracking based on the morphological skeleton. The result is a sequence of photorealistic artificial images that show the development of the specimen within the interval between observations.

  14. Reserve growth in oil pools of Alberta: Model and forecast

    USGS Publications Warehouse

    Verma, M.; Cook, T.

    2010-01-01

    Reserve growth is recognized as a major component of additions to reserves in most oil provinces around the world, particularly in mature provinces. It takes place as a result of the discovery of new pools/reservoirs and extensions of known pools within existing fields, improved knowledge of reservoirs over time leading to a change in estimates of original oil-in-place, and improvement in recovery factor through the application of new technology, such as enhanced oil recovery methods, horizontal/multilateral drilling, and 4D seismic. A reserve growth study was conducted on oil pools in Alberta, Canada, with the following objectives: 1) evaluate historical oil reserve data in order to assess the potential for future reserve growth; 2) develop reserve growth models/ functions to help forecast hydrocarbon volumes; 3) study reserve growth sensitivity to various parameters (for example, pool size, porosity, and oil gravity); and 4) compare reserve growth in oil pools and fields in Alberta with those from other large petroleum provinces around the world. The reported known recoverable oil exclusive of Athabasca oil sands in Alberta increased from 4.5 billion barrels of oil (BBO) in 1960 to 17 BBO in 2005. Some of the pools that were included in the existing database were excluded from the present study for lack of adequate data. Therefore, the known recoverable oil increased from 4.2 to 13.9 BBO over the period from 1960 through 2005, with new discoveries contributing 3.7 BBO and reserve growth adding 6 BBO. This reserve growth took place mostly in pools with more than 125,000 barrels of known recoverable oil. Pools with light oil accounted for most of the total known oil volume, therefore reflecting the overall pool growth. Smaller pools, in contrast, shrank in their total recoverable volumes over the years. Pools with heavy oil (gravity less than 20o API) make up only a small share (3.8 percent) of the total recoverable oil; they showed a 23-fold growth compared to

  15. Modeling fatigue crack growth for life-extending control

    NASA Astrophysics Data System (ADS)

    Patankar, Ravindra Prakash

    1999-12-01

    This dissertation presents a nonlinear dynamic model of fatigue crack growth in the state-space setting under variable amplitude cyclic load. The model is especially suited to the needs of real-time decision-making for life-extending control. The state variables are crack length and crack opening stress. The model is capable of capturing the effects of a single-cycle overload, block loads, random loads, and irregular sequences through a fading memory algorithm. Model predictions are in good agreement with experimental data on 7075-T6 and 2024-T3 aluminum alloys. Compiled results also demonstrate that the proposed model compares well with one of the most comprehensive models, FASTRAN-II that is used by the aircraft industry. Specifically, the state-space model recursively computes the crack opening stress via a simple functional relationship based on the principle of fading memory and does not require the storage of the stress history for its execution. Therefore, savings in both computation time and memory requirements are significant. The need for a reliable damage model for life-extending control is addressed with reference to the colossal inaccuracies that could occur in controller synthesis for a reusable rocket engine if a simplistic damage model is used under variable-amplitude load conditions. The seemingly counter-intuitive notion of overload injection could be gainfully utilized for life-extending optimization. The proof of this concept is demonstrated on a laboratory test apparatus by life-extension of test specimens with intentionally injected overload pulses at specific intervals. A stochastic model of fatigue crack growth under variable-amplitude load is proposed using the framework of the state-space model. The stochastic model is validated with four sets of constant-amplitude load test data and a set under variable-amplitude load test. The crack growth process is observed to be nearly deterministic for a cyclic load applied to a given specimen

  16. Probabilistic Model of Microbial Cell Growth, Division, and Mortality ▿

    PubMed Central

    Horowitz, Joseph; Normand, Mark D.; Corradini, Maria G.; Peleg, Micha

    2010-01-01

    After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability Pd(t)δt, dead with probability Pm(t)δt, or alive but undivided with the probability 1 − [Pd(t) + Pm(t)]δt, where t is time, Pd(t) expresses the probability of division for an individual cell per unit of time, and Pm(t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat's properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population's size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With Pd(t) and Pm(t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data. PMID:19915038

  17. A full lifespan model of vertebrate lens growth

    PubMed Central

    Šikić, Hrvoje; Shi, Yanrong; Lubura, Snježana

    2017-01-01

    The mathematical determinants of vertebrate organ growth have yet to be elucidated fully. Here, we utilized empirical measurements and a dynamic branching process-based model to examine the growth of a simple organ system, the mouse lens, from E14.5 until the end of life. Our stochastic model used difference equations to model immigration and emigration between zones of the lens epithelium and included some deterministic elements, such as cellular footprint area. We found that the epithelial cell cycle was shortened significantly in the embryo, facilitating the rapid growth that marks early lens development. As development progressed, epithelial cell division becomes non-uniform and four zones, each with a characteristic proliferation rate, could be discerned. Adjustment of two model parameters, proliferation rate and rate of change in cellular footprint area, was sufficient to specify all growth trajectories. Modelling suggested that the direction of cellular migration across zonal boundaries was sensitive to footprint area, a phenomenon that may isolate specific cell populations. Model runs consisted of more than 1000 iterations, in each of which the stochastic behaviour of thousands of cells was followed. Nevertheless, sequential runs were almost superimposable. This remarkable degree of precision was attributed, in part, to the presence of non-mitotic flanking regions, which constituted a path by which epithelial cells could escape the growth process. Spatial modelling suggested that clonal clusters of about 50 cells are produced during migration and that transit times lengthen significantly at later stages, findings with implications for the formation of certain types of cataract. PMID:28280571

  18. Modelling of strongly coupled particle growth and aggregation

    NASA Astrophysics Data System (ADS)

    Gruy, F.; Touboul, E.

    2013-02-01

    The mathematical modelling of the dynamics of particle suspension is based on the population balance equation (PBE). PBE is an integro-differential equation for the population density that is a function of time t, space coordinates and internal parameters. Usually, the particle is characterized by a unique parameter, e.g. the matter volume v. PBE consists of several terms: for instance, the growth rate and the aggregation rate. So, the growth rate is a function of v and t. In classical modelling, the growth and the aggregation are independently considered, i.e. they are not coupled. However, current applications occur where the growth and the aggregation are coupled, i.e. the change of the particle volume with time is depending on its initial value v0, that in turn is related to an aggregation event. As a consequence, the dynamics of the suspension does not obey the classical Von Smoluchowski equation. This paper revisits this problem by proposing a new modelling by using a bivariate PBE (with two internal variables: v and v0) and by solving the PBE by means of a numerical method and Monte Carlo simulations. This is applied to a physicochemical system with a simple growth law and a constant aggregation kernel.

  19. Predicting the peak growth velocity in the individual child: validation of a new growth model.

    PubMed

    Busscher, Iris; Kingma, Idsart; de Bruin, Rob; Wapstra, Frits Hein; Verkerke, Gijsvertus J; Veldhuizen, Albert G

    2012-01-01

    Predicting the peak growth velocity in an individual patient with adolescent idiopathic scoliosis is essential or determining the prognosis of the disorder and timing of the (surgical) treatment. Until the present time, no accurate method has been found to predict the timing and magnitude of the pubertal growth spurt in the individual child. A mathematical model was developed in which the partial individual growth velocity curve was linked to the generic growth velocity curve. The generic curve was shifted and stretched or shrunk, both along the age axis and the height velocity axis. The individual age and magnitude of the PGV were obtained from the new predicted complete growth velocity curve. Predictions were made using 2, 1.5, 1 and 0.5 years of the available longitudinal data of the individual child, starting at different ages. The predicted values of 210 boys and 162 girls were compared to the child's own original values of the PGV. The individual differences were compared to differences obtained when using the generic growth velocity curve as a standard. Using 2 years of data as input for the model, all predictions of the age of the PGV in boys and girls were significantly better in comparison to using the generic values. Using only 0.5 years of data as input, the predictions with a starting age from 13 to 15.5 years in boys and from 9.5 to 14.5 years in girls were significantly better. Similar results were found for the predictions of the magnitude of the PGV. This model showed highly accurate results in predicting the individual age and magnitude of the PGV, which can be used in the treatment of patients with adolescent idiopathic scoliosis.

  20. Monotonic entropy growth for a nonlinear model of random exchanges.

    PubMed

    Apenko, S M

    2013-02-01

    We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

  1. Environmental control of carbon allocation matters for modelling forest growth.

    PubMed

    Guillemot, Joannès; Francois, Christophe; Hmimina, Gabriel; Dufrêne, Eric; Martin-StPaul, Nicolas K; Soudani, Kamel; Marie, Guillaume; Ourcival, Jean-Marc; Delpierre, Nicolas

    2017-04-01

    We aimed to evaluate the importance of modulations of within-tree carbon (C) allocation by water and low-temperature stress for the prediction of annual forest growth with a process-based model. A new C allocation scheme was implemented in the CASTANEA model that accounts for lagged and direct environmental controls of C allocation. Different approaches (static vs dynamic) to modelling C allocation were then compared in a model-data fusion procedure, using satellite-derived leaf production estimates and biometric measurements at c. 10(4) sites. The modelling of the environmental control of C allocation significantly improved the ability of CASTANEA to predict the spatial and year-to-year variability of aboveground forest growth along regional gradients. A significant effect of the previous year's water stress on the C allocation to leaves and wood was reported. Our results also are consistent with a prominent role of the environmental modulation of sink demand in the wood growth of the studied species. Data available at large scales can inform forest models about the processes driving annual and seasonal C allocation. Our results call for a greater consideration of C allocation drivers, especially sink-demand fluctuations, for the simulations of current and future forest productivity with process-based models.

  2. 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.

  3. Growth of Byssochlamys Nivea in Pineapple Juice Under the Effect of Water Activity and Ascospore Age

    PubMed Central

    Zimmermann, M.; Miorelli, S.; Massaguer, P.R.; Aragão, G.M.F.

    2011-01-01

    The study of thermal resistant mould, including Byssochlamys nivea, is of extreme importance since it has been associated with fruit and fruit products. The aim of this work is to analyze the influence of water activity (aw) and ascospore age (I) on the growth of Byssochlamys nivea in pineapple juice. Mold growth was carried out under different conditions of water activity (aw) (0.99, 0.96, 0.95, 0.93, 0.90) and ascospore age (I) (30, 51, 60, 69, 90 days). Growth parameters as length of adaptation phase (λ), maximum specific growth rate (µmax) and maximum diameter reached by the colony (A) were obtained through the fit of the Modified Gompertz model to experimental data (measuring radial colony diameter). Statistica 6.0 was used for statistical analyses (significance level α = 0.05). The results obtained clearly showed that water activity is statistically significant and that it influences all growth parameters, while ascospore age does not have any statistically significant influence on growth parameters. Also, these data showed that by increasing aw from 0.90 to 0.99, the λ value substantially decreased, while µmax and A values rose. The data contributed for the understanding of the behavior of B. nivea in pineapple juice. Therefore, it provided mathematical models that can well predict growth parameters, also helping on microbiological control and products’ shelf life determination. PMID:24031622

  4. A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces

    SciTech Connect

    Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H.

    2014-02-02

    In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

  5. Simulation of optical diagnostics for crystal growth: models and results

    NASA Astrophysics Data System (ADS)

    Banish, Michele R.; Clark, Rodney L.; Kathman, Alan D.; Lawson, Shelah M.

    1991-12-01

    A computer simulation of a two-color holographic interferometric (TCHI) optical system was performed using a physical (wave) optics model. This model accurately simulates propagation through time-varying, 2-D or 3-D concentration and temperature fields as a wave phenomenon. The model calculates wavefront deformations that can be used to generate fringe patterns. This simulation modeled a proposed TriGlycine sulphate TGS flight experiment by propagating through the simplified onion-like refractive index distribution of the growing crystal and calculating the recorded wavefront deformation. The phase of this wavefront was used to generate sample interferograms that map index of refraction variation. Two such fringe patterns, generated at different wavelengths, were used to extract the original temperature and concentration field characteristics within the growth chamber. This proves feasibility for this TCHI crystal growth diagnostic technique. This simulation provides feedback to the experimental design process.

  6. 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

  7. Growth Model Comparison Study: A Summary of Results

    ERIC Educational Resources Information Center

    Auty, Bill; Brockmann, Frank

    2012-01-01

    School accountability is subject to considerable scrutiny. It generates sharp political debate, policy challenges, and continuous discussion. Growth models are now a part of that discussion. To many practitioners the sheer volume of "important to know" information is daunting. The members of the Technical Issues in Large Scale Assessment…

  8. 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.

  9. Building Context with Tumor Growth Modeling Projects in Differential Equations

    ERIC Educational Resources Information Center

    Beier, Julie C.; Gevertz, Jana L.; Howard, Keith E.

    2015-01-01

    The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss…

  10. Developmental Trajectories of Adolescent Popularity: A Growth Curve Modelling Analysis

    ERIC Educational Resources Information Center

    Cillessen, Antonius H. N.; Borch, Casey

    2006-01-01

    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…

  11. A Role for M-Matrices in Modelling Population Growth

    ERIC Educational Resources Information Center

    James, Glyn; Rumchev, Ventsi

    2006-01-01

    Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results,…

  12. Multiscale Models in the Biomechanics of Plant Growth

    PubMed Central

    Fozard, John A.

    2015-01-01

    Plant growth occurs through the coordinated expansion of tightly adherent cells, driven by regulated softening of cell walls. It is an intrinsically multiscale process, with the integrated properties of multiple cell walls shaping the whole tissue. Multiscale models encode physical relationships to bring new understanding to plant physiology and development. PMID:25729061

  13. Twelve Frequently Asked Questions about Growth Curve Modeling

    ERIC Educational Resources Information Center

    Curran, Patrick J.; Obeidat, Khawla; Losardo, Diane

    2010-01-01

    Longitudinal data analysis has long played a significant role in empirical research within the developmental sciences. The past decade has given rise to a host of new and exciting analytic methods for studying between-person differences in within-person change. These methods are broadly organized under the term "growth curve models." The…

  14. Multiplicative Modeling of Children's Growth and Its Statistical Properties

    NASA Astrophysics Data System (ADS)

    Kuninaka, Hiroto; Matsushita, Mitsugu

    2014-03-01

    We develop a numerical growth model that can predict the statistical properties of the height distribution of Japanese children. Our previous studies have clarified that the height distribution of schoolchildren shows a transition from the lognormal distribution to the normal distribution during puberty. In this study, we demonstrate by simulation that the transition occurs owing to the variability of the onset of puberty.

  15. Diagnostics of Robust Growth Curve Modeling Using Student's "t" Distribution

    ERIC Educational Resources Information Center

    Tong, Xin; Zhang, Zhiyong

    2012-01-01

    Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors…

  16. Phase transitions in tumor growth: II prostate cancer cell lines

    NASA Astrophysics Data System (ADS)

    Llanos-Pérez, J. A.; Betancourt-Mar, A.; De Miguel, M. P.; Izquierdo-Kulich, E.; Royuela-García, M.; Tejera, E.; Nieto-Villar, J. M.

    2015-05-01

    We propose a mechanism for prostate cancer cell lines growth, LNCaP and PC3 based on a Gompertz dynamics. This growth exhibits a multifractal behavior and a "second order" phase transition. Finally, it was found that the cellular line PC3 exhibits a higher value of entropy production rate compared to LNCaP, which is indicative of the robustness of PC3, over to LNCaP and may be a quantitative index of metastatic potential tumors.

