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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

    2006-04-01

    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. 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). PMID:26628036

  14. Evaluation of nitrogenous substrates such as peptones from fish:a new method based on Gompertz modeling of microbial growth.

    PubMed

    Dufossé, L; De La Broise, D; Guerard, F

    2001-01-01

    Fish peptones from tuna, cod, salmon, and unspecified fish were compared with a casein one by using a new method based on Gompertz modeling of microbial growth. Cumulative results obtained from six species of bacteria, yeasts, and fungi showed that, in most cases, these fish peptones are very effective. Nevertheless, this study raised some questions about the standardization of fish raw material, the enzymatic hydrolysis of fish proteins, and the composition of the culture medium used for testing the peptones.

  15. 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.

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

    PubMed Central

    Hirsch, Henry R.

    2008-01-01

    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. PMID:19424855

  3. 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…

  4. 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.

  5. 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.

  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. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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).

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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

    2013-08-01

    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.

  19. 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.

  20. 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. PMID:18501595

  1. 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.

  2. 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.

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

    PubMed Central

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

    2012-01-01

    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. PMID:24812444

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. [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.

  9. [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. PMID:26349222

  10. Using the Gompertz-Strehler model of aging and mortality to explain mortality trends in industrialized countries.

    PubMed

    Riggs, J E; Millecchia, R J

    1992-09-01

    Mortality trends in industrialized countries are characterized by declines in vascular disease (ischemic heart disease and stroke) and rises in cancers and degenerative diseases. These trends are typically analyzed by examining each disorder in isolation using the perspective of genetic and environmental influences. However, longitudinal Gompertzian analysis and the Gompertz-Strehler model of aging and mortality as modified by Lestienne suggest that age-specific mortality rates, for both general and disease-specific mortality, are an interrelated deterministic function of aggregate genetic, environmental and competitive influences. Consequently, evolving mortality trends and patterns appear to be influenced by three factors (with deterministic competition being the third factor), rather than just two factors (genetic and environmental) as commonly depicted. PMID:1434950

  11. 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.

  12. Two-parameter logistic and Weibull equations provide better fits to survival data from isogenic populations of Caenorhabditis elegans in axenic culture than does the Gompertz model.

    PubMed

    Vanfleteren, J R; De Vreese, A; Braeckman, B P

    1998-11-01

    We have fitted Gompertz, Weibull, and two- and three-parameter logistic equations to survival data obtained from 77 cohorts of Caenorhabditis elegans in axenic culture. Statistical analysis showed that the fitting ability was in the order: three-parameter logistic > two-parameter logistic = Weibull > Gompertz. Pooled data were better fit by the logistic equations, which tended to perform equally well as population size increased, suggesting that the third parameter is likely to be biologically irrelevant. Considering restraints imposed by the small population sizes used, we simply conclude that the two-parameter logistic and Weibull mortality models for axenically grown C. elegans generally provided good fits to the data, whereas the Gompertz model was inappropriate in many cases. The survival curves of several short- and long-lived mutant strains could be predicted by adjusting only the logistic curve parameter that defines mean life span. We conclude that life expectancy is genetically determined; the life span-altering mutations reported in this study define a novel mean life span, but do not appear to fundamentally alter the aging process.

  13. [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.

  14. 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.

  15. 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…

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. [Individual growth modeling of the penshell Atrina maura (Bivalvia: Pinnidae) using a multi model inference approach].

    PubMed

    Aragón-Noriega, Eugenio Alberto

    2013-09-01

    Growth models of marine animals, for fisheries and/or aquaculture purposes, are based on the popular von Bertalanffy model. This tool is mostly used because its parameters are used to evaluate other fisheries models, such as yield per recruit; nevertheless, there are other alternatives (such as Gompertz, Logistic, Schnute) not yet used by fishery scientists, that may result useful depending on the studied species. The penshell Atrina maura, has been studied for fisheries or aquaculture supplies, but its individual growth has not yet been studied before. The aim of this study was to model the absolute growth of the penshell A. maura using length-age data. For this, five models were assessed to obtain growth parameters: von Bertalanffy, Gompertz, Logistic, Schnute case 1 and Schnute and Richards. The criterion used to select the best models was the Akaike information criterion, as well as the residual squared sum and R2 adjusted. To get the average asymptotic length, the multi model inference approach was used. According to Akaike information criteria, the Gompertz model better described the absolute growth of A. maura. Following the multi model inference approach the average asymptotic shell length was 218.9 mm (IC 212.3-225.5) of shell length. I concluded that the use of the multi model approach and the Akaike information criteria represented the most robust method for growth parameter estimation of A. maura and the von Bertalanffy growth model should not be selected a priori as the true model to obtain the absolute growth in bivalve mollusks like in the studied species in this paper.

  1. 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.