  17. Modeling high speed growth of large rods of cesium iodide crystals by edge-defined film-fed growth (EFG)

    NASA Astrophysics Data System (ADS)

    Yeckel, Andrew

    2016-09-01

    A thermocapillary model of edge-defined film-fed growth (EFG) is developed to analyze an experimental system for high speed growth of cesium iodide as a model system for halide scintillator production. The model simulates heat transfer and fluid dynamics in the die, melt, and crystal under conditions of steady growth. Appropriate mass, force, and energy balances are used to compute self-consistent shapes of the growth interface and melt-vapor meniscus. The model is applied to study the effects of growth rate, die geometry, and furnace heat transfer on the limits of system operability. An inverse problem formulation is used to seek operable states at high growth rates by adjusting the overall temperature level and thermal gradient in the furnace. The model predicts that steady growth is feasible at rates greater than 20 mm/h for crystals up to 18 mm in diameter under reasonable furnace gradients.

  18. Modeling of thin-film GaAs growth

    NASA Technical Reports Server (NTRS)

    Heinbockel, J. H.

    1981-01-01

    A solid Monte Carlo model is constructed for the simulation of crystal growth. The model assumes thermally accommodated adatoms impinge upon the surface during a delta time interval. The surface adatoms are assigned a random energy from a Boltzmann distribution, and this energy determines whether the adatoms evaporate, migrate, or remain stationary during the delta time interval. For each addition or migration of an adatom, potential wells are adjusted to reflect the absorption, migration, or desorption potential changes.

  19. Mathematical Modeling of Branching Morphogenesis and Vascular Tumor Growth

    NASA Astrophysics Data System (ADS)

    Yan, Huaming

    Feedback regulation of cell lineages is known to play an important role in tissue size control, but the effect in tissue morphogenesis has yet to be explored. We first use a non-spatial model to show that a combination of positive and negative feedback on stem and/or progenitor cell self-renewal leads to bistable or bi-modal growth behaviors and ultrasensitivity to external growth cues. Next, a spatiotemporal model is used to demonstrate spatial patterns such as local budding and branching arise in this setting, and are not consequences of Turing-type instabilities. We next extend the model to a three-dimensional hybrid discrete-continuum model of tumor growth to study the effects of angiogenesis, tumor progression and cancer therapies. We account for the crosstalk between the vasculature and cancer stem cells (CSCs), and CSC transdifferentiation into vascular endothelial cells (gECs), as observed experimentally. The vasculature stabilizes tumor invasiveness but considerably enhances growth. A gEC network structure forms spontaneously within the hypoxic core, consistent with experimental findings. The model is then used to study cancer therapeutics. We demonstrate that traditional anti-angiogenic therapies decelerate tumor growth, but make the tumor highly invasive. Chemotherapies help to reduce tumor sizes, but cannot control the invasion. Anti-CSC therapies that promote differentiation or disturb the stem cell niche effectively reduce tumor invasiveness. However, gECs inherit mutations present in CSCs and are resistant to traditional therapies. We show that anti-gEC treatments block the support on CSCs by gECs, and reduce both tumor size and invasiveness. Our study suggests that therapies targeting the vasculature, CSCs and gECs, when combined, are highly synergistic and are capable of controlling both tumor size and shape.

  20. Numerical solution of the Penna model of biological aging with age-modified mutation rate

    NASA Astrophysics Data System (ADS)

    Magdoń-Maksymowicz, M. S.; Maksymowicz, A. Z.

    2009-06-01

    In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a) , where a is the parent’s age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a . As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a) , a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1) . The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe

  1. Replicating vesicles as models of primitive cell growth and division.

    PubMed

    Hanczyc, Martin M; Szostak, Jack W

    2004-12-01

    Primitive cells, lacking the complex bio-machinery present in modern cells, would have had to rely on the self-organizing properties of their components and on interactions with their environment to achieve basic cellular functions such as growth and division. Many bilayer-membrane vesicles, depending on their composition and environment, can exhibit complex morphological changes such as growth, fusion, fission, budding, internal vesicle assembly and vesicle-surface interactions. The rich dynamic properties of these vesicles provide interesting models of how primitive cellular replication might have occurred in response to purely physical and chemical forces.

  2. A computational model for cancer growth by using complex networks

    NASA Astrophysics Data System (ADS)

    Galvão, Viviane; Miranda, José G. V.

    2008-09-01

    In this work we propose a computational model to investigate the proliferation of cancerous cell by using complex networks. In our model the network represents the structure of available space in the cancer propagation. The computational scheme considers a cancerous cell randomly included in the complex network. When the system evolves the cells can assume three states: proliferative, non-proliferative, and necrotic. Our results were compared with experimental data obtained from three human lung carcinoma cell lines. The computational simulations show that the cancerous cells have a Gompertzian growth. Also, our model simulates the formation of necrosis, increase of density, and resources diffusion to regions of lower nutrient concentration. We obtain that the cancer growth is very similar in random and small-world networks. On the other hand, the topological structure of the small-world network is more affected. The scale-free network has the largest rates of cancer growth due to hub formation. Finally, our results indicate that for different average degrees the rate of cancer growth is related to the available space in the network.

  3. A reaction-diffusion model for long bones growth.

    PubMed

    Garzón-Alvarado, D A; García-Aznar, J M; Doblaré, M

    2009-10-01

    Bone development is characterized by differentiation and growth of chondrocytes from the proliferation zone to the hypertrophying one. These two cellular processes are controlled by a complex signalling regulatory loop between different biochemical signals, whose production depends on the current cell density, constituting a coupled cell-chemical system. In this work, a mathematical model of the process of early bone growth is presented, extending and generalizing other earlier approaches on the same topic. A reaction-diffusion regulatory loop between two chemical factors: parathyroid hormone-related peptide (PTHrP) and Indian hedgehog (Ihh) is hypothesized, where PTHrP is activated by Ihh and inhibits Ihh production. Chondrocytes proliferation and hypertrophy are described by means of population equations being both regulated by the PTHrP and Ihh concentrations. In the initial stage of bone growth, these two cellular proceses are considered to be directionally dependent, modelling the well known column cell formation, characteristic of endochondral ossification. This coupled set of equations is solved within a finite element framework, getting an estimation of the chondrocytes spatial distribution, growth of the diaphysis and formation of the epiphysis of a long bone. The results obtained are qualitatively similar to the actual physiological ones and quantitatively close to some available experimental data. Finally, this extended approach allows finding important relations between the model parameters to get stability of the physiological process and getting additional insight on the spatial and directional distribution of cells and paracrine factors.

  4. Emergent properties of a computational model of tumour growth

    PubMed Central

    2016-01-01

    While there have been enormous advances in our understanding of the genetic drivers and molecular pathways involved in cancer in recent decades, there also remain key areas of dispute with respect to fundamental theories of cancer. The accumulation of vast new datasets from genomics and other fields, in addition to detailed descriptions of molecular pathways, cloud the issues and lead to ever greater complexity. One strategy in dealing with such complexity is to develop models to replicate salient features of the system and therefore to generate hypotheses which reflect on the real system. A simple tumour growth model is outlined which displays emergent behaviours that correspond to a number of clinically relevant phenomena including tumour growth, intra-tumour heterogeneity, growth arrest and accelerated repopulation following cytotoxic insult. Analysis of model data suggests that the processes of cell competition and apoptosis are key drivers of these emergent behaviours. Questions are raised as to the role of cell competition and cell death in physical cancer growth and the relevance that these have to cancer research in general is discussed. PMID:27413638

  5. A Big Bang model of human colorectal tumor growth.

    PubMed

    Sottoriva, Andrea; Kang, Haeyoun; Ma, Zhicheng; Graham, Trevor A; Salomon, Matthew P; Zhao, Junsong; Marjoram, Paul; Siegmund, Kimberly; Press, Michael F; Shibata, Darryl; Curtis, Christina

    2015-03-01

    What happens in early, still undetectable human malignancies is unknown because direct observations are impractical. Here we present and validate a 'Big Bang' model, whereby tumors grow predominantly as a single expansion producing numerous intermixed subclones that are not subject to stringent selection and where both public (clonal) and most detectable private (subclonal) alterations arise early during growth. Genomic profiling of 349 individual glands from 15 colorectal tumors showed an absence of selective sweeps, uniformly high intratumoral heterogeneity (ITH) and subclone mixing in distant regions, as postulated by our model. We also verified the prediction that most detectable ITH originates from early private alterations and not from later clonal expansions, thus exposing the profile of the primordial tumor. Moreover, some tumors appear 'born to be bad', with subclone mixing indicative of early malignant potential. This new model provides a quantitative framework to interpret tumor growth dynamics and the origins of ITH, with important clinical implications.

  6. An autoregressive growth model for longitudinal item analysis.

    PubMed

    Jeon, Minjeong; Rabe-Hesketh, Sophia

    2016-09-01

    A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students' self-esteem.

  7. Modelling Aspergillus flavus growth and aflatoxins production in pistachio nuts.

    PubMed

    Marín, Sonia; Ramos, Antonio J; Sanchis, V

    2012-12-01

    Aflatoxins (AFs) are the main contaminants in pistachio nuts. AFs production in pistachio has been attributed to Aspergillus flavus. The aim of this study was to apply existing models to predict growth and AFs production by an A. flavus isolated from pistachios as a function of moisture content and storage temperature of pistachios in order to test their usefulness and complementarities. A full factorial design was used: the moisture content levels assayed were 10, 15, 20, 25 and 30% and incubation temperatures were 10, 15, 20, 25, 30, 37 and 42 °C. Both kinetic and probability models were built to predict growth of the strain under the assayed conditions. Among the assayed models, cardinal ones gave a good quality fit for radial growth rate data. Moreover, the progressive approach, which was developed based on a reduced number of experimental points led to an improved prediction in the validation step. This is quite significant as may allow for improved experimental designs, less costly than full factorial ones. Probability model proved to be concordant in 91% of the calibration set observations. Even though the validation set included conditions around the growth/no-growth interface, there was a 100% agreement in the predictions from the data set (n = 16, cut off = 0.5) after 60 days. Similarly, the probability for AF presence was rightly predicted in 89% of the cases. According to our results EC maximum aflatoxin levels would be surpassed in a period as short as 1 month if pistachio nuts reach 20 °C, unless %mc is ≤10%.

  8. 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.

  9. River water temperature and fish growth forecasting models

    NASA Astrophysics Data System (ADS)

    Danner, E.; Pike, A.; Lindley, S.; Mendelssohn, R.; Dewitt, L.; Melton, F. S.; Nemani, R. R.; Hashimoto, H.

    2010-12-01

    Water is a valuable, limited, and highly regulated resource throughout the United States. When making decisions about water allocations, state and federal water project managers must consider the short-term and long-term needs of agriculture, urban users, hydroelectric production, flood control, and the ecosystems downstream. In the Central Valley of California, river water temperature is a critical indicator of habitat quality for endangered salmonid species and affects re-licensing of major water projects and dam operations worth billions of dollars. There is consequently strong interest in modeling water temperature dynamics and the subsequent impacts on fish growth in such regulated rivers. However, the accuracy of current stream temperature models is limited by the lack of spatially detailed meteorological forecasts. To address these issues, we developed a high-resolution deterministic 1-dimensional stream temperature model (sub-hourly time step, sub-kilometer spatial resolution) in a state-space framework, and applied this model to Upper Sacramento River. We then adapted salmon bioenergetics models to incorporate the temperature data at sub-hourly time steps to provide more realistic estimates of salmon growth. The temperature model uses physically-based heat budgets to calculate the rate of heat transfer to/from the river. We use variables provided by the TOPS-WRF (Terrestrial Observation and Prediction System - Weather Research and Forecasting) model—a high-resolution assimilation of satellite-derived meteorological observations and numerical weather simulations—as inputs. The TOPS-WRF framework allows us to improve the spatial and temporal resolution of stream temperature predictions. The salmon growth models are adapted from the Wisconsin bioenergetics model. We have made the output from both models available on an interactive website so that water and fisheries managers can determine the past, current and three day forecasted water temperatures at

  10. Percentile growth charts for biomedical studies using a porcine model.

    PubMed

    Corson, A M; Laws, J; Laws, A; Litten, J C; Lean, I J; Clarke, L

    2008-12-01

    Increasing rates of obesity and heart disease are compromising quality of life for a growing number of people. There is much research linking adult disease with the growth and development both in utero and during the first year of life. The pig is an ideal model for studying the origins of developmental programming. The objective of this paper was to construct percentile growth curves for the pig for use in biomedical studies. The body weight (BW) of pigs was recorded from birth to 150 days of age and their crown-to-rump length was measured over the neonatal period to enable the ponderal index (PI; kg/m3) to be calculated. Data were normalised and percentile curves were constructed using Cole's lambda-mu-sigma (LMS) method for BW and PI. The construction of these percentile charts for use in biomedical research will allow a more detailed and precise tracking of growth and development of individual pigs under experimental conditions.

  11. Assessing uncertainty in a stand growth model by Bayesian synthesis

    SciTech Connect

    Green, E.J.; MacFarlane, D.W.; Valentine, H.T.; Strawderman, W.E.

    1999-11-01

    The Bayesian synthesis method (BSYN) was used to bound the uncertainty in projections calculated with PIPESTEM, a mechanistic model of forest growth. The application furnished posterior distributions of (a) the values of the model's parameters, and (b) the values of three of the model's output variables--basal area per unit land area, average tree height, and tree density--at different points in time. Confidence or credible intervals for the output variables were obtained directly from the posterior distributions. The application also provides estimates of correlation among the parameters and output variables. BSYN, which originally was applied to a population dynamics model for bowhead whales, is generally applicable to deterministic models. Extension to two or more linked models is discussed. A simple worked example is included in an appendix.

  12. Modelling the thermal effects of spherulite growth in rhyolitic lava

    NASA Astrophysics Data System (ADS)

    Tuffen, H.; Cordonnier, B.; Castro, J. M.

    2012-12-01

    Rhyolitic lava flows, sills and dykes commonly comprise a spherulitic interior enveloped by a glassy carapace. Spherulite crystallisation has long been assumed to be a "passive" process that occurs during cooling of the lava around and below its glass transition temperature (~600-700 °C). It has also been suggested to be self-limiting due to diffusion controlled growth, creating only a small proportion of spherulites embedded in glass (snowflake obsidian). However, textures in rhyolitic lava bodies at Hrafntinnuhryggur, Krafla, Iceland indicate that near-complete spherulite crystallisation can occur, and suggest that parts of the lava spatially associated with zones of spherulite and lithophysae growth may be significantly heated. Evidence for heating includes melting of parts of the glassy lava carapace by lower-viscosity, invading melt of identical composition. Additionally, spherulitic crystal morphologies have been grown experimentally at undercoolings of only 100 °C. As the liquidus temperature of dry rhyolite may approach 1200 °C, this means that spherulites could continue to grow in degassed magma at temperatures of >900 °C, well above the initial magma temperature. We use new constraints on spherulite growth rates to model the thermal effects of spherulite growth within rhyolitic lava bodies, using three growth laws (size- and temperature-dependent, diffusion controlled and linear) and a variety of initial temperatures, nucleation densities and seed nuclei sizes. Models consider both latent heat release due to crystallisation and conductive cooling. Model results indicate that, when lava bodies are sufficiently large, spherulite growth can cause considerable heating (possibly >150 °C), enabling parts of lava bodies to heat to above the initial eruption temperature. This heating can lead to a viscosity reduction of orders of magnitude and trigger vesiculation. Model results indicate that cooling rates of between 10-3 to 10-5 °C/s ought to mark the

  13. 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.

  14. 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…

  15. Dynamic Modeling of Aerobic Growth of Shewanella oneidensis. Predicting Triauxic Growth, Flux Distributions and Energy Requirement for Growth

    SciTech Connect

    Song, Hyun-Seob; Ramkrishna, Doraiswami; Pinchuk, Grigoriy E.; Beliaev, Alex S.; Konopka, Allan; Fredrickson, Jim K.

    2013-01-01

    A model-based analysis is conducted to investigate metabolism of Shewanella oneidensis MR-1 strain in aerobic batch culture, which exhibits an intriguing growth pattern by sequentially consuming substrate (i.e., lactate) and by-products (i.e., pyruvate and acetate). A general protocol is presented for developing a detailed network-based dynamic model for S. oneidensis based on the Lumped Hybrid Cybernetic Model (LHCM) framework. The L-HCM, although developed from only limited data, is shown to accurately reproduce exacting dynamic metabolic shifts, and provide reasonable estimates of energy requirement for growth. Flux distributions in S. oneidensis predicted by the L-HCM compare very favorably with 13C-metabolic flux analysis results reported in the literature. Predictive accuracy is enhanced by incorporating measurements of only a few intracellular fluxes, in addition to extracellular metabolites. The L-HCM developed here for S. oneidensis is consequently a promising tool for the analysis of intracellular flux distribution and metabolic engineering.

  16. Analysis of Pseudomonas aeruginosa growth and virulence in modelled microgravity

    NASA Astrophysics Data System (ADS)

    Guadarrama, Seratna; Pulcini, Elinor de L.; Broadaway, Susan C.; Pyle, Barry H.

    2005-08-01

    Stress, radiation and microgravity cause astronauts to experience secondary immunosuppression. Spaceflight conditions enhance bacterial growth and alter antimicrobial susceptibility. Clinostats are used to model microgravity effects at 1xg. In controls rotated on the vertical axis, the g-vector acts on cells as in static cultures. Salmonella enterica serovar T yphimurium virulence genes are up-regulated in modelled microgravity (MMG); a MMG regulon has been postulated. We hypothesize that the virulence of P. aeruginosa (PA) may be affected similarly by microgravity, which could be observed in MMG. This study focused on regulation of the ETA protein by PA during growth in MMG. PA103 was grown in an ETA production medium at 37°C. One series of media was inoculated with frozen cultures and grown using horizontal (MMG) or static incubation. Another series inoculated with refrigerated cultures included vertical rotating controls. Analyses included optical density (OD), agar plate counts (PC) on R2A, ETA ELISA, and protein expression by 2-D gel analyses. Growth and ETA results differed depending on inoculum, with minor effects of MMG. Proteomic analysis of 2-D gels indicate differences in protein expression with MMG. Growth and ETA results show that consistent methodology is critical when studying environmental effects. This study provides information on the relationships between environmental changes and virulence regulation, especially for flight experiments, when ground experiments are used to predict potential spaceflight effects.

  17. Analysis of Pdeudomonas aeruginosa Growth and Virulence in Modelled Microgravity

    NASA Technical Reports Server (NTRS)

    Guadarrama, Seratna; deL. Pulcini, Elinor; Broadaway, Susan C.; Pyle, Barry H.

    2005-01-01

    Stress, radiation and microgravity cause astronauts to experience secondary immunosuppression. Spaceflight conditions enhance bacterial growth and alter antimicrobial susceptibility. Clinostats are used to model microgravity effects at lxg. In controls rotated on the vertical axis, the g-vector acts on cells as in static cultures. Salmonella enterica serovar Typhimurium virulence genes are up-regulated in modelled microgravity (MMG); a MMG regulon has been postulated. We hypothesize that the virulence of P. aeruginosa (PA) may be affected similarly by microgravity, which could be observed in MMG. This study focused on regulation of the ETA protein by PA during growth in MMG. PA103 was grown in an ETA production medium at 37 C. One series of media was inoculated with frozen cultures and grown using horizontal (MMG) or static incubation. Another series inoculated with refrigerated cultures included vertical rotating controls. Analyses included optical density (OD), agar plate counts (PC) on R2A, ETA ELISA, and protein expression by 2-D gel analyses. Growth and ETA results differed depending on inoculum, with minor effects of MMG. Proteomic analysis of 2-D gels indicate differences in protein expression with MMG. Growth and ETA results show that consistent methodology is critical when studying environmental effects. This study provides information on the relationships between environmental changes and virulence regulation, especially for flight experiments, when ground experiments are used to predict potential spaceflight effects.

  18. T Model of Growth and its Application in Systems of Tumor-Immune Dynamics

    PubMed Central

    Tabatabai, Mohammad A.; Eby, Wayne M.; Singh, Karan P.; Bae, Sejong

    2015-01-01

    In this paper we introduce a new growth model called T growth model. This model is capable of representing sigmoidal growth as well as biphasic growth. This dual capability is achieved without introducing additional parameters. The T model is useful in modeling cellular proliferation or regression of cancer cells, stem cells, bacterial growth and drug dose-response relationships. We recommend usage of the T growth model for the growth of tumors as part of any system of differential equations. Use of this model within a system will allow more flexibility in representing the natural rate of tumor growth. For illustration, we examine some systems of tumor-immune interaction in which the T growth rate is applied. We also apply the model to a set of tumor growth data. PMID:23906156

  19. Future Air Traffic Growth and Schedule Model User's Guide

    NASA Technical Reports Server (NTRS)

    Kimmel, William M. (Technical Monitor); Smith, Jeremy C.; Dollyhigh, Samuel M.

    2004-01-01

    The Future Air Traffic Growth and Schedule Model was developed as an implementation of the Fratar algorithm to project future traffic flow between airports in a system and of then scheduling the additional flights to reflect current passenger time-of-travel preferences. The methodology produces an unconstrained future schedule from a current (or baseline) schedule and the airport operations growth rates. As an example of the use of the model, future schedules are projected for 2010 and 2022 for all flights arriving at, departing from, or flying between all continental United States airports that had commercial scheduled service for May 17, 2002. Inter-continental US traffic and airports are included and the traffic is also grown with the Fratar methodology to account for their arrivals and departures to the continental US airports. Input data sets derived from the Official Airline Guide (OAG) data and FAA Terminal Area Forecast (TAF) are included in the examples of the computer code execution.

  20. Future Air Traffic Growth and Schedule Model, Supplement

    NASA Technical Reports Server (NTRS)

    Kimmel, William M. (Technical Monitor); Smith, Jeremy C.; Dollyhigh, Samuel M.

    2004-01-01

    The Future Air Traffic Growth and Schedule Model was developed as an implementation of the Fratar algorithm to project future traffic flow between airports in a system and of then scheduling the additional flights to reflect current passenger time-of-travel preferences. The methodology produces an unconstrained future schedule from a current (or baseline) schedule and the airport operations growth rates. As an example of the use of the model, future schedules are projected for 2010 and 2022 for all flights arriving at, departing from, or flying between all continental United States airports that had commercial scheduled service for May 17, 2002. Inter-continental US traffic and airports are included and the traffic is also grown with the Fratar methodology to account for their arrivals and departures to the continental US airports. Input data sets derived from the Official Airline Guide (OAG) data and FAA Terminal Area Forecast (TAF) are included in the examples of the computer code execution.

  1. Microstructurally based model of fatigue initiation and growth

    NASA Technical Reports Server (NTRS)

    Brockenbrough, J. R.; Hinkle, A. J.; Magnusen, P. E.; Bucci, R. J.

    1994-01-01

    A model to calculate fatigue life is developed based on the assumption that fatigue life is entirely composed of crack growth from an initial microstructural inhomogeneity. Specifically, growth is considered to start from either an ellipsoidal void, a cracked particle, or a debonded particle. The capability of predicting fatigue life from material microstructure is based on linear elastic fracture mechanics principles, the sizes of the crack-initiating microstructural inhomogeneities, and an initiation parameter that is proportional to the cyclic plastic zone size. A key aspect of this modeling approach is that it is linked with a general purpose probability program to analyze the effect of the distribution of controlling microstructural features within the material. This enables prediction of fatigue stress versus life curves for various specimen geometries using distributional statistics obtained from characterizations of the microstructure. Results are compared to experimental fatigue data from an aluminum alloy.

  2. 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

  3. Effects of the environment on fish juvenile growth in West African stressful estuaries

    NASA Astrophysics Data System (ADS)

    Diouf, K.; Guilhaumon, F.; Aliaume, C.; Ndiaye, P.; Chi, T. Do; Panfili, J.

    2009-06-01

    The knowledge of juvenile fish growth in extreme environmental conditions is a key to the understanding of adaptive responses and to the relevant management of natural populations. The juvenile growth of an extreme euryhaline tilapia species, Sarotherodon melanotheron (Cichlidae), was examined across a salinity gradient (20-118) in several West African estuarine ecosystems. Juveniles were collected during the reproduction period of two consecutive years (2003 and 2004) in six locations in the Saloum (Senegal) and Gambia estuaries. Age and growth were estimated using daily otolith microincrements. For each individual, otolith growth rates showed three different stages (slow, fast, decreasing): around 4 ± 0.5 μm d -1 during the first five days, 9 ± 0.5 μm d -1 during the next 15 days and 4 ± 0.50 μm d -1 at 60 days. Growth modelling and model comparisons were objectively made within an information theory framework using the multi-model inference from five growth models (linear, power, Gompertz, von Bertalanffy, and logistic). The combination of both the model adjustment inspection and the information theory model selection procedure allowed identification of the final set of models, including the less parameterised ones. The estimated growth rates were variable across spatial scales but not across temporal scales (except for one location), following exactly the salinity gradient with growth decrease towards the hypersaline conditions. The salinity gradient was closely related to all measured variables (condition factor, mean age, multi-model absolute growth rate) demonstrating the strong effect of hypersaline environmental conditions—induced by climate changes—on fish populations at an early stage.

  4. Modelling of Verneuil process for the sapphire crystal growth

    NASA Astrophysics Data System (ADS)

    Barvinschi, Floricica; Santailler, Jean-Louis; Duffar, Thierry; Le Gal, Hervé

    1999-03-01

    The finite element software FIDAP was used to simulate the Verneuil crystal growth process. The turbulent combustion between hydrogen and oxygen, giving water, the hydrodynamics of the gas phase, the inlet and outlet chemical species flow resulting from the combustion and the heat transfer in the furnace (including internal wall-to-wall radiation) are taken into account. A problem with 10 degrees of freedom per node is generated, solved and the results of the axisymmetric model have shown that the coupling of all these phenomena can be achieved in one numerical model. The effects of transparency of the crystal is discussed. A qualitative agreement between some experimental observations and the model is found, so that modelling may be a good tool for studying the Verneuil process. Nevertheless, some improvements of the model in conjunction with other experimental validations appear necessary.

  5. Roughness and growth in a continuous fluid invasion model

    NASA Astrophysics Data System (ADS)

    Hecht, Inbal; Taitelbaum, Haim

    2004-10-01

    We have studied interface characteristics in a continuous fluid invasion model, first introduced by Cieplak and Robbins [Phys. Rev. Lett. 60, 2042 (1988)]. In this model, the interface grows as a response to an applied quasistatic pressure, which induces various types of instabilities. We suggest a variant of the model, which differs from the original model by the order of instabilities treatment. This order represents the relative importance of the physical mechanisms involved in the system. This variant predicts the existence of a third, intermediate regime, in the behavior of the roughness exponent as a function of the wetting properties of the system. The gradual increase of the roughness exponent in this third regime can explain the scattered experimental data for the roughness exponent in the literature. The growth exponent in this model was found to be around zero, due to the initial rough interface.

  6. Dynamic Metabolic Modeling of Denitrifying Bacterial Growth: The Cybernetic Approach

    SciTech Connect

    Song, Hyun-Seob; Liu, Chongxuan

    2015-06-29

    Denitrification is a multistage reduction process converting nitrate ultimately to nitrogen gas, carried out mostly by facultative bacteria. Modeling of the denitrification process is challenging due to the complex metabolic regulation that modulates sequential formation and consumption of a series of nitrogen oxide intermediates, which serve as the final electron acceptors for denitrifying bacteria. In this work, we examined the effectiveness and accuracy of the cybernetic modeling framework in simulating the growth dynamics of denitrifying bacteria in comparison with kinetic models. In four different case studies using the literature data, we successfully simulated diauxic and triauxic growth patterns observed in anoxic and aerobic conditions, only by tuning two or three parameters. In order to understand the regulatory structure of the cybernetic model, we systematically analyzed the effect of cybernetic control variables on simulation accuracy. The results showed that the consideration of both enzyme synthesis and activity control through u- and v-variables is necessary and relevant and that uvariables are of greater importance in comparison to v-variables. In contrast, simple kinetic models were unable to accurately capture dynamic metabolic shifts across alternative electron acceptors, unless an inhibition term was additionally incorporated. Therefore, the denitrification process represents a reasonable example highlighting the criticality of considering dynamic regulation for successful metabolic modeling.

  7. Mechanistic modeling of turkey growth response to genotype and nutrition.

    PubMed

    Rivera-Torres, V; Ferket, P R; Sauvant, D

    2011-10-01

    Along with the fast genetic improvement, nutritional and environmental effects on poultry growth performance have made it necessary to develop growth models that have the flexibility to adapt to different genotypes and growing conditions. A mechanistic simulation model of energy and nutrient utilization in growing turkeys is presented herein. The model consists of simulating the average homeorhetic and homeostatic regulations associated with the utilization of circulating glucose, fatty acid, AA, and acetyl-CoA for protein and lipid retention in carcass, viscera, and feathers in a turkey population. Homeorhesis plays a major role in the control of protein and lipid turnover for the definition of genetic potential and feed intake, whereas homeostasis adjusts growth rate through protein and lipid turnover rates and, therefore, BW gain and feed intake to the growing conditions. Also, homeostasis enables the maintenance of a dynamic balance state during all the growing period through the control of circulating nutrient concentration. The model was developed and calibrated with experimental data that described energy utilization in male and female growing turkeys. Then, the ability of the model to adapt to genotypes and to predict the average response of a turkey population to dietary energy was evaluated. Model calibration showed simulations of energy and nutrient utilization that fitted well with the experimental data because ME was satisfyingly partitioned into heat production and energy retention as protein and lipid, and nutrient intake accurately partitioned BW gain into carcass, viscera, and feathers. The evaluation of the model was also satisfactory because BW gain and feed-to-gain ratio were globally in accordance with the observations in different male and female genotypes, in spite of an overestimation of the feed-to-gain ratio during the first weeks of age. Model evaluation showed that the BW gain and feed intake response of growing turkeys to dietary energy

  8. Growth mixture modeling with non-normal distributions.

    PubMed

    Muthén, Bengt; Asparouhov, Tihomir

    2015-03-15

    A limiting feature of previous work on growth mixture modeling is the assumption of normally distributed variables within each latent class. With strongly non-normal outcomes, this means that several latent classes are required to capture the observed variable distributions. Being able to relax the assumption of within-class normality has the advantage that a non-normal observed distribution does not necessitate using more than one class to fit the distribution. It is valuable to add parameters representing the skewness and the thickness of the tails. A new growth mixture model of this kind is proposed drawing on recent work in a series of papers using the skew-t distribution. The new method is illustrated using the longitudinal development of body mass index in two data sets. The first data set is from the National Longitudinal Survey of Youth covering ages 12-23 years. Here, the development is related to an antecedent measuring socioeconomic background. The second data set is from the Framingham Heart Study covering ages 25-65 years. Here, the development is related to the concurrent event of treatment for hypertension using a joint growth mixture-survival model.