  2. 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.

  3. A comparison and catalog of intrinsic tumor growth models.

    PubMed

    Sarapata, E A; de Pillis, L G

    2014-08-01

    Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are several competing canonical tumor growth models that are often implemented, how to determine which of the models should be used for which tumor types remains an open question. In this work, we determine the best fit growth dynamics and associated parameter ranges for ten different tumor types by fitting growth functions to at least five sets of published experimental growth data per type of tumor. These time-series tumor growth data are used to determine which of the five most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor.

  4. Comparison of mathematical models of lactic acid bacteria growth in vacuum-packaged raw beef stored at different temperatures.

    PubMed

    Li, M Y; Sun, X M; Zhao, G M; Huang, X Q; Zhang, J W; Tian, W; Zhang, Q H

    2013-04-01

    The lactic acid bacteria grown in vacuum-packaged raw beef under 7, 10, 15, and 20 °C has been studied in this paper. Four primary models, the modified Gompertz, logistic, Baranyi, and Huang model were used for data fitting. Statistical criteria such as the bias factor and accuracy factor, mean square error, Akaike's information criterion, and the residual distribution were used for comparing the models. The result showed that all of the 4 models can fit the data well and they were not significantly different in the performance. They were equally capable of describing bacterial growth, but the growth rate and lag time estimated from the modified Gompertz model were a little higher than other models. The estimate for the lag time was not accurate as the growth rate.

  5. 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.

  6. Non-linear Growth Models in Mplus and SAS

    PubMed Central

    Grimm, Kevin J.; Ram, Nilam

    2013-01-01

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

  7. Analysis of mathematical models of Pseudomonas spp. growth in pallet-package pork stored at different temperatures.

    PubMed

    Li, Miaoyun; Niu, Huimin; Zhao, Gaiming; Tian, Lu; Huang, Xianqing; Zhang, Jianwei; Tian, Wei; Zhang, Qiuhui

    2013-04-01

    Pseudomonas of pallet-packaged raw pork grown at 0, 5, 10, 15, 20 and 25°C has been studied in this paper. The modified Gompertz, Baranyi and Huang models were used for data fitting. Statistical criteria such as residual sum of squares, mean square error, Akaike's information criterion, and pseudo-R(2) were used to evaluate model performance. Results showed that there was an apparent decline in Pseudomonas growth at initial-storage phase at low temperatures. The modified Gompertz model outperformed the others at 5, 15, and 20°C, while Baranyi model was appropriate for 0 and 25°C. The Huang model was optimal at 10°C. No single model can give a consistently preferable goodness-of-fit for all growth data. The Gompertz model, with the smallest average values of RSS, AIC, MSE and the biggest pseudo-R(2) at all temperatures, is the most appropriate model to describe the growth of Pseudomonas of raw pork under pallet packaging.

  8. Analysis of mathematical models of Pseudomonas spp. growth in pallet-package pork stored at different temperatures.

    PubMed

    Li, Miaoyun; Niu, Huimin; Zhao, Gaiming; Tian, Lu; Huang, Xianqing; Zhang, Jianwei; Tian, Wei; Zhang, Qiuhui

    2013-04-01

    Pseudomonas of pallet-packaged raw pork grown at 0, 5, 10, 15, 20 and 25°C has been studied in this paper. The modified Gompertz, Baranyi and Huang models were used for data fitting. Statistical criteria such as residual sum of squares, mean square error, Akaike's information criterion, and pseudo-R(2) were used to evaluate model performance. Results showed that there was an apparent decline in Pseudomonas growth at initial-storage phase at low temperatures. The modified Gompertz model outperformed the others at 5, 15, and 20°C, while Baranyi model was appropriate for 0 and 25°C. The Huang model was optimal at 10°C. No single model can give a consistently preferable goodness-of-fit for all growth data. The Gompertz model, with the smallest average values of RSS, AIC, MSE and the biggest pseudo-R(2) at all temperatures, is the most appropriate model to describe the growth of Pseudomonas of raw pork under pallet packaging. PMID:23313972

  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. PMID:24933474

  11. 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.

  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. 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.

  15. 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. PMID:22108854

  16. 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

  17. 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.

  18. 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

  19. A growth model for primary cancer (II). New rules, progress curves and morphology transitions

    NASA Astrophysics Data System (ADS)

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

    1999-10-01

    In the present paper we extend the analysis of another model recently proposed to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as chemotactic interactions among cells. The tumour patterns generated by two distinct growth rules are characterised by its gyration radius, surface roughness, total number of cancer cells, and number of cells on tumour periphery. Our results indicate that very distinct morphological patterns follow Gompertz growth curves and their gyration radii increase linearly in time and scale, in the asymptotic limit, as a square root of the total number of tumour cells. In contrast, these distinct tumour patterns exhibit different scaling laws for their surfaces. Thus, some biological features of malignant behaviour seem to influence particularly the structure of the tumour border, while its gyration radius and progress curve are described by more robust functions. Finally, for both rules used, morphology transitions as well as a transient behaviour up to the onset of the phase of rapid growth in the Gompertz curves are observed.