  9. Plane strain crack growth models for fatigue crack growth life predictions

    SciTech Connect

    Bloom, J.M.; Daniewicz, S.R.; Hechmer, J.L.

    1996-02-01

    Experimental data and analytical models have shown that a growing fatigue crack produces a plastic wake. This, in turn, leads to residual compressive stresses acting over the crack faces during the unloading portion of the fatigue cycle. This crack closure effect results in an applied stress intensity factor during unloading which is greater than that associated with the K{sub min}, thus producing a crack-driving force which is less than {Delta}K = K{sub max} {minus} K{sub min}. Life predictions which do not account for this crack closure effect give inaccurate life estimates, especially for fully reversed loadings. This paper discusses the development of a crack closure expression for the 4-point bend specimen using numerical results obtained from a modified strip-yield model. Data from tests of eight 4-point bend specimens were used to estimate the specimen constraint factor (stress triaxiality effect). The constraint factor was then used in the estimation of the crack opening stresses for each of the bend tests. The numerically estimated crack opening stresses were used to develop an effective stress intensity factor range, {Delta}K{sub eff}. The resulting crack growth rate data when plotted versus {Delta}K{sub eff} resulted in a material fatigue crack growth rate property curve independent of test specimen type, stress level, and R-ratio. Fatigue crack growth rate data from center-cracked panels using Newman`s crack closure model, from compact specimens using Eason`s R-ratio expression, and from bend specimens using the model discussed in this paper are all shown to fall along the same straight line (on log-log paper) when plotted versus {Delta}K{sub eff}, even though crack closure differs for each specimen type.

  10. Velocity selection in the symmetric model of dendritic crystal growth

    NASA Technical Reports Server (NTRS)

    Barbieri, Angelo; Hong, Daniel C.; Langer, J. S.

    1987-01-01

    An analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth is presented. The analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needle-like solidification fronts in the limit of small under-cooling Delta. For the two-dimensional symmetric model with a capillary anisotropy of strength alpha, it is found that the velocity is proportional to (Delta to the 4th) times (alpha exp 7/4). The application of the method in three dimensions is also described.

  11. Simulation model for plant growth in controlled environment systems

    NASA Technical Reports Server (NTRS)

    Raper, C. D., Jr.; Wann, M.

    1986-01-01

    The role of the mathematical model is to relate the individual processes to environmental conditions and the behavior of the whole plant. Using the controlled-environment facilities of the phytotron at North Carolina State University for experimentation at the whole-plant level and methods for handling complex models, researchers developed a plant growth model to describe the relationships between hierarchial levels of the crop production system. The fundamental processes that are considered are: (1) interception of photosynthetically active radiation by leaves, (2) absorption of photosynthetically active radiation, (3) photosynthetic transformation of absorbed radiation into chemical energy of carbon bonding in solube carbohydrates in the leaves, (4) translocation between carbohydrate pools in leaves, stems, and roots, (5) flow of energy from carbohydrate pools for respiration, (6) flow from carbohydrate pools for growth, and (7) aging of tissues. These processes are described at the level of organ structure and of elementary function processes. The driving variables of incident photosynthetically active radiation and ambient temperature as inputs pertain to characterization at the whole-plant level. The output of the model is accumulated dry matter partitioned among leaves, stems, and roots; thus, the elementary processes clearly operate under the constraints of the plant structure which is itself the output of the model.

  12. How Well Does Growth Mixture Modeling Identify Heterogeneous Growth Trajectories? A Simulation Study Examining GMM's Performance Characteristics

    ERIC Educational Resources Information Center

    Peugh, James; Fan, Xitao

    2012-01-01

    Growth mixture modeling (GMM) has become a more popular statistical method for modeling population heterogeneity in longitudinal data, but the performance characteristics of GMM enumeration indexes in correctly identifying heterogeneous growth trajectories are largely unknown. Few empirical studies have addressed this issue. This study considered…

  13. Persistent G. lamblia impairs growth in a murine malnutrition model

    PubMed Central

    Bartelt, Luther A.; Roche, James; Kolling, Glynis; Bolick, David; Noronha, Francisco; Naylor, Caitlin; Hoffman, Paul; Warren, Cirle; Singer, Steven; Guerrant, Richard

    2013-01-01

    Giardia lamblia infections are nearly universal among children in low-income countries and are syndemic with the triumvirate of malnutrition, diarrhea, and developmental growth delays. Amidst the morass of early childhood enteropathogen exposures in these populations, G. lamblia–specific associations with persistent diarrhea, cognitive deficits, stunting, and nutrient deficiencies have demonstrated conflicting results, placing endemic pediatric giardiasis in a state of equipoise. Many infections in endemic settings appear to be asymptomatic/subclinical, further contributing to uncertainty regarding a causal link between G. lamblia infection and developmental delay. We used G. lamblia H3 cyst infection in a weaned mouse model of malnutrition to demonstrate that persistent giardiasis leads to epithelial cell apoptosis and crypt hyperplasia. Infection was associated with a Th2-biased inflammatory response and impaired growth. Malnutrition accentuated the severity of these growth decrements. Faltering malnourished mice exhibited impaired compensatory responses following infection and demonstrated an absence of crypt hyperplasia and subsequently blunted villus architecture. Concomitantly, severe malnutrition prevented increases in B220+ cells in the lamina propria as well as mucosal Il4 and Il5 mRNA in response to infection. These findings add insight into the potential role of G. lamblia as a “stunting” pathogen and suggest that, similarly, malnourished children may be at increased risk of G. lamblia–potentiated growth decrements. PMID:23728173

  14. Altered tumor cell growth and tumorigenicity in models of microgravity

    NASA Astrophysics Data System (ADS)

    Yamauchi, K.; Taga, M.; Furian, L.; Odle, J.; Sundaresan, A.; Pellis, N.; Andrassy, R.; Kulkarni, A.

    Spaceflight environment and microgravity (MG) causes immune dysfunction and is a major health risk to humans, especially during long-term space missions. The effects of microgravity environment on tumor growth and carcinogenesis are yet unknown. Hence, we investigated the effects of simulated MG (SMG) on tumor growth and tumorigenicity using in vivo and in vitro models. B16 melanoma cells were cultured in static flask (FL) and rotating wall vessel bioreactors (BIO) to measure growth and properties, melanin production and apoptosis. BIO cultures had 50% decreased growth (p<0.01), increased doubling time and a 150% increase in melanin production (p<0.05). Flow cytometric analysis showed increased apoptosis in BIO. When BIO cultured melanoma cells were inoculated sc in mice there was a significant increase in tumorigenicity as compared to FL cells. Thus SMG may have supported &selected highly tumorigenic cells and it is pos sible that in addition to decreased immune function MG may alter tumor cell characteristics and invasiveness. Thus it is important to study effects of microgravity environment and its stressors using experimental tumors and SMG to understand and evaluate carcinogenic responses to true microgravity. Further studies on carcinogenic events and their mechanisms will allow us develop and formulate countermeasures and protect space travelers. Additional results will be presented. (Supported by NASA NCC8-168 grant, ADK)

  15. Models of lipid droplets growth and fission in adipocyte cells

    SciTech Connect

    Boschi, Federico; Rizzatti, Vanni; Zamboni, Mauro; Sbarbati, Andrea

    2015-08-15

    (fission and the decrease through neutral lipid exit from pre-existing droplets) to reproduce their size reduction observed in lipolytic conditions. The results suggest that each single process, considered alone, can not be considered the only responsible for the size variation observed, but more than one of them, playing together, can quite well reproduce the experimental data. - Highlights: The growth and fission of the lipid droplets (LDs) were computationally simulated. To write and test the growth and fission models more than 110,000 LDs were measured. The usual processes considered alone, are not able to justify the experimental data. Some processes, playing together, can explain the growth and fission.

  16. Evaluating Model Fit for Growth Curve Models: Integration of Fit Indices from SEM and MLM Frameworks

    ERIC Educational Resources Information Center

    Wu, Wei; West, Stephen G.; Taylor, Aaron B.

    2009-01-01

    Evaluating overall model fit for growth curve models involves 3 challenging issues. (a) Three types of longitudinal data with different implications for model fit may be distinguished: balanced on time with complete data, balanced on time with data missing at random, and unbalanced on time. (b) Traditional work on fit from the structural equation…

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  18. Media alert in an SIS epidemic model with logistic growth.

    PubMed

    Wang, Lianwen; Zhou, Da; Liu, Zhijun; Xu, Dashun; Zhang, Xinan

    2017-03-01

    In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium.

  19. 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.

  20. Contract Over Target Baseline (OTB) Effect on Earned Value Management’s Cost Performance Index (CPI)

    DTIC Science & Technology

    2010-06-17

    In 2009, Trahan found that the Gompertz growth curve better predicted program Estimates at Completion (EAC) for OTB contracts. In 2010, Thickstun...In 2009, Trahan found that nonlinear growth modeling, specifically the Gompertz growth curve, better predicted program Estimates at Completion...models only outperform index-based models at early stages of completion (Tracy, 2005). In 2009 Trahan produced three EAC models using the Gompertz

  1. The growth of structure in interacting dark energy models

    SciTech Connect

    Caldera-Cabral, Gabriela; Maartens, Roy; Schaefer, Bjoern Malte E-mail: roy.maartens@port.ac.uk

    2009-07-01

    If dark energy interacts with dark matter, there is a change in the background evolution of the universe, since the dark matter density no longer evolves as a{sup −3}. In addition, the non-gravitational interaction affects the growth of structure. In principle, these changes allow us to detect and constrain an interaction in the dark sector. Here we investigate the growth factor and the weak lensing signal for a new class of interacting dark energy models. In these models, the interaction generalises the simple cases where one dark fluid decays into the other. In order to calculate the effect on structure formation, we perform a careful analysis of the perturbed interaction and its effect on peculiar velocities. Assuming a normalization to today's values of dark matter density and overdensity, the signal of the interaction is an enhancement (suppression) of both the growth factor and the lensing power, when the energy transfer in the background is from dark matter to dark energy (dark energy to dark matter)

  2. A simple model for dislocation emission mediated dynamic nanovoid growth

    NASA Astrophysics Data System (ADS)

    Wilkerson, Justin; Ramesh, K. T.

    2015-06-01

    Failure of ductile metals has long been attributed to the microscopic processes of void nucleation, growth, and finally coalescence leading to fracture. Our traditional view of void nucleation is associated with interface debonding at second-phase particles. However, much of this understanding has been gleaned from observations of quasi-static fracture surfaces. Under more extreme dynamic loading conditions second-phase particles may not necessarily be the dominant source of void nucleating material defects, and a few key experimental observations of laser spall surfaces seem to support this assertion. Here, we motivate an alternative mechanism to the traditional view, namely shock-induced vacancy generation and clustering followed by nanovoid growth mediated by dislocation emission. This mechanism only becomes active at very large stresses, and thus it is desirable to establish a closed-form criterion for the macroscopic stress required to activate dislocation emission in porous materials. Following an approach similar to Lubarda and co-workers, we make use of stability arguments applied to the analytic solutions of the elastic interactions of dislocations and voids to derive the desired criterion. We then propose a dynamic nanovoid growth law that is motivated by the kinetics of dislocation emission. The resulting failure model is validated against a number of molecular dynamics simulations with favorable agreement. Lastly, we make use of our simple model to predict some interesting anomalous behaviors associated with high surface energies and nonlinear elasticity.

  3. 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.

  4. 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.

  5. A mathematical model of tumour angiogenesis: growth, regression and regrowth.

    PubMed

    Vilanova, Guillermo; Colominas, Ignasi; Gomez, Hector

    2017-01-01

    Cancerous tumours have the ability to recruit new blood vessels through a process called angiogenesis. By stimulating vascular growth, tumours get connected to the circulatory system, receive nutrients and open a way to colonize distant organs. Tumour-induced vascular networks become unstable in the absence of tumour angiogenic factors (TAFs). They may undergo alternating stages of growth, regression and regrowth. Following a phase-field methodology, we propose a model of tumour angiogenesis that reproduces the aforementioned features and highlights the importance of vascular regression and regrowth. In contrast with previous theories which focus on vessel remodelling due to the absence of flow, we model an alternative regression mechanism based on the dependency of tumour-induced vascular networks on TAFs. The model captures capillaries at full scale, the plastic dynamics of tumour-induced vessel networks at long time scales, and shows the key role played by filopodia during angiogenesis. The predictions of our model are in agreement with in vivo experiments and may prove useful for the design of antiangiogenic therapies.

  6. Micromechanical model of crack growth in fiber reinforced brittle materials

    NASA Technical Reports Server (NTRS)

    Rubinstein, Asher A.; Xu, Kang

    1990-01-01

    A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution.

  7. Generalized model for solid-on-solid interface growth.

    PubMed

    Richele, M F; Atman, A P F

    2015-05-01

    We present a probabilistic cellular automaton (PCA) model to study solid-on-solid interface growth in which the transition rules depend on the local morphology of the profile obtained from the interface representation of the PCA. We show that the model is able to reproduce a wide range of patterns whose critical roughening exponents are associated to different universality classes, including random deposition, Edwards-Wilkinson, and Kardar-Parisi-Zhang. By means of the growth exponent method, we consider a particular set of the model parameters to build the two-dimensional phase diagram corresponding to a planar cut of the higher dimensional parameter space. A strong indication of phase transition between different universality classes can be observed, evincing different regimes of deposition, from layer-by-layer to Volmer-Weber and Stransk-Krastanov-like modes. We expect that this model can be useful to predict the morphological properties of interfaces obtained at different surface deposition problems, since it allows us to simulate several experimental situations by setting the values of the specific transition probabilities in a very simple and direct way.

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  9. Simulating cancer growth with multiscale agent-based modeling.

    PubMed

    Wang, Zhihui; Butner, Joseph D; Kerketta, Romica; Cristini, Vittorio; Deisboeck, Thomas S

    2015-02-01

    There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we further describe several experimentally testable hypotheses generated by those models. We also discuss some of the current challenges of multiscale agent-based cancer models.

  10. Polarity-Driven Geometrical Cluster Growth Model of Budding Yeast

    NASA Astrophysics Data System (ADS)

    Cabral, Reniel B.; Lim, May T.

    We present a polarity-driven activator-inhibitor model of budding yeast in a two-dimensional medium wherein impeding metabolites secretion (or growth inhibitors) and growth directionality are determined by the local nutrient level. We found that colony size and morphological features varied with nutrient concentration. A branched-type morphology is associated with high impeding metabolite concentration together with a high fraction of distal budding, while opposite conditions (low impeding metabolite concentration, high fraction of proximal budding) promote Eden-type patterns. Increasing the anisotropy factor (or polarity) produced other spatial patterns akin to the electrical breakdown under varying electric field. Rapid changes in the colony morphology, which we conjecture to be equivalent to a transition from an inactive quiescent state to an active budding state, appeared when nutrients were limited.

  11. Existence of Periodic Solutions for a Modified Growth Solow Model

    NASA Astrophysics Data System (ADS)

    Fabião, Fátima; Borges, Maria João

    2010-10-01

    In this paper we analyze the dynamic of the Solow growth model with a Cobb-Douglas production function. For this purpose, we consider that the labour growth rate, L'(t)/L(t), is a T-periodic function, for a fixed positive real number T. We obtain the closed form solutions for the fundamental Solow equation with the new description of L(t). Using notions of the qualitative theory of ordinary differential equations and nonlinear functional analysis, we prove that there exists one T-periodic solution for the Solow equation. From the economic point of view this is a new result which allows a more realistic interpretation of the stylized facts.

  12. Modeling hairy root tissue growth in in vitro environments using an agent-based, structured growth model.

    PubMed

    Lenk, Felix; Sürmann, Almuth; Oberthür, Patrick; Schneider, Mandy; Steingroewer, Juliane; Bley, Thomas

    2014-06-01

    An agent-based model for simulating the in vitro growth of Beta vulgaris hairy root cultures is described. The model fitting is based on experimental results and can be used as a virtual experimentator for root networks. It is implemented in the JAVA language and is designed to be easily modified to describe the growth of diverse biological root networks. The basic principles of the model are outlined, with descriptions of all of the relevant algorithms using the ODD protocol, and a case study is presented in which it is used to simulate the development of hairy root cultures of beetroot (Beta vulgaris) in a Petri dish. The model can predict various properties of the developing network, including the total root length, branching point distribution, segment distribution and secondary metabolite accumulation. It thus provides valuable information that can be used when optimizing cultivation parameters (e.g., medium composition) and the cultivation environment (e.g., the cultivation temperature) as well as how constructional parameters change the morphology of the root network. An image recognition solution was used to acquire experimental data that were used when fitting the model and to evaluate the agreement between the simulated results and practical experiments. Overall, the case study simulation closely reproduced experimental results for the cultures grown under equivalent conditions to those assumed in the simulation. A 3D-visualization solution was created to display the simulated results relating to the state of the root network and its environment (e.g., oxygen and nutrient levels).

  13. A multiphase model for three-dimensional tumor growth

    NASA Astrophysics Data System (ADS)

    Sciumè, G.; Shelton, S.; Gray, W. G.; Miller, C. T.; Hussain, F.; Ferrari, M.; Decuzzi, P.; Schrefler, B. A.

    2013-01-01

    Several mathematical formulations have analyzed the time-dependent behavior of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the thermodynamically constrained averaging theory. A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TCs), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HCs); and an interstitial fluid for the transport of nutrients. The equations are solved by a finite element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTSs) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behavior: initially, the rapidly growing TCs tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable TCs whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case—mostly due to the relative adhesion of the TCs and HCs to the ECM, and the less favorable transport of nutrients. In particular, for HCs adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas TC

  14. A multiphase model for three-dimensional tumor growth

    PubMed Central

    Sciumè, G; Shelton, S; Gray, WG; Miller, CT; Hussain, F; Ferrari, M; Decuzzi, P; Schrefler, BA

    2014-01-01

    Several mathematical formulations have analyzed the time-dependent behaviour of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the Thermodynamically Constrained Averaging Theory (TCAT). A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TC), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HC); and an interstitial fluid (IF) for the transport of nutrients. The equations are solved by a Finite Element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTS) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behaviour: initially, the rapidly growing tumor cells tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable tumor cells whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case – mostly due to the relative adhesion of the tumor and healthy cells to the ECM, and the less favourable transport of nutrients. In particular, for tumor cells adhering less avidly to the ECM, the healthy tissue is progressively displaced

  15. Growth of the human eye lens

    PubMed Central

    2007-01-01

    Purpose To analyze human lens growth from the accumulation of wet weight as a function of age. Methods Wet weights were assembled for over 1,100 human lenses, ranging in age from 6 months prenatal to 99 years postnatal, and were examined using various growth models. Initially, prenatal and postnatal data were examined separately, to determine the growth modes and then all data were fitted to a single equation. Results Variations in weights due to tissue handling procedures and the unavailability of statistical data for averaged sets precluded the use of >500 values in the present analysis. Regression of age on log lens weight for the remaining 614 lenses indicated that, unlike other species, human lens growth appears to take place in two distinct phases. It was found that asymptotic growth during prenatal life and early childhood generates about 149 mg of tissue in a process, which can be modelled with a Gompertz function. Soon after birth, growth becomes linear, dropping to 1.38 mg/year, and this rate is maintained throughout the rest of life. The relationship of lens wet weight with age over the whole of the lifespan could best be described with the expression, W=1.38Ab + 149exp^[exp^(1.6-3Ac)], where W is lens weight in mg, Ab is postnatal age in years and Ac is the time since conception in years. Comparison of 138 male and 64 female lenses indicated that there was no statistically significant difference between male and female lens weights in the linear (adult) growth mode. Conclusions Human lens growth differs from growth in other species in that it occurs in two distinct modes. The first follows a sigmoidal relationship and provides an initial burst of rapid growth during prenatal development with an apparent termination at or shortly after birth. The second growth mode is linear, adding 1.38 mg/year to lens wet weight, throughout life. Because of the variability in available lens wet weight data, further studies, preferably using lens dry weights or protein

  16. An overview of reliability growth models and their potential use for NASA applications

    NASA Technical Reports Server (NTRS)

    Taneja, V. S.; Safie, F. M.

    1992-01-01

    An overview is provided of reliability growth literature over the past 25 years. This includes a thorough literature review of different areas of the application of reliability growth such as design, prediction, tracking/management, and demonstration. Various reliability growth models use different bases on how they characterize growth. Different models are discussed. Also, the use is addressed of reliability growth models to NASA applications. This includes the application of these models to the space shuttle main engine. For potential NASA applications, we classify growth models in two groups, which are characterized.

  17. [Autowaves in a model of growth of an invasive tumor].

    PubMed

    Kolobov, A V; Gubernov, V V; Polezhaev, A A

    2009-01-01

    A mathematical model for the invasive tumour growth has been constructed, which takes cell division, death, and motility into account. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumour proliferation rate and structure. The model adequately describes the experimentally measured rate of tumour proliferation. The existence of autowave solutions has been demonstrated, and their properties have been investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the speed selection and the convergence of the initial conditions to the automodel solution.

  18. Stochastic resonance in a generalized Von Foerster population growth model

    SciTech Connect

    Lumi, N.; Mankin, R.

    2014-11-12

    The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.

  19. 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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  20. Searching for new mathematical growth model approaches for Listeria monocytogenes.

    PubMed

    Valero, A; Hervás, C; García-Gimeno, R M; Zurera, G

    2007-01-01

    Different secondary modeling approaches for the estimation of Listeria monocytogenes growth rate as a function of temperature (4 to 30 degrees C), citric acid (0% to 0.4% w/v), and ascorbic acid (0% to 0.4% w/v) are presented. Response surface (RS) and square-root (SR) models are proposed together with different artificial neural networks (ANN) based on product functions units (PU), sigmoidal functions units (SU), and a novel approach based on the use of hybrid functions units (PSU), which results from a combination of PU and SU. In this study, a significantly better goodness-of-fit was obtained in the case of the ANN models presented, reflected by the lower SEP values obtained (< 24.23 for both training and generalization datasets). Among these models, the SU model provided the best generalization capacity, displaying lower RMSE and SEP values, with fewer parameters compared to the PU and PSU models. The bias factor (B(f)) and accuracy factor (A(f)) of the mathematical validation dataset were above 1 in all cases, providing fail-safe predictions. The balance between generalization properties and the ease of use is the main consideration when applying secondary modeling approaches to achieve accurate predictions about the behavior of microorganisms.

  1. Modelling the interaction between flooding events and economic growth

    NASA Astrophysics Data System (ADS)

    Grames, Johanna; Fürnkranz-Prskawetz, Alexia; Grass, Dieter; Viglione, Alberto; Blöschl, Günter

    2016-04-01

    Recently socio-hydrology models have been proposed to analyze the interplay of community risk-coping culture, flooding damage and economic growth. These models descriptively explain the feedbacks between socio-economic development and natural disasters such as floods. Complementary to these descriptive models, we develop a dynamic optimization model, where the inter-temporal decision of an economic agent interacts with the hydrological system. This interdisciplinary approach matches with the goals of Panta Rhei i.e. to understand feedbacks between hydrology and society. It enables new perspectives but also shows limitations of each discipline. Young scientists need mentors from various scientific backgrounds to learn their different research approaches and how to best combine them such that interdisciplinary scientific work is also accepted by different science communities. In our socio-hydrology model we apply a macro-economic decision framework to a long-term flood-scenario. We assume a standard macro-economic growth model where agents derive utility from consumption and output depends on physical capital that can be accumulated through investment. To this framework we add the occurrence of flooding events which will destroy part of the capital. We identify two specific periodic long term solutions and denote them rich and poor economies. Whereas rich economies can afford to invest in flood defense and therefore avoid flood damage and develop high living standards, poor economies prefer consumption instead of investing in flood defense capital and end up facing flood damages every time the water level rises. Nevertheless, they manage to sustain at least a low level of physical capital. We identify optimal investment strategies and compare simulations with more frequent and more intense high water level events.

  2. The boundary for growth of Zygosaccharomyces bailii in acidified products described by models for time to growth and probability of growth.

    PubMed

    Jenkins, P; Poulos, P G; Cole, M B; Vandeven, M H; Legan, J D

    2000-02-01

    Models to predict days to growth and probability of growth of Zygosaccharomyces bailii in high-acid foods were developed, and the equations are presented here. The models were constructed from measurements of growth of Z. bailii using automated turbidimetry over a 29-day period at various pH, NaCl, fructose, and acetic acid levels. Statistical analyses were carried out using Statistical Analysis Systems LIFEREG procedures, and the data were fitted to log-logistic models. Model 1 predicts days to growth based on two factors, combined molar concentration of salt plus sugar and undissociated acetic acid. This model allows a growth/no-growth boundary to be visualized. The boundary is comparable with that established by G. Tuynenburg Muys (Process Biochem. 6:25-28, 1971), which still forms the basis of industry assumptions about the stability of acidic foods. Model 2 predicts days to growth based on the four independent factors of salt, sugar, acetic acid, and pH levels and is, therefore, much more useful for product development. Validation data derived from challenge studies in retail products from the U.S. market are presented for Model 2, showing that the model gives reliable, fail-safe predictions and is suitable for use in predicting growth responses of Z. bailii in high-acid foods. Model 3 predicts probability of growth of Z. bailii in 29 days. This model is most useful for spoilage risk assessment. All three models showed good agreement between predictions and observed values for the underlying data.

  3. Modeling fatigue crack growth in cross ply titanium matrix composites

    NASA Technical Reports Server (NTRS)

    Bakuckas, J. G., Jr.; Johnson, W. S.

    1993-01-01

    In this study, the fatigue crack growth behavior of fiber bridging matrix cracks in cross-ply SCS-6/Ti-15-3 and SCS-6/Timetal-21S laminates containing center holes was investigated. Experimental observations revealed that matrix cracking was far more extensive and wide spread in the SCS-6/Ti-15-3 laminates compared to that in the SCS-6/Timetal-21S laminates. In addition, the fatigue life of the SCS-6/Ti-15-3 laminates was significantly longer than that of the SCS-6/Timetal-21S laminates. The matrix cracking observed in both material systems was analyzed using a fiber bridging (FB) model which was formulated using the boundary correction factors and weight functions for center hole specimen configurations. A frictional shear stress is assumed in the FB model and was used as a curve fitting parameter to model matrix crack growth data. The higher frictional shear stresses calculated in the SCS-6/Timetal-21S laminates resulted in lower stress intensity factors in the matrix and higher axial stresses in the fibers compared to those in the SCS-6/Ti-15-3 laminates at the same applied stress levels.

  4. Modeling biological tissue growth: discrete to continuum representations.

    PubMed

    Hywood, Jack D; Hackett-Jones, Emily J; Landman, Kerry A

    2013-09-01

    There is much interest in building deterministic continuum models from discrete agent-based models governed by local stochastic rules where an agent represents a biological cell. In developmental biology, cells are able to move and undergo cell division on and within growing tissues. A growing tissue is itself made up of cells which undergo cell division, thereby providing a significant transport mechanism for other cells within it. We develop a discrete agent-based model where domain agents represent tissue cells. Each agent has the ability to undergo a proliferation event whereby an additional domain agent is incorporated into the lattice. If a probability distribution describes the waiting times between proliferation events for an individual agent, then the total length of the domain is a random variable. The average behavior of these stochastically proliferating agents defining the growing lattice is determined in terms of a Fokker-Planck equation, with an advection and diffusion term. The diffusion term differs from the one obtained Landman and Binder [J. Theor. Biol. 259, 541 (2009)] when the rate of growth of the domain is specified, but the choice of agents is random. This discrepancy is reconciled by determining a discrete-time master equation for this process and an associated asymmetric nonexclusion random walk, together with consideration of synchronous and asynchronous updating schemes. All theoretical results are confirmed with numerical simulations. This study furthers our understanding of the relationship between agent-based rules, their implementation, and their associated partial differential equations. Since tissue growth is a significant cellular transport mechanism during embryonic growth, it is important to use the correct partial differential equation description when combining with other cellular functions.

  5. Modelling the solution growth of TGS crystals in low gravity

    NASA Technical Reports Server (NTRS)

    Nadarajah, Arunan; Rosenberger, Franz; Alexander, J. Iwan D.

    1990-01-01

    The experimental growth of triglycine sulfate (TGS) crystals from aqueous solution is modeled here in two dimensions using the PHOENICS finite volume code. Simulations are carried out for steady, impulsive, and periodic accelerations in order to determine tolerable acceleration levels. Scaling arguments are used to estimate the times required for thermal and solutal variations from the initial equilibrium state to be diffusively transported throughout the system, and to obtain order of magnitude information on the relative magnitudes of diffusive and convective transport. The computed concentration fields reflect the features of the concentration distributions found experimentally during experiments conducted aboard Spacelab 3 in 1985.

  6. Minimal models of growth and decline of microbial populations.

    PubMed

    Juška, Alfonsas

    2011-01-21

    Dynamics of growth and decline of microbial populations were analysed and respective models were developed in this investigation. Analysis of the dynamics was based on general considerations concerning the main properties of microorganisms and their interactions with the environment which was supposed to be affected by the activity of the population. Those considerations were expressed mathematically by differential equations or systems of the equations containing minimal sets of parameters characterizing those properties. It has been found that: (1) the factors leading to the decline of the population have to be considered separately, namely, accumulation of metabolites (toxins) in the medium and the exhaustion of resources; the latter have to be separated again into renewable ('building materials') and non-renewable (sources of energy); (2) decline of the population is caused by the exhaustion of sources of energy but no decline is predicted by the model because of the exhaustion of renewable resources; (3) the model determined by the accumulation of metabolites (toxins) in the medium does not suggest the existence of a separate 'stationary phase'; (4) in the model determined by the exhaustion of energy resources the 'stationary' and 'decline' phases are quite discernible; and (5) there is no symmetry in microbial population dynamics, the decline being slower than the rise. Mathematical models are expected to be useful in getting insight into the process of control of the dynamics of microbial populations. The models are in agreement with the experimental data.