  20. 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.

  1. Effects of temperature, water activity, and syrup film composition on the growth of Wallemia sebi: development and assessment of a model predicting growth lags in syrup agar and crystalline sugar.

    PubMed

    Vindeløv, Jannik; Arneborg, Nils

    2002-04-01

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

  2. 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)...

  3. 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.

  4. The Gompertz function does not measure ageing.

    PubMed

    Driver, C

    2001-01-01

    The Gompertz transform of the distribution function for the age at death expresses mortality in a form R = R0e(alphat) where R0 is the mortality at time zero and alpha is the rate of increase of mortality, frequently taken as the rate of ageing. The slope of the line alpha is frequently used as a measure of the rate of ageing. It is argued that it is incorrect to use alpha in this way. To support this contention, a paradox is produced whereby selection for longevity increases alpha, which could lead to the absurd conclusion that selection for longevity increases the rate of ageing.

  5. 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.

  6. 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.

  7. A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate.

    PubMed

    Spina, Serena; Giorno, Virginia; Román-Román, Patricia; Torres-Ruiz, Francisco

    2014-11-01

    A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered. A strategy to select the inter-jump intervals is given so that the first passage time of the process through a constant boundary is as large as possible and the cancer size remains under this control threshold during the treatment. A computational analysis is performed for different choices of involved parameters. Finally, an estimation of parameters based on the maximum likelihood method is provided and some simulations are performed to illustrate the validity of the proposed procedure.

  8. 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.

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

    PubMed

    Burger, Oskar; Missov, Trifon I

    2016-11-01

    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.

  10. 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.

  11. 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.

  12. 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.

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

    PubMed Central

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

    1995-01-01

    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. PMID:7591979

  14. Evaluating growth models of Pseudomonas spp. in seasoned prepared chicken stored at different temperatures by the principal component analysis (PCA).

    PubMed

    Li, Miaoyun; Li, Yuanhui; Huang, Xianqing; Zhao, Gaiming; Tian, Wei

    2014-06-01

    The growth of Pseudomonas of pallet-packaged seasoned prepared chicken products under selected storage temperatures (5°°C, 10°°C, 15°°C, 20°°C and 25°°C) has been studied in this paper. The modified Gompertz, Baranyi and Huang models were used for data fitting. Statistical criteria such as residual sum of squares, mean square error, Akaike's information criterion, Pseudo-R(2) were used to evaluate model performance. Results showed that RSS (Residual sum of squares) index contribution rate was more than 90% of the variability, which could be explained by the first principal components analyzed by the principal component analysis (PCA). The index values reported in Sichuan-style chicken skewers and chicken flesh and bones were about 94.85% and 93.345% respectively, and both the rate were better than the standard (85%). Therefore, RSS can be used as the main evaluating index to analyze and compare the difference of those three models. With the smallest average values of RSS and the biggest pseudo-R2 at most temperatures, the Baranyi model was more suitable to fit the data of Pseudomonas obtained from the two prepared chicken products than Gompertz model and Huang model. PMID:24549196

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

    PubMed Central

    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. PMID:25072033

  16. Availability growth modeling

    SciTech Connect

    Wendelberger, J.R.

    1998-12-01

    In reliability modeling, the term availability is used to represent the fraction of time that a process is operating successfully. Several different definitions have been proposed for different types of availability. One commonly used measure of availability is cumulative availability, which is defined as the ratio of the amount of time that a system is up and running to the total elapsed time. During the startup phase of a process, cumulative availability may be treated as a growth process. A procedure for modeling cumulative availability as a function of time is proposed. Estimates of other measures of availability are derived from the estimated cumulative availability function. The use of empirical Bayes techniques to improve the resulting estimates is also discussed.

  17. 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

    2015-01-01

    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.

  18. 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.

  19. 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.

  20. 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. PMID:26988400

  1. How could the Gompertz-Makeham law evolve.

    PubMed

    Golubev, A

    2009-05-01

    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.

  2. 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.

  3. 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…

  4. Modeling slug growth in pipelines

    SciTech Connect

    Scott, S.L.

    1987-01-01

    Experimental studies recently performed in large diameter flow lines in the Prudhoe Bay Field of Alaska reveal the occurrence of slug growth. These data form the basis for developing a mechanistic model to account for slug growth phenomena. Two distinct types of slug growth are observed. In large diameter pipes, the wavy entry region can extend for great distances. Over this wavy entry region slug formation occurs at various locations. This results in a wavy region, often of substantial length, being trapped between successive slugs. The overriding of this wavy region by the slug produces rapid slug growth, termed developing growth. Once the wave region has been consumed by the following slug a second type of slug growth dominates, called long term slug growth. This growth is controlled by two mechanisms: dissipation and coalescence of slugs, and gas expansion caused by decreasing pressure and mass transfer from the liquid to the gas. Developing slug growth is modeled by application of the integral mass and momentum balances over the liquid slug body coupled with a slug formation mechanism. This mechanism is based on the exit of a slug from the flow line outlet triggering slug formation while maintaining a preset pressure drop in the flow line. A modified long term growth model is presented utilizing the Black-Oil model to describe the phase behavior of the fluids. The prediction of the proposed model is shown to compare favorably with the available slug growth data.

  5. Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models.

    PubMed

    Dalgaard, P; Koutsoumanis, K

    2001-01-01

    Maximum specific growth rate (mu(max)) and lag time (lambda) were estimated from viable count and absorbance data and compared for different microorganisms, incubation systems and growth conditions. Data from 176 growth curves and 120 absorbance detection times of serially diluted cultures were evaluated using different mathematical growth models. Accurate estimates of mu(max) and lambda were obtained from individual absorbance growth curves by using the Richard model, with values of the parameter m fixed to 0.5, 1.0 or 2.0 to describing different degrees of growth dampening, as well as from absorbance detection times of serially diluted cultures. It is suggested to apply the two techniques complementarily for accurate, rapid and inexpensive estimation of microbial growth parameter values from absorbance data. In contrast, considerable limitations were demonstrated for the ability of the Exponential, the Gompertz and the Logistic models to estimate mu(max) and lambda values accurately from absorbance data. Limitations of these models were revealed due the wide range of growth conditions studies.

  6. 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.

  7. 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. PMID:26298697

  8. 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.

  9. 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…

  10. 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,…

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

    PubMed

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

    2006-05-12

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

  12. 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.

  13. Partitioning of retained energy in broilers and birds with intermediate growth rate.

    PubMed

    Lopez, G; de Lange, K; Leeson, S

    2007-10-01

    An experiment was conducted to study energy retained (TER) as fat (TERF) and protein (TERP) in 3 strains of birds with different growth rate; commercial broilers, Barred Plymouth Rock, and Leghorns. Birds were fed ad libitum a diet providing 3,100 kcal of AMEn/kg and 20% CP from 0 to 42 d. Body composition, TER, TERF, and TERP were determined at 0, 7, 10, 15, 19, 23, 28, 33, 37, and 42 d of age. The TER, TERF, and TERP were derived from whole body analyses. Linear and nonlinear models (quadratic, allometric, and Gompertz equation) were used as a means to characterize observed patterns of energy deposition. The TER, TERF, and TERP increased quadratically (P < 0.001) over time in all 3 strains of birds. Over 42 d, broilers deposited a constant proportion (50%) of body energy as fat and protein (P < 0.001). When applying the Gompertz equation to relate empty BW (EBW) to time, the estimated value for EBW at maturity of the broilers was unrealistically high (11.1 kg) and estimated poorly (SE 5.5 kg). Quadratic equations may be used as an alternative for Gompertz equations to represent growth of EBW, TER, TERF, or TERP vs. time in chickens between 0 and 42 d of age. Within the BW ranges that were evaluated in this study, allometric functions or Gompertz equations can be used to relate TERF and TERP to EBW, but model parameters differ between bird strains. Based on the Gompertz equation and in broilers, the maximum rate of TERF and TERP was reached at 1.16 and 1.22 kg of EBW, respectively, and then declines slowly as BW increases. Quantifying and partitioning TER as TERF and TERP as major components of ME requirements can be used to establish models that have economic consequences to the broiler industry.

  14. 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…

  15. Stochastic Models of Human Growth.

    ERIC Educational Resources Information Center

    Goodrich, Robert L.

    Stochastic difference equations of the Box-Jenkins form provide an adequate family of models on which to base the stochastic theory of human growth processes, but conventional time series identification methods do not apply to available data sets. A method to identify structure and parameters of stochastic difference equation models of human…

  16. Czochralski crystal growth: Modeling study

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

  17. 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

  18. 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.

  19. 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.

  20. 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

  1. Modeling of intermediate phase growth

    SciTech Connect

    Umantsev, A.