  7. Modeling the growth of an altered layer in mineral weathering

    NASA Astrophysics Data System (ADS)

    Reis, Fábio D. A. Aarão

    2015-10-01

    A stochastic reaction-diffusion model on a lattice is introduced to describe the growth kinetics of an altered layer in the weathering of a mineral. Particles R represent H2O that permanently fills the outer surface and diffuse on M (mineral) and A (altered) sites with coefficients DM and DA , respectively. The transformation M + R → A occurs with rate r, representing the irreversible formation of the altered material in a region of molecular size, viz. the lattice site of size a. These assumptions agree with predictions of the interfacial dissolution-reprecipitation mechanism, although the model does not describe the chemistry of dissolution reactions or precipitation processes. Scaling concepts are used to distinguish kinetic regimes and their crossovers, and are supported by simulation results. In the short time reactive regime, the thickness of the altered layer increases linearly in time and filling of that layer by particles R is high. In the long time diffusive regime, the altered layer thickness grows as (DA t) 1 / 2 . Modeling of single crystals require very small values of DM , which produces atomically narrow interfaces between the altered material and the mineral and absence of R in the latter, in agreement with recent experimental results. If r growth velocity of the altered layer by a factor lAM / a , but no fluid in the bulk mineral. Estimates of the order of magnitude of transformation rates and of diffusion coefficients are obtained by application of the model to some recently studied systems: calcite dissolution, labradorite weathering, and silicate glass weathering. Effects of dissolution of the altered layer are analyzed. Significant differences between the model and leached layer theories are discussed.

  8. Age, growth and maturity of the pelagic thresher Alopias pelagicus and the scalloped hammerhead Sphyrna lewini.

    PubMed

    Drew, M; White, W T; Dharmadi; Harry, A V; Huveneers, C

    2015-01-01

    Indonesia has the greatest reported chondrichthyan catches worldwide, with c.110,000 t caught annually. The pelagic thresher (Alopias pelagicus) and scalloped hammerhead (Sphryna lewini) together comprise about 25% of the total catches of sharks landed in Indonesia. Age and growth parameters were estimated for A. pelagicus and S. lewini from growth-band counts of thin-cut vertebral sections. Alopias pelagicus (n = 158) and S. lewini (n = 157) vertebrae were collected from three Indonesian fish markets over a 5 year period. A multi-model analysis was used to estimate growth parameters for both species. The models of best fit for males and females for A. pelagicus was the three-parameter logistic (L∞ = 3169 mm LT , k = 0·2) and the two-parameter von Bertalanffy models (L∞ = 3281 mm LT , k = 0·12). Age at maturity was calculated to be 10·4 and 13·2 years for males and females, respectively, and these are the oldest estimated for this species. The samples of S. lewini were heavily biased towards females, and the model of best fit for males and females was the three-parameter Gompertz (L∞ = 2598 mm LT , k = 0·15) and the two-parameter Gompertz (L∞ = 2896 mm LT , k= 0·16). Age at maturity was calculated to be 8·9 and 13·2 years for males and females, respectively. Although numerous age and growth studies have previously been undertaken on S. lewini, few studies have been able to obtain adequate samples from all components of the population because adult females, adult males and juveniles often reside in different areas. For the first time, sex bias in this study was towards sexually mature females, which are commonly lacking in previous biological studies on S. lewini. Additionally, some of the oldest aged specimens and highest age at maturity for both species were observed in this study. Both species exhibit slow rates of growth and late age at maturity, highlighting the need for a re-assessment of the relative resilience of these two

  9. Sample Size Requirements in Single- and Multiphase Growth Mixture Models: A Monte Carlo Simulation Study

    ERIC Educational Resources Information Center

    Kim, Su-Young

    2012-01-01

    Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the…

  10. A Proposed Model for Protein Crystal Nucleation and Growth

    NASA Technical Reports Server (NTRS)

    Pusey, Marc; Curreri, Peter A. (Technical Monitor)

    2002-01-01

    How does one take a molecule, strongly asymmetric in both shape and charge distribution, and assemble it into a crystal? We propose a model for the nucleation and crystal growth process for tetragonal lysozyme, based upon fluorescence, light, neutron, and X-ray scattering data, size exclusion chromatography experiments, dialysis kinetics, AFM, and modeling of growth rate data, from this and other laboratories. The first species formed is postulated to be a 'head to side' dimer. Through repeating associations involving the same intermolecular interactions this grows to a 4(sub 3) helix structure, that in turn serves as the basic unit for nucleation and subsequent crystal growth. High salt attenuates surface charges while promoting hydrophobic interactions. Symmetry facilitates subsequent helix-helix self-association. Assembly stability is enhanced when a four helix structure is obtained, with each bound to two neighbors. Only two unique interactions are required. The first are those for helix formation, where the dominant interaction is the intermolecular bridging anion. The second is the anti-parallel side-by-side helix-helix interaction, guided by alternating pairs of symmetry related salt bridges along each side. At this stage all eight unique positions of the P4(sub3)2(sub 1),2(sub 1) unit cell are filled. The process is one of a) attenuating the most strongly interacting groups, such that b) the molecules begin to self-associate in defined patterns, so that c) symmetry is obtained, which d) propagates as a growing crystal. Simple and conceptually obvious in hindsight, this tells much about what we are empirically doing when we crystallize macromolecules. By adjusting the growth parameters we are empirically balancing the intermolecular interactions, preferentially attenuating the dominant strong (for lysozyme the charged groups) while strengthening the lesser strong (hydrophobic) interactions. In the general case for proteins the lack of a singularly defined

  11. Information models of software productivity - Limits on productivity growth

    NASA Technical Reports Server (NTRS)

    Tausworthe, Robert C.

    1992-01-01

    Research into generalized information-metric models of software process productivity establishes quantifiable behavior and theoretical bounds. The models establish a fundamental mathematical relationship between software productivity and the human capacity for information traffic, the software product yield (system size), information efficiency, and tool and process efficiencies. An upper bound is derived that quantifies average software productivity and the maximum rate at which it may grow. This bound reveals that ultimately, when tools, methodologies, and automated assistants have reached their maximum effective state, further improvement in productivity can only be achieved through increasing software reuse. The reuse advantage is shown not to increase faster than logarithmically in the number of reusable features available. The reuse bound is further shown to be somewhat dependent on the reuse policy: a general 'reuse everything' policy can lead to a somewhat slower productivity growth than a specialized reuse policy.

  12. A mathematical model of pre-diagnostic glioma growth

    PubMed Central

    Sturrock, Marc; Hao, Wenrui; Schwartzbaum, Judith; Rempala, Grzegorz A.

    2015-01-01

    Due to their location, the malignant gliomas of the brain in humans are very difficult to treat in advanced stages. Blood-based biomarkers for glioma are needed for more accurate evaluation of treatment response as well as early diagnosis. However, biomarker research in primary brain tumors is challenging given their relative rarity and genetic diversity. It is further complicated by variations in the permeability of the blood brain barrier that affects the amount of marker released into the bloodstream. Inspired by recent temporal data indicating a possible decrease in serum glucose levels in patients with gliomas yet to be diagnosed, we present an ordinary differential equation model to capture early stage glioma growth. The model contains glioma-glucose-immune interactions and poses a potential mechanism by which this glucose drop can be explained. We present numerical simulations, parameter sensitivity analysis, linear stability analysis and a numerical experiment whereby we show how a dormant glioma can become malignant. PMID:26073722

  13. Network-based model of the growth of termite nests.

    PubMed

    Eom, Young-Ho; Perna, Andrea; Fortunato, Santo; Darrouzet, Eric; Theraulaz, Guy; Jost, Christian

    2015-12-01

    We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general.

  14. Hugl-1 inhibits glioma cell growth in intracranial model.

    PubMed

    Liu, Xuejiao; Lu, Dong; Ma, Peng; Liu, Huaqiang; Cao, Yuewen; Sang, Ben; Zhu, Xianlong; Shi, Qiong; Hu, Jinxia; Yu, Rutong; Zhou, Xiuping

    2015-10-01

    Drosophila lethal (2) giant larvae (lgl) has been reported as a tumor suppressor and could regulate the Drosophila hippo signaling. Human giant larvae-1(Hugl-1), one human homologue of Drosophila lgl, also has been reported to be involved in the development of some human cancers. However, whether Hugl-1 is associated with the pathogenesis of malignant gliomas remains poorly understood. In the present work, we examined the effect of Hugl-1 on glioma cell growth both in vitro and in vivo. Firstly, we found that Hugl-1 protein levels decreased in the human glioma tissues, suggesting that Hugl-1 is involved in glioma progression. Unfortunately, either stably or transiently over-expressing Hugl-1 did not affect glioma cell proliferation in vitro. In addition, Hugl-1 over-expression did not regulate hippo signaling pathway. Interestingly, over-expression of Hugl-1 not only inhibited gliomagenesis but also markedly inhibited cell proliferation and promoted the apoptosis of U251 cells in an orthotopic model of nude mice. Taken together, this study provides the evidence that Hugl-1 inhibits glioma cell growth in intracranial model of nude mice, suggesting that Hugl-1 might be a potential tumor target for glioma therapy.

  15. Network-based model of the growth of termite nests

    NASA Astrophysics Data System (ADS)

    Eom, Young-Ho; Perna, Andrea; Fortunato, Santo; Darrouzet, Eric; Theraulaz, Guy; Jost, Christian

    2015-12-01

    We present a model for the growth of the transportation network inside nests of the social insect subfamily Termitinae (Isoptera, termitidae). These nests consist of large chambers (nodes) connected by tunnels (edges). The model based on the empirical analysis of the real nest networks combined with pruning (edge removal, either random or weighted by betweenness centrality) and a memory effect (preferential growth from the latest added chambers) successfully predicts emergent nest properties (degree distribution, size of the largest connected component, average path lengths, backbone link ratios, and local graph redundancy). The two pruning alternatives can be associated with different genuses in the subfamily. A sensitivity analysis on the pruning and memory parameters indicates that Termitinae networks favor fast internal transportation over efficient defense strategies against ant predators. Our results provide an example of how complex network organization and efficient network properties can be generated from simple building rules based on local interactions and contribute to our understanding of the mechanisms that come into play for the formation of termite networks and of biological transportation networks in general.

  16. A model of bubble growth leading to xylem conduit embolism.

    PubMed

    Hölttä, T; Vesala, T; Nikinmaa, E

    2007-11-07

    The dynamics of a gas bubble inside a water conduit after a cavitation event was modeled. A distinction was made between a typical angiosperm conduit with a homogeneous pit membrane and a typical gymnosperm conduit with a torus-margo pit membrane structure. For conduits with torus-margo type pits pit membrane deflection was also modeled and pit aspiration, the displacement of the pit membrane to the low pressure side of the pit chamber, was found to be possible while the emboli was still small. Concurrent with pit aspiration, the high resistance to water flow out of the conduit through the cell walls or aspirated pits will make the embolism process slow. In case of no pit aspiration and always for conduits with homogeneous pit membranes, embolism growth is more rapid but still much slower than bubble growth in bulk water under similar water tension. The time needed for the embolism to fill a whole conduit was found to be dependent on pit and cell wall conductance, conduit radius, xylem water tension, pressure rise in adjacent conduits due to water freed from the embolising conduit, and the rigidity and structure of the pits in the case of margo-torus type pit membrane. The water pressure in the conduit hosting the bubble was found to occur almost immediately after bubble induction inside a conduit, creating a sudden tension release in the conduit, which can be detected by acoustic and ultra-acoustic monitoring of xylem cavitation.

  17. Integrative models of vascular remodeling during tumor growth

    PubMed Central

    Rieger, Heiko; Welter, Michael

    2015-01-01

    Malignant solid tumors recruit the blood vessel network of the host tissue for nutrient supply, continuous growth, and gain of metastatic potential. Angiogenesis (the formation of new blood vessels), vessel cooption (the integration of existing blood vessels into the tumor vasculature), and vessel regression remodel the healthy vascular network into a tumor-specific vasculature that is in many respects different from the hierarchically organized arterio-venous blood vessel network of the host tissues. Integrative models based on detailed experimental data and physical laws implement in silico the complex interplay of molecular pathways, cell proliferation, migration, and death, tissue microenvironment, mechanical and hydrodynamic forces, and the fine structure of the host tissue vasculature. With the help of computer simulations high-precision information about blood flow patterns, interstitial fluid flow, drug distribution, oxygen and nutrient distribution can be obtained and a plethora of therapeutic protocols can be tested before clinical trials. In this review, we give an overview over the current status of integrative models describing tumor growth, vascular remodeling, blood and interstitial fluid flow, drug delivery, and concomitant transformations of the microenvironment. © 2015 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. PMID:25808551

  18. Gene duplication models for directed networks with limits on growth

    NASA Astrophysics Data System (ADS)

    Enemark, Jakob; Sneppen, Kim

    2007-11-01

    Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted that growth via duplication would act as an implicit means of preferential attachment, and thereby provide the observed broad degree distributions of molecular networks. Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not a result of unidirectional growth. We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. We find that this in itself generates the observed scaling of transcription factors for genome sites in prokaryotes. The dynamical model can generate a scale-free degree distribution, p(k)\\propto 1/k^{\\gamma } , with exponent γ = 1 in the non-growing case, and with γ>1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions could generate features of genetic regulatory networks. Our steady state degree distribution is however too broad to be consistent with data, thereby suggesting that selective pruning acts as a main additional constraint on duplicated genes. Our analysis shows that gene duplication can only be a main cause for the observed broad degree distributions if there are also substantial recombinations between upstream regions of genes.