    2007-01-15

    We introduced a continuum method for modeling of intermediate phase growth and numerically simulated three common experimental situations relevant to the physical metallurgy of soldering: growth of intermetallic compound layer from an unlimited amount of liquid and solid solders and growth of the compound from limited amounts of liquid solder. We found qualitative agreements with the experimental regimes of growth in all cases. For instance, the layer expands in both directions with respect to the base line when it grows from solid solder, and grows into the copper phase when the solder is molten. The quantitative agreement with the sharp-interface approximation was also achieved in these cases. In the cases of limited amounts of liquid solder we found the point of turnaround when the compound/solder boundary changed the direction of its motion. Although such behavior had been previously observed experimentally, the simulations revealed important information: the turnaround occurs approximately at the time of complete saturation of solder with copper. This result allows us to conclude that coarsening of the intermetallic compound structure starts only after the solder is practically saturated with copper.

  2. 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.

  3. 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. PMID:16937212

  4. 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.

  5. 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…

  6. 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

  7. 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.

  8. 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…

  9. 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…

  10. 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)

  11. 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.

  12. A universal model of ontogenetic growth

    NASA Astrophysics Data System (ADS)

    Martyushev, Leonid M.; Terentiev, Pavel S.

    2015-06-01

    The assumption that a single growth equation can be used to describe all biological objects on different organizational levels and a dimensional analysis are applied in order to substantiate universal model of ontogenetic growth. This model (the mass of a growing organism is a power function of time) is valid only in the initial period of growth. For the whole period of growth, a generalization of the model is advanced; it provides the same accuracy as previously known models of quantitative description of kinetic curves. Within the scope of the developed model, a number of interesting results related to allometry and biological time are obtained.

  13. 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.

  14. The Potential of Growth Mixture Modelling

    ERIC Educational Resources Information Center

    Muthen, Bengt

    2006-01-01

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

  15. 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.

  16. 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.

  17. 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

  18. Growth pattern of the maxillary sinus in the miniature pig (Sus scrofa).

    PubMed

    Koppe, T; Klauke, T; Lee, S H; Schumacher, G

    2000-01-01

    The biological role of the paranasal sinuses is obscure, can be elucidated through a cross-sectional growth study of the maxillary sinus in miniature pigs. The maxillary sinus area was obtained from lateral cephalograms of left skull halves of 103 female miniature pigs of known ages, from newborn to 24 months. Out of several nonlinear models, the growth of the maxillary sinus was best described with the Gompertz model. The first derivative of the Gompertz curve revealed an increase in the growth rates of the maxillary sinus until 4 months, after which sinus growth slowed down. The eruption of the permanent molars did not seem to have a significant influence on this growth pattern. Furthermore, growth in maxillary sinus size in the miniature pig does not follow growth in skull size closely, which showed the highest growth rates in newborn animals. In addition, a correlation analysis revealed that the relationship between maxillary sinus area and different characteristics of the masticatory apparatus (including linear cranial dimensions, and the dry weight of the masseter and zygomatico-mandibularis muscles) were influenced greatly by skull size. These results suggest that the existence of pneumatic cavities within the mammalian skull is not satisfactorily explained solely by an architectural theory. Epigenetic factors are likely to influence the final shape of the maxillary sinus.

  19. 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.

  20. 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.

  1. 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. PMID:27596102

  2. Modeling Heterogeneity of Latent Growth Depending on Initial Status

    ERIC Educational Resources Information Center

    Klein, Andreas G.; Muthen, Bengt O.

    2006-01-01

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

  3. 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…

  4. A Microkinetic Model of Calcite Step Growth.

    PubMed

    Andersson, M P; Dobberschütz, S; Sand, K K; Tobler, D J; De Yoreo, J J; Stipp, S L S

    2016-09-01

    In spite of decades of research, mineral growth models based on ion attachment and detachment rates fail to predict behavior beyond a narrow range of conditions. Here we present a microkinetic model that accurately reproduces calcite growth over a very wide range of published experimental data for solution composition, saturation index, pH and impurities. We demonstrate that polynuclear complexes play a central role in mineral growth at high supersaturation and that a classical complexation model is sufficient to reproduce measured rates. Dehydration of the attaching species, not the mineral surface, is rate limiting. Density functional theory supports our conclusions. The model provides new insights into the molecular mechanisms of mineral growth that control biomineralization, mineral scaling and industrial material synthesis. PMID:27532505

  5. [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.

  6. 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.

  7. 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.

  8. 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.

  9. A stochastic model of eye lens growth.

    PubMed

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

    2015-07-01

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

  10. 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.

  11. 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.

  12. On a Competitive Model of Laplacian Growth

    NASA Astrophysics Data System (ADS)

    Loutsenko, Igor; Yermolayeva, Oksana; Zinsmeister, Michel

    2011-11-01

    We introduce a competitive model of Laplacian growth in both stochastic and deterministic versions. This defines two different aggregation laws with probabilities λ and 1- λ. The parameter λ varying from 0 to 1 is used to weight a ratio between the inner and outer harmonic measures that leads to a competition between the Eden-like process and the DLA solved with site-sticking conditions. We perform numerical and qualitative analysis of the competitive growth.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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)

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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

  3. 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…

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

    PubMed

    Grady, Matthew W; Beretvas, S Natasha

    2010-05-28

    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 modeling (GCM). This study introduces a cross-classified multiple membership growth curve model (CCMM-GCM) for modeling, for example, academic achievement trajectories in the presence of student mobility. Real data are used to demonstrate and compare growth curve model estimates using the CCMM-GCM and a conventional GCM that ignores student mobility. Results indicate that the CCMM-GCM represents a promising option for modeling growth for multiple membership data structures.

  5. 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…

  6. 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.

  7. 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. PMID:24879700

  8. Adaptive importance sampling for network growth models

    PubMed Central

    Holmes, Susan P.

    2016-01-01

    Network Growth Models such as Preferential Attachment and Duplication/Divergence are popular generative models with which to study complex networks in biology, sociology, and computer science. However, analyzing them within the framework of model selection and statistical inference is often complicated and computationally difficult, particularly when comparing models that are not directly related or nested. In practice, ad hoc methods are often used with uncertain results. If possible, the use of standard likelihood-based statistical model selection techniques is desirable. With this in mind, we develop an Adaptive Importance Sampling algorithm for estimating likelihoods of Network Growth Models. We introduce the use of the classic Plackett-Luce model of rankings as a family of importance distributions. Updates to importance distributions are performed iteratively via the Cross-Entropy Method with an additional correction for degeneracy/over-fitting inspired by the Minimum Description Length principle. This correction can be applied to other estimation problems using the Cross-Entropy method for integration/approximate counting, and it provides an interpretation of Adaptive Importance Sampling as iterative model selection. Empirical results for the Preferential Attachment model are given, along with a comparison to an alternative established technique, Annealed Importance Sampling. PMID:27182098

  9. 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

  10. A random rule model of surface growth

    NASA Astrophysics Data System (ADS)

    Mello, Bernardo A.

    2015-02-01

    Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model, Mello et al. (2001) [5]. In this paper I modify the etching model to perform sequential, instead of random, substrate scan. The randomicity is introduced not in the site selection but in the choice of the rule to be followed in each site. The change positively affects the study of dynamic and asymptotic properties, by reducing the finite size effect and the short-time anomaly and by increasing the saturation time. It also has computational benefits: better use of the cache memory and the possibility of parallel implementation.

  11. Biofilm growth: a lattice Monte Carlo model

    NASA Astrophysics Data System (ADS)

    Tao, Yuguo; Slater, Gary

    2011-03-01

    Biofilms are complex colonies of bacteria that grow in contact with a wall, often in the presence of a flow. In the current work, biofilm growth is investigated using a new two-dimensional lattice Monte Carlo algorithm based on the Bond-Fluctuation Algorithm (BFA). One of the distinguishing characteristics of biofilms, the synthesis and physical properties of the extracellular polymeric substance (EPS) in which the cells are embedded, is explicitly taken into account. Cells are modelled as autonomous closed loops with well-defined mechanical and thermodynamic properties, while the EPS is modelled as flexible polymeric chains. This BFA model allows us to add biologically relevant features such as: the uptake of nutrients; cell growth, division and death; the production of EPS; cell maintenance and hibernation; the generation of waste and the impact of toxic molecules; cell mutation and evolution; cell motility. By tuning the structural, interactional and morphologic parameters of the model, the cell shapes as well as the growth and maturation of various types of biofilm colonies can be controlled.

  12. 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.

  13. A one dimensional model of population growth

    NASA Astrophysics Data System (ADS)

    Ribeiro, Fabiano L.; Ribeiro, Kayo N.

    2015-09-01

    In this work, a one dimensional population growth model is proposed. The model, based on the cooperative and competitive individual-individual distance-dependent interaction, allows us to get a full analytical solution. With this analytical approach, it was possible to investigate the dynamics of the population according to some parameters, as intrinsic growth rate, strength of the interaction between individuals, and the distance-dependent interaction. As a consequence of the individuals' interaction, a rich phase diagram to which the population has access was observed. The phases observed are: convergence to carrying capacity, exponential growth, divergence at finite time, and extinction. Moreover, it was also observed that some phases are strictly dependent on the initial condition. For instance, in the cooperative regime with negative intrinsic growth rate, the population can diverge or become extinct according to the initial population size. The phases accessible to the population can be seen as a macroscopic behavior which emerges from the interaction among the individuals (the microscopic level).

  14. A nonparametric software reliability growth model

    NASA Technical Reports Server (NTRS)

    Miller, Douglas R.; Sofer, Ariela

    1988-01-01

    Miller and Sofer have presented a nonparametric method for estimating the failure rate of a software program. The method is based on the complete monotonicity property of the failure rate function, and uses a regression approach to obtain estimates of the current software failure rate. This completely monotone software model is extended. It is shown how it can also provide long-range predictions of future reliability growth. Preliminary testing indicates that the method is competitive with parametric approaches, while being more robust.