  19. Modelling the interaction between flooding events and economic growth

    NASA Astrophysics Data System (ADS)

    Grames, Johanna; Grass, Dieter; Prskawetz, Alexia; Blöschl, Günther

    2015-04-01

    Socio-hydrology describes the interaction between the socio-economy, water and population dynamics. Recent models analyze the interplay of community risk-coping culture, flooding damage and economic growth (Di Baldassarre, 2013, Viglione, 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. This is the first economic growth model describing the interaction between the consumption and investment decisions of an economic agent and the occurrence of flooding events: Investments in defense capital can avoid floods even when the water level is high, but on the other hand such investment competes with investment in productive capital and hence may reduce the level of consumption. When floods occur, the flood damage therefore depends on the existing defense capital. The aim is to find an optimal tradeoff between investments in productive versus defense capital such as to optimize the stream of consumption in the long-term. We assume a non-autonomous exogenous periodic rainfall function (Yevjevich et.al. 1990, Zakaria 2001) which implies that the long-term equilibrium will be periodic . With our model we aim to derive mechanisms that allow consumption smoothing in the long term, and at the same time allow for optimal investment in flood defense to maximize economic output. We choose an aggregate welfare function that depends on the consumption level of the society as the objective function. I.e. we assume a social planer with perfect foresight that maximizes the aggregate welfare function. Within our model framework we can also study whether the path and level of defense capital (that protects people from floods) is related to the time preference rate of the social planner. Our model also allows to investigate how the frequency

  20. Analysis of the Stability of Teacher-Level Growth Scores from the Student Growth Percentile Model. REL 2016-104

    ERIC Educational Resources Information Center

    Lash, Andrea; Makkonen, Reino; Tran, Loan; Huang, Min

    2016-01-01

    This study, undertaken at the request of the Nevada Department of Education, examined the stability over years of teacher-level growth scores from the Student Growth Percentile (SGP) model, which many states and districts have selected as a measure of effectiveness in their teacher evaluation systems. The authors conducted a generalizability study…

  1. An Examination of Growth in Vocabulary and Phonological Awareness in Early Childhood: An Individual Growth Model Approach

    ERIC Educational Resources Information Center

    Cassano, Christina Marie

    2013-01-01

    The present study used individual growth modeling to examine the role of specific forms (i.e., receptive, expressive, and definitional vocabulary and grammatical skill) and levels of oral vocabulary skill (i.e., 25th, 50th, or 75th percentile) in phonological awareness growth during the preschool and kindergarten years. Sixty-one,…

  2. Matrix models and stochastic growth in Donaldson-Thomas theory

    NASA Astrophysics Data System (ADS)

    Szabo, Richard J.; Tierz, Miguel

    2012-10-01

    We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

  3. Matrix models and stochastic growth in Donaldson-Thomas theory

    SciTech Connect

    Szabo, Richard J.; Tierz, Miguel

    2012-10-15

    We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

  4. Modelling spatial patterns of urban growth in Africa

    PubMed Central

    Linard, Catherine; Tatem, Andrew J.; Gilbert, Marius

    2013-01-01

    The population of Africa is predicted to double over the next 40 years, driving exceptionally high urban expansion rates that will induce significant socio-economic, environmental and health changes. In order to prepare for these changes, it is important to better understand urban growth dynamics in Africa and better predict the spatial pattern of rural-urban conversions. Previous work on urban expansion has been carried out at the city level or at the global level with a relatively coarse 5–10 km resolution. The main objective of the present paper was to develop a modelling approach at an intermediate scale in order to identify factors that influence spatial patterns of urban expansion in Africa. Boosted Regression Tree models were developed to predict the spatial pattern of rural-urban conversions in every large African city. Urban change data between circa 1990 and circa 2000 available for 20 large cities across Africa were used as training data. Results showed that the urban land in a 1 km neighbourhood and the accessibility to the city centre were the most influential variables. Results obtained were generally more accurate than results obtained using a distance-based urban expansion model and showed that the spatial pattern of small, compact and fast growing cities were easier to simulate than cities with lower population densities and a lower growth rate. The simulation method developed here will allow the production of spatially detailed urban expansion forecasts for 2020 and 2025 for Africa, data that are increasingly required by global change modellers. PMID:25152552

  5. Predicting Over Target Baseline (OTB) Acquisition Contracts

    DTIC Science & Technology

    2010-03-01

    perform better under specific circumstances. In 2009, Captain Trahan investigated the use of a Gompertz growth model for developing EACs. She found...the Gompertz growth model to develop better EACs. Furthermore, an OTB, by definition, recognizes a cost overrun. Therefore, the ability to predict...EACs) are calculated and look briefly at some of the past EAC research. Then we look specifically at calculating EACs using the Gompertz growth

  6. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

    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.

  8. 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

  9. 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.

  10. Growth Mixture Modeling: Application to Reading Achievement Data from a Large-Scale Assessment

    ERIC Educational Resources Information Center

    Bilir, Mustafa Kuzey; Binici, Salih; Kamata, Akihito

    2008-01-01

    The popularity of growth modeling has increased in psychological and cognitive development research as a means to investigate patterns of changes and differences between observation units over time. Random coefficient modeling, such as multilevel modeling and latent growth curve modeling as a special application of structural equation modeling are…

  11. Age and growth of chub mackerel ( Xcomber japonicus) in the East China and Yellow Seas using sectioned otolith samples

    NASA Astrophysics Data System (ADS)

    Li, Gang; Chen, Xinjun; Feng, Bo

    2008-11-01

    Although chub mackerel ( Scomber japonicus) is a primary pelagic fish species, we have only limited knowledge on its key life history processes. The present work studied the age and growth of chub mackerel in the East China and Yellow Seas. Age was determined by interpreting and counting growth rings on the sagitta otoliths of 252 adult fish caught by the Chinese commercial purse seine fleet during the period from November 2006 to January 2007 and 150 juveniles from bottom trawl surveys on the spawning ground in May 2006. The difference between the assumed birth date of 1st April and date of capture was used to adjust the age determined from counting the number of complete translucent rings. The parameters of three commonly used growth models, the von Bertalanffy, Logistic and Gompertz models, were estimated using the maximum likelihood method. Based on the Akaike Information Criterion ( AIC), the von Bertalanffy growth model was found to be the most appropriate model. The size-at-age and size-at-maturity values were also found to decrease greatly compared with the results achieved in the 1950s, which was caused by heavy exploitation over the last few decades.

  12. Development of a multi-classification neural network model to determine the microbial growth/no growth interface.

    PubMed

    Fernández-Navarro, Francisco; Valero, Antonio; Hervás-Martínez, César; Gutiérrez, Pedro A; García-Gimeno, Rosa M; Zurera-Cosano, Gonzalo

    2010-07-15

    Boundary models have been recognized as useful tools to predict the ability of microorganisms to grow at limiting conditions. However, at these conditions, microbial behaviour can vary, being difficult to distinguish between growth or no growth. In this paper, the data from the study of Valero et al. [Valero, A., Pérez-Rodríguez, F., Carrasco, E., Fuentes-Alventosa, J.M., García-Gimeno, R.M., Zurera, G., 2009. Modelling the growth boundaries of Staphylococcus aureus: Effect of temperature, pH and water activity. International Journal of Food Microbiology 133 (1-2), 186-194] belonging to growth/no growth conditions of Staphylococcus aureus against temperature, pH and a(w) were divided into three categorical classes: growth (G), growth transition (GT) and no growth (NG). Subsequently, they were modelled by using a Radial Basis Function Neural Network (RBFNN) in order to create a multi-classification model that was able to predict the probability of belonging at one of the three mentioned classes. The model was developed through an over sampling procedure using a memetic algorithm (MA) in order to balance in part the size of the classes and to improve the accuracy of the classifier. The multi-classification model, named Smote Memetic Radial Basis Function (SMRBF) provided a quite good adjustment to data observed, being able to correctly classify the 86.30% of training data and the 82.26% of generalization data for the three observed classes in the best model. Besides, the high number of replicates per condition tested (n=30) produced a smooth transition between growth and no growth. At the most stringent conditions, the probability of belonging to class GT was higher, thus justifying the inclusion of the class in the new model. The SMRBF model presented in this study can be used to better define microbial growth/no growth interface and the variability associated to these conditions so as to apply this knowledge to a food safety in a decision-making process.

  13. A Morpho-Elastic Model of Hyphal Tip Growth in Filamentous Organisms

    NASA Astrophysics Data System (ADS)

    Goriely, A.; Tabor, M.; Tongen, A.

    The growth of filamentous cells is modeled through the use of exact, nonlinear, elasticity theory for shells and membranes. The biomechanical model is able to capture the generic features of growth of a broad array of cells including actinomycetes, fungi, and root hairs. It also provides the means of studying the effects of external surface stresses. The growth mechanism is modeled by a process of incremental elastic growth in which the cell wall responds elastically to the continuous addition of new material.

  14. Modelling of frost formation and growth on microstuctured surface

    NASA Astrophysics Data System (ADS)

    Muntaha, Md. Ali; Haider, Md. Mushfique; Rahman, Md. Ashiqur

    2016-07-01

    Frost formation on heat exchangers is an undesirable phenomenon often encountered in different applications where the cold surface with a temperature below freezing point of water is exposed to humid air. The formation of frost on the heat transfer surface results in an increase in pressure drop and reduction in heat transfer, resulting in a reduction of the system efficiency. Many factors, including the temperature and moisture content of air, cold plate temperature, surface wettability etc., are known to affect frost formation and growth. In our present study, a model for frost growth on rectangular, periodic microgroove surfaces for a range of microgroove dimension (ten to hundreds of micron) is presented. The mathematical model is developed analytically by solving the governing heat and mass transfer equations with appropriate boundary conditions using the EES (Engineering Equation Solver) software. For temperature, a convective boundary condition at frost-air interface and a fixed cold plate surface temperature is used. Instead of considering the saturation or super-saturation models, density gradient at the surface is obtained by considering experimentally-found specified heat flux. The effect of surface wettability is incorporated by considering the distribution of condensed water droplets at the early stage of frost formation. Thickness, density and thermal conductivity of frost layer on the micro-grooved surfaces are found to vary with the dimension of the grooves. The variation of density and thickness of the frost layer on these micro-grooved surfaces under natural convection is numerally determined for a range of plate temperature and air temperature conditions and is compared with experimental results found in the open literature.

  15. Formation of algae growth constitutive relations for improved algae modeling.

    SciTech Connect

    Gharagozloo, Patricia E.; Drewry, Jessica Louise.

    2013-01-01

    This SAND report summarizes research conducted as a part of a two year Laboratory Directed Research and Development (LDRD) project to improve our abilities to model algal cultivation. Algae-based biofuels have generated much excitement due to their potentially large oil yield from relatively small land use and without interfering with the food or water supply. Algae mitigate atmospheric CO2 through metabolism. Efficient production of algal biofuels could reduce dependence on foreign oil by providing a domestic renewable energy source. Important factors controlling algal productivity include temperature, nutrient concentrations, salinity, pH, and the light-to-biomass conversion rate. Computational models allow for inexpensive predictions of algae growth kinetics in these non-ideal conditions for various bioreactor sizes and geometries without the need for multiple expensive measurement setups. However, these models need to be calibrated for each algal strain. In this work, we conduct a parametric study of key marine algae strains and apply the findings to a computational model.

  16. [Calculating the intrinsic growth rate: comparison of definition and model].

    PubMed

    Voronov, D A

    2005-01-01

    It was shown that well known equation r = ln[N(t2)/N(t1)]/(t2 - t1) is the definition of the average value of intrinsic growth rate of population r within any given interval of time t2-t1 and changing arbitrarity its numbers N(t). The common opinion considering the equation as suitable only for exponentially growing population was found to be incorrect. The fundamentally different approach is based on the calculation of r within the framework of demographic model, realized as Euler - Lotka equation or population projection matrices. However this model requires simultaneous realization of several assumptions improbable for natural populations: exponential change in population size, stable age structure and maintaining constant age-dependent birth and death rates. The calculation of r by definition requires the data on the dynamics of population numbers, whereas calculation on the basis of the model requires the demographic tables of birth and death rate, but not the population numbers. With the example of American ginseng it was shown that evalution of r by definition and model approaches could produce opposite results.

  17. Exploring the performance of logistic regression model types on growth/no growth data of Listeria monocytogenes.

    PubMed

    Gysemans, K P M; Bernaerts, K; Vermeulen, A; Geeraerd, A H; Debevere, J; Devlieghere, F; Van Impe, J F

    2007-03-20

    Several model types have already been developed to describe the boundary between growth and no growth conditions. In this article two types were thoroughly studied and compared, namely (i) the ordinary (linear) logistic regression model, i.e., with a polynomial on the right-hand side of the model equation (type I) and (ii) the (nonlinear) logistic regression model derived from a square root-type kinetic model (type II). The examination was carried out on the basis of the data described in Vermeulen et al. [Vermeulen, A., Gysemans, K.P.M., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2006-this issue. Influence of pH, water activity and acetic acid concentration on Listeria monocytogenes at 7 degrees C: data collection for the development of a growth/no growth model. International Journal of Food Microbiology. .]. These data sets consist of growth/no growth data for Listeria monocytogenes as a function of water activity (0.960-0.990), pH (5.0-6.0) and acetic acid percentage (0-0.8% (w/w)), both for a monoculture and a mixed strain culture. Numerous replicates, namely twenty, were performed at closely spaced conditions. In this way detailed information was obtained about the position of the interface and the transition zone between growth and no growth. The main questions investigated were (i) which model type performs best on the monoculture and the mixed strain data, (ii) are there differences between the growth/no growth interfaces of monocultures and mixed strain cultures, (iii) which parameter estimation approach works best for the type II models, and (iv) how sensitive is the performance of these models to the values of their nonlinear-appearing parameters. The results showed that both type I and II models performed well on the monoculture data with respect to goodness-of-fit and predictive power. The type I models were, however, more sensitive to anomalous data points. The situation was different for the mixed strain culture. In

  18. Phase field modelling on the growth dynamics of double voids of different sizes during czochralski silicon crystal growth

    NASA Astrophysics Data System (ADS)

    Guan, X. J.; Wang, J.

    2017-02-01

    To investigate their dynamics and interaction mechanisms, the growth process of the two voids with different sizes during Czochralski silicon crystal growth were simulated by use of an established phase field model and its corresponding program code. On the basis of the several phase field numerical simulation cases, the evolution laws of the double voids were acquired as follows: the phase field model is capable to simulate the growth process of double voids with different sizes; there are two modes of their growth, that is, either mutual integration or competitive growth; the exact moment of their fusion can be also captured, and it is τ of 7.078 (simulation time step of 14156) for the initial vacancy concentration of 0.02 and the initial space between two void centers of 44Δx.

  19. Lessons from a canine model of compensatory lung growth.

    PubMed

    Hsia, Connie C W

    2004-01-01

    For over a century, canines have been used to study adaptation to surgical lung resection or pneumonectomy (PNX) that results in a quantifiable and reproducible loss of lung units. As reviewed by Schilling (1965), the first successful experimental pneumonectomies were performed in dogs and rabbits in 1881. By the early 1920s, it was appreciated that dogs can function normally with one remaining lung that increases in volume to fill the thoracic cavity (Andrus, 1923; Heuer and Andrus, 1922; Heuer and Dunn, 1920); these pioneering observations paved the way for surgeons to perform major lung resection in patients. Reports in the 1950s (Schilling et al., 1956) detail surprisingly well-preserved work performance in dogs following staged resection of up to 70% of lung mass. Since then, the bulk of the literature on post-PNX adaptation has shifted to rodents, especially for defining molecular mediators of compensatory lung growth. Because rodents are smaller and easier to handle, more animals can be studied over a shorter duration, resulting in time and cost savings. On the other hand, key aspects of lung anatomy, development, and time course of response in the rodent do not mimic those in the human subject, and few rodent studies have related structural adaptation to functional consequences. In larger mammals, anatomical lung development more closely resembles that in humans, and physiological function can be readily measured. Because dogs are natural athletes, functional limits of compensation can be characterized relatively easily by stressing oxygen transport at peak exercise. Thus, the canine model remains useful for relating structure to function, defining sources and limits of adaptation as well as evaluating therapeutic manipulation. This chapter summarizes key concepts of compensatory lung growth that have been consolidated from canine studies: (i) structure-function relationships during adaptation, (ii) dysanaptic (unequal) nature of compensation, and (iii

  20. Wavelength-modulated tunable diode-laser absorption spectrometry for real-time monitoring of microbial growth.

    PubMed

    Shao, Jie; Xiang, Jindong; Axner, Ove; Ying, Chaofu

    2016-03-20

    It is important to monitor and assess the growth of micro-organisms under various conditions. Yet, thus far there has been no technique to do this with the required speed and accuracy. This work demonstrates swift and accurate assessment of the concentration of carbon dioxide that is produced by use of a wavelength-modulated tunable diode-laser based absorption spectroscopy (WM-TDLAS). It is shown by experiments on two types of bacteria, Staphylococcus aureus and Candida albicans, that the technique can produce high signal-to-noise-ratio data from bacteria grown in confined spaces and exposed to limited amounts of nutrients that can be used for extraction of growth parameters by fitting of the Gompertz model. By applying the technique to S. aureus bacteria at various temperatures (in the 25°C to 42°C range), it is specifically shown that both the maximum growth rate and the so-called lag time have a strong temperature dependence (under the specific conditions with a maximum of the former at 37°C) that matches conventional models well for bacterial growth. Hence, it is demonstrated that WM-TDLAS monitoring CO2 is a user-friendly, non-intrusive, and label-free technique that swiftly, and with high signal-to-noise-ratio, can be used for rapid (on the Hz scale) and accurate assessment of bacterial growth.