  15. Comparison of growth kinetics for healthy and heat-injured Listeria monocytogenes in eight enrichment broths.

    PubMed

    Silk, Todd M; Roth, Tatiana M T; Donnelly, C W

    2002-08-01

    Detection of Listeria in food products is often limited by performance of enrichment media used to support growth of Listeria to detectable levels. In this study, growth curves were generated using healthy and heat-injured Listeria monocytogenes strain F5069 in three nonselective and five selective enrichment broths. Nonselective enrichment media included the current Food and Drug Administration Bacteriological Analytical Manual Listeria enrichment broth base (BAM), Listeria repair broth (LRB), and Trypticase soy broth. Selective enrichment media included BAM with selective agents and LRB with selective agents, BCM L. monocytogenes preenrichment broth, Fraser broth, and UVM-modified Listeria enrichment broth. The Gompertz equation was used to model the growth of L. monocytogenes. Gompertz parameters were used to calculate exponential growth rate, lag-phase duration (LPD), generation time, maximum population density (MPD), and time required for repair of injured cells. Statistical differences (P < 0.05) in broth performance were noted for LPD and MPD when healthy and injured cells were inoculated into the broths. With the exception of Fraser broth, there were no significant differences in the time required for the repair of injured cells. Results indicate that the distinction between selective and nonselective broths in their ability to grow healthy Listeria and to repair sublethally injured cells is not solely an elementary issue of presence or absence of selective agents.

  16. Macrophyte growth in shallow streams: biomass model

    SciTech Connect

    Wright, R.M.; Mc Donnell, A.J.

    1986-10-01

    An assessment was made of the water quality and the magnitude of growth of rooted aquatic macrophytes in a nutrient-enriched, shallow stream system in order to provide a basis for evaluating the recovery of the ecosystem following the implementation of a program of phosphorus removal. Field investigations defined the temporal and spatial changes of plant biomass in selected study sections. A model to predict changes in macrophyte biomass as a function of varying environmental factors including nutrient flux was developed, calibrated and validated. The potential of the biomass model as a management tool to assess the impact of nutrient reductions on stream oxygen budgets was demonstrated.

  17. 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.

  18. 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.

  19. 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.

  20. 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

    2015-01-01

    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

  1. 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

  2. Growth/reflectance model interface for wheat and corresponding model

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  3. Universal Accretion Growth Using Sandpile Models

    NASA Astrophysics Data System (ADS)

    Datta, Srabani; McKie, Shane; Spencer, Ralph

    2015-08-01

    The Bak-Tang- Wiesenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around thesystem till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power-law distribution in cascade sizes having slope -5/3. This self-similarity of structureis synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions influid turbulence. We apply the BTW sandpile model to study growth on a 2 dimensional rotating lattice in a magnetic field. In this paper, we show that this is a naturally occuring universal process giving rise to scale-freestructures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a widerange of objects including molecular clouds, accretion disks and perhaps galaxies.

  4. 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.

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

    ERIC Educational Resources Information Center

    Blank, Rolf K.

    2010-01-01

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

  6. Stochastic model for tumor growth with immunization

    NASA Astrophysics Data System (ADS)

    Bose, Thomas; Trimper, Steffen

    2009-05-01

    We analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution Ps is derived depending on the finite correlation time, the immunization rate, and the strength of the cross correlation. Ps offers a maximum which becomes more pronounced for increasing immunization rate. The mean-first-passage time is also calculated in order to find out under which conditions the tumor can suffer extinction. Its characteristics are again controlled by the degree of immunization and the strength of the cross correlation. The behavior observed can be interpreted in terms of a biological model of tumor evolution.

  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. Langevin equations for competitive growth models

    NASA Astrophysics Data System (ADS)

    Silveira, F. A.; Aarão Reis, F. D. A.

    2012-01-01

    Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension ν and the nonlinear coefficient λ of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p→0. The superposition of those scaling factors gives ν˜p2 for random deposition with surface relaxation (RDSR) as the CD, and ν˜p, λ˜p3/2 for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p dependence of λ, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients.

  9. 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,…

  10. 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.

  11. 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…

  12. 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

  13. The research on Virtual Plants Growth Based on DLA Model

    NASA Astrophysics Data System (ADS)

    Zou, YunLan; Chai, Bencheng

    This article summarizes the separated Evolutionary Algorithm in fractal algorithm of Diffusion Limited Aggregation model (i.e. DLA model) and put forward the virtual plant growth realization in computer based on DLA model. The method is carried out in the VB6.0 environment to achieve and verify the plant growth based on DLA model.

  14. 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.