  1. Modeling growth of fatigue cracks which originate at rivet holes

    NASA Technical Reports Server (NTRS)

    Mear, Mark E.

    1989-01-01

    When a structural component is subjected to repeated stress cycles, it can fail at stresses which are well below the tensile strength of the material. The processes leading to this failure are termed fatigue. Instances of fatigue failure in aircraft have become an increasing concern. The crack leading to failure often originate at rivet holes and then grow in response to stress cycles which occur during the operation of the aircraft. A necessary step to preventing failures in todays fleet of aging aircraft is to increase the frequency and quality of inspections; steps were already taken in this direction. There is also a need for modeling of fatigue crack growth in the aircraft structures so that improvements in design can be established and predictions of the life of the components can be made. The purpose is to provide a method to accurately predict the growth of fatigue cracks and to use this method to make predictions about the life of aircraft structural components. The method relies on the formulation and numerical solution of a singular integral equation(s) for an arbitrarily shaped crack(s) which propagate in response to the applied loading. Of special interest to the aging aircraft studies are cracks which originate at circular holes (i.e., rivet holes), but other crack geometries can be treated equally as well.

  2. Exact solutions of kinetic equations in an autocatalytic growth model.

    PubMed

    Jędrak, Jakub

    2013-02-01

    Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke [J. Am. Chem. Soc. 119, 10382 (1997)]. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ(k)=s(k)(ξ(1))[proportionality]ξ(1)(k)/k was obtained, while in the latter, the functional form of s(k)(ξ(1)) is more complicated. In both cases, ξ(1)(t)=h(μ)(M(μ)(t)) is a function of the moments of the mass distribution. Both functions, s(k)(ξ(1)) and h(μ)(M(μ)), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system.

  3. Growth plate abnormalities in a new dwarf mouse model: tich.

    PubMed

    Brown, R A; Bird, L; Blunn, G W; Archer, J R

    1994-03-01

    Growth plate cartilage calcification has been examined in a recently described mouse mutant, tich, which is co-isogenic with the A.TL strain. Long bones were studied from 1-day-old and 1-month-old mice which carried a homozygous recessive gene mutation making them short limbed and dumpy. Specimens were studied by routine histology, scanning electron microscopy and radiography. In 1-day-old tich mice the front of calcified cartilage was recessed behind the advancing periosteum and bone. No similar recess was seen in control mice. At 1 month of age, a number of the long bone growth plates were irregularly thickened, particularly in the central area. This produced a central tongue of non-calcified cartilage (particularly prominent in the proximal tibia) which gave rise to a corresponding pit in the calcified cartilage layer, in macerated specimens. This was accompanied by poor resorption of calcified cartilage. At both ages the presence of the respective defects was radiographically confirmed. At present it is not known whether this is primarily a defect of calcification or resorption but its presence, apparently from a single mutation in a genetically defined mouse strain, makes it a potentially valuable model.

  4. A biological model for controlling interface growth and morphology.

    SciTech Connect

    Hoyt, Jeffrey John; Holm, Elizabeth Ann

    2004-01-01

    Biological systems create proteins that perform tasks more efficiently and precisely than conventional chemicals. For example, many plants and animals produce proteins to control the freezing of water. Biological antifreeze proteins (AFPs) inhibit the solidification process, even below the freezing point. These molecules bond to specific sites at the ice/water interface and are theorized to suppress solidification chemically or geometrically. In this project, we investigated the theoretical and experimental data on AFPs and performed analyses to understand the unique physics of AFPs. The experimental literature was analyzed to determine chemical mechanisms and effects of protein bonding at ice surfaces, specifically thermodynamic freezing point depression, suppression of ice nucleation, decrease in dendrite growth kinetics, solute drag on the moving solid/liquid interface, and stearic pinning of the ice interface. Stearic pinning was found to be the most likely candidate to explain experimental results, including freezing point depression, growth morphologies, and thermal hysteresis. A new stearic pinning model was developed and applied to AFPs, with excellent quantitative results. Understanding biological antifreeze mechanisms could enable important medical and engineering applications, but considerable future work will be necessary.

  5. Ignition and Growth Modeling of LX-17 Hockey Puck Experiments

    SciTech Connect

    Tarver, C M

    2004-04-19

    Detonating solid plastic bonded explosives (PBX) formulated with the insensitive molecule triaminotrinitrobenzene (TATB) exhibit measurable reaction zone lengths, curved shock fronts, and regions of failing chemical reaction at abrupt changes in the charge geometry. A recent set of ''hockey puck'' experiments measured the breakout times of diverging detonation waves in ambient temperature LX-17 (92.5 % TATB plus 7.5% Kel-F binder) and the breakout times at the lower surfaces of 15 mm thick LX-17 discs placed below the detonator-booster plane. The LX-17 detonation waves in these discs grow outward from the initial wave leaving regions of unreacted or partially reacted TATB in the corners of these charges. This new experimental data is accurately simulated for the first time using the Ignition and Growth reactive flow model for LX-17, which is normalized to a great deal of detonation reaction zone, failure diameter and diverging detonation data. A pressure cubed dependence for the main growth of reaction rate yields excellent agreement with experiment, while a pressure squared rate diverges too quickly and a pressure quadrupled rate diverges too slowly in the LX-17 below the booster equatorial plane.

  6. Modeling of crossbred cattle growth, comparison between cubic and piecewise random regression models.

    PubMed

    Mirzaei, H R; Pitchford, W S; Verbyla, A P

    2011-09-27

    Two analyses, cubic and piecewise random regression, were conducted to model growth of crossbred cattle from birth to about two years of age, investigating the ability of a piecewise procedure to fit growth traits without the complications of the cubic model. During a four-year period (1994-1997) of the Australian "Southern Crossbreeding Project", mature Hereford cows (N = 581) were mated to 97 sires of Angus, Belgian Blue, Hereford, Jersey, Limousin, South Devon, and Wagyu breeds, resulting in 1141 steers and heifers born over four years. Data included 13 (for steers) and eight (for heifers) live body weight measurements, made approximately every 50 days from birth until slaughter. The mixed model included fixed effects of sex, sire breed, age (linear, quadratic and cubic), and their interactions between sex and sire breed with age. Random effects were sire, dam, management (birth location, year, post-weaning groups), and permanent environmental effects and for each of these when possible, their interactions with linear, quadratic and cubic growth. In both models, body weights of all breeds increased over pre-weaning period, held fairly steady (slightly flattening) over the dry season then increased again towards the end of the feedlot period. The number of estimated parameters for the cubic model was 22 while for the piecewise model it was 32. It was concluded that the piecewise model was very similar to the cubic model in the fit to the data; with the piecewise model being marginally better. The piecewise model seems to fit the data better at the end of the growth period.

  7. 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

  8. Overview: early history of crop growth and photosynthesis modeling.

    PubMed

    El-Sharkawy, Mabrouk A

    2011-02-01

    As in industrial and engineering systems, there is a need to quantitatively study and analyze the many constituents of complex natural biological systems as well as agro-ecosystems via research-based mechanistic modeling. This objective is normally addressed by developing mathematically built descriptions of multilevel biological processes to provide biologists a means to integrate quantitatively experimental research findings that might lead to a better understanding of the whole systems and their interactions with surrounding environments. Aided with the power of computational capacities associated with computer technology then available, pioneering cropping systems simulations took place in the second half of the 20th century by several research groups across continents. This overview summarizes that initial pioneering effort made to simulate plant growth and photosynthesis of crop canopies, focusing on the discovery of gaps that exist in the current scientific knowledge. Examples are given for those gaps where experimental research was needed to improve the validity and application of the constructed models, so that their benefit to mankind was enhanced. Such research necessitates close collaboration among experimentalists and model builders while adopting a multidisciplinary/inter-institutional approach.

  9. Modeling Circumgalactic Gas During the Peak Epoch of Galaxy Growth

    NASA Astrophysics Data System (ADS)

    Dave, Romeel

    During the peak of cosmic star formation at z=1-4, galaxy growth is increasingly believed to be modulated by large-scale inflows and outflows of baryons that intimately connect galaxies to their surrounding circumgalactic medium (CGM). Unfortunately, direct observational signatures of these baryon cycling processes are elusive and fragmented, owing to the diffuse and multi- phase nature of the CGM. This proposal aims to use advanced multi-scale cosmological hydrodynamic simulations to investigate how inflows and outflows within circumgalactic gas are manifested in present and future observables, and how those observables in turn constrain the physical processes driving galaxy evolution. The simulation methodology includes ``random" cosmological runs, ``zoom" runs of individual halos, and radiative transfer to better model the ionization conditions. We will focus on absorption and emission signatures in HI and metal lines using common rest-UV and rest-optical tracers. Key questions include: How do metal absorbers trace the enrichment and ionization conditions within circumgalactic gas? How much absorption arises from inflow versus outflow, and what are the characteristic absorption, emission, and/or kinematic signatures of each? What emission lines from CGM gas are predicted to be observable, and how does the combination of emission and absorption constrain CGM properties? What are the roles of metallicity, ionization, and large-scale structure in establishing the correlations of metal absorbers and galaxies on CGM scales? How do all these CGM properties relate to host galaxy properties such as mass, and how do they vary with outflow model? The overall goal is to develop a comprehensive hierarchical-based framework for assembling various observations of circumgalactic gas into a unified scenario for how inflows and outflows govern the growth of galaxies.

  10. A statistical model of diurnal variation in human growth hormone

    NASA Technical Reports Server (NTRS)

    Klerman, Elizabeth B.; Adler, Gail K.; Jin, Moonsoo; Maliszewski, Anne M.; Brown, Emery N.

    2003-01-01

    The diurnal pattern of growth hormone (GH) serum levels depends on the frequency and amplitude of GH secretory events, the kinetics of GH infusion into and clearance from the circulation, and the feedback of GH on its secretion. We present a two-dimensional linear differential equation model based on these physiological principles to describe GH diurnal patterns. The model characterizes the onset times of the secretory events, the secretory event amplitudes, as well as the infusion, clearance, and feedback half-lives of GH. We illustrate the model by using maximum likelihood methods to fit it to GH measurements collected in 12 normal, healthy women during 8 h of scheduled sleep and a 16-h circadian constant-routine protocol. We assess the importance of the model components by using parameter standard error estimates and Akaike's Information Criterion. During sleep, both the median infusion and clearance half-life estimates were 13.8 min, and the median number of secretory events was 2. During the constant routine, the median infusion half-life estimate was 12.6 min, the median clearance half-life estimate was 11.7 min, and the median number of secretory events was 5. The infusion and clearance half-life estimates and the number of secretory events are consistent with current published reports. Our model gave an excellent fit to each GH data series. Our analysis paradigm suggests an approach to decomposing GH diurnal patterns that can be used to characterize the physiological properties of this hormone under normal and pathological conditions.

  11. 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

  12. Models of Jupiter's Growth Incorporating Thermal and Hydrodynamics Constraints

    NASA Astrophysics Data System (ADS)

    D'Angelo, G.; Lissauer, J. J.; Hubickyj, O.; Bodenheimer, P.

    2008-12-01

    We have modeled the growth of Jupiter incorporating both thermal and hydrodynamical constraints on its accretion of gas from the circumsolar disk. We have used a planetary formation code, based on a Henyey- type stellar evolution code, to compute the planet's internal structure and a three-dimensional hydrodynamics code to calculate the planet's interactions with the protoplanetary disk. Our principal results are: (1) Three dimensional hydrodynamics calculations show that the flow of gas in the circumsolar disk limits the region occupied by the planet's tenuous gaseous envelope to within about 0.25 Rh (Hill sphere radii) of the planet's center, which is much smaller than the value of ~ 1 Rh that was assumed in previous studies. (2) This smaller size of the planet's envelope increases the planet's accretion time, but only by 5-- 10%. In general, in agreement with previous results of Hubickyj et al. [Hubickyj, O., Bodenheimer, P., Lissauer, J.J., 2005. Icarus, 179, 415-431], Jupiter formation times are in the range 2.5--3 Myr, assuming a protoplanetary disk with solid surface density of 10 g/cm2 and dust opacity in the protoplanet's envelope equal to 2% that of interstellar material. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. (3) In a protoplanetary disk whose alpha-viscosity parameter is ~ 0.004, giant planets will grow to several times the mass of Jupiter unless the disk has a small local surface density when the planet begins to accrete gas hydrodynamically, or the disk is dispersed very soon thereafter. The large number of planets known with masses near Jupiter's compared with the smaller number of substantially more massive planets is more naturally explained by planetary growth within circumstellar disks whose alpha-viscosity parameter is ~ 0.0004. (4) Capture of Jupiter's irregular

  13. 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…

  14. Specification Search for Identifying the Correct Mean Trajectory in Polynomial Latent Growth Models

    ERIC Educational Resources Information Center

    Kim, Minjung; Kwok, Oi-Man; Yoon, Myeongsun; Willson, Victor; Lai, Mark H. C.

    2016-01-01

    This study investigated the optimal strategy for model specification search under the latent growth modeling (LGM) framework, specifically on searching for the correct polynomial mean or average growth model when there is no a priori hypothesized model in the absence of theory. In this simulation study, the effectiveness of different starting…

  15. Modeling Growth of SAT Reading Performance Using Repeated Measures Data

    ERIC Educational Resources Information Center

    Deng, Hui; Wiley, Andrew

    2008-01-01

    Presented at the Annual National Council on Measurement in Education (NCME) in New York in March 2008. This presentation explores the growth trajectory of the SAT Reading scores and examine what demographics and variation may cause changes and affect growth.

  16. Modelling the growth curve of Maine-Anjou beef cattle using heteroskedastic random coefficients models

    PubMed Central

    Robert-Granié, Christèle; Heude, Barbara; Foulley, Jean-Louis

    2002-01-01

    A heteroskedastic random coefficients model was described for analyzing weight performances between the 100th and the 650th days of age of Maine-Anjou beef cattle. This model contained both fixed effects, random linear regression and heterogeneous variance components. The objective of this study was to analyze the difference of growth curves between animals born as twin and single bull calves. The method was based on log-linear models for residual and individual variances expressed as functions of explanatory variables. An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances. Likelihood ratio tests were used to assess hypotheses about parameters of this model. Growth of Maine-Anjou cattle was described by a third order regression on age for a mean growth curve, two correlated random effects for the individual variability and independent errors. Three sources of heterogeneity of residual variances were detected. The difference of weight performance between bulls born as single and twin bull calves was estimated to be equal to about 15 kg for the growth period considered. PMID:12270103

  17. 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.

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

    PubMed Central

    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 (r2 > 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. PMID:26539483

  19. A Longitudinal Study on State Mathematics and Reading Assessments: Comparisons of Growth Models on Students' Achievement Scores

    ERIC Educational Resources Information Center

    Chiu, Pui Chi

    2012-01-01

    This study examines student growth on mathematics and reading assessments across academic years (Spring 2006 through Spring 2009) using three different growth models: hierarchical linear model (HLM), value-added model (VAM), and student growth percentile model (SGP). Comparisons across these three growth models were conducted to investigate the…

  20. Analysis of a diffuse interface model of multispecies tumor growth

    NASA Astrophysics Data System (ADS)

    Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

    2017-04-01

    We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726–54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn–Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.