  15. Numeric Modeling of Granular Asteroid Growth

    NASA Astrophysics Data System (ADS)

    Beaumont, Benjamin; Lazzati, D.

    2014-01-01

    It is believed that planetesimals and asteroids are created by the constructive collisions of smaller objects, loosely bound under the effect of self-gravity and/or contact forces. However, the internal dynamics of these collisions and whether they trigger growth or fragmentation are poorly understood. Prior research in the topic has established regimes for the results of constructive collisions of particles under contact forces, but neglects gravity, a critical component once particles are no longer touching, and force chains, an uneven distribution of force inherent to granular materials. We run simulations binary collisions of clusters of particles modeled as hard spheres. Our simulations take into account self-gravity, dissipation of energy, friction, and use a potential function for overlapping particles to study force chains. We present here the collision outcome for clusters with variable masses, particle counts, velocities, and impact parameter. We compare our results to other models and simulations, and find that the collisions remain constructive at higher energies than classically predicted.

  16. 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.

  17. 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.

  18. 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

  19. [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.

  20. 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,…

  1. The Effect of Sample Size on Latent Growth Models.

    ERIC Educational Resources Information Center

    Hamilton, Jennifer; Gagne, Phillip E.; Hancock, Gregory R.

    A Monte Carlo simulation approach was taken to investigate the effect of sample size on a variety of latent growth models. A fully balanced experimental design was implemented, with samples drawn from multivariate normal populations specified to represent 12 unique growth models. The models varied factorially by crossing number of time points,…

  2. 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,…

  3. 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

  4. Evaluating Intercept-Slope Interactions in Latent Growth Modeling

    ERIC Educational Resources Information Center

    Sun, Ronghua; Willson, Victor L.

    2009-01-01

    The effects of misspecifying intercept-covariate interactions in a 4 time-point latent growth model were the focus of this investigation. The investigation was motivated by school growth studies in which students' entry-level skills may affect their rate of growth. We studied the latent interaction of intercept and a covariate in predicting growth…

  5. 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…

  6. 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.

  7. 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.

  8. 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…

  9. Extended Eden model reproduces growth of an acellular slime mold

    NASA Astrophysics Data System (ADS)

    Wagner, Geri; Halvorsrud, Ragnhild; Meakin, Paul

    1999-11-01

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

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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. PMID:15092277

  15. 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.

  16. 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.

  17. 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.

  18. 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 mixed-effects…

  19. The Growth of Structural Equation Modeling: 1994-2001

    ERIC Educational Resources Information Center

    Hershberger, Scott L.

    2003-01-01

    This study examines the growth and development of structural equation modeling (SEM) from the years 1994 to 2001. The synchronous development and growth of the Structural Equation Modeling journal was also examined. Abstracts located on PsycINFO were used as the primary source of data. The major results of this investigation were clear: (a) The…

  20. Development and evaluation of a biophysical tree growth model

    SciTech Connect

    Korol, R.L.H.

    1993-01-01

    Current research indicates projected climate change may influence the growth of individual trees. Therefore, growth and yield models that can respond to potential changes in climate need to be developed. TREE-BGC, a variant of the ecosystem process model FOREST-BGC, calculates the cycling of carbon, water and nitrogen in and through forested ecosystems. TREE-BGC allocates stand level estimates of photosynthesis (PSN) to each tree using a competition algorithm that incorporates tree height, radiation-use efficiency, and absorbed photosynthetically active radiation. This model was used to simulate the growth of trees grown in a dense and an open stand near Kamloops, B.C. Mortality occurred when the maintenance respiration demands of the tree exceeded the carbon allocated to the tree. The competition algorithm dynamically allocated stand estimates of PSN to individual trees such that the predicted reductions in diameter growth with stand density were similar to the observed reductions in diameter growth. Model results were tested statistically, using goodness-of-fit procedures to compare the cumulative diameter distributions, and the stand basal area and volume growth after a 20-year period. Model behavior was tested by simulating the growth, over a 100 year period, of individual trees initially grown at different stand densities. Plot level estimates of basal area growth and volume growth were highly correlated with actual measurements (r[sup 2] = 0.94 and 0.96, respectively; n = 24). The simulated cumulative diameter and height distributions were not significantly different than the actual cumulative diameter and height distributions for 23 of the 24 plots ([alpha] = 0.05). The model predicted volume growth to within 20 m[sup 3] ha[sup [minus]1], and basal area growth to within 10 m[sup 2] ha[sup [minus]1]. Individual tree diameter and height growth rates reflected the influences of competition, as did stand basal area and volume growth, and stand density.

  1. 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

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

    PubMed

    Hirst, Andrew G; Forster, Jack

    2013-10-01

    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.

  3. Growth/no growth models for heat-treated psychrotrophic Bacillus cereus spores under cold storage.

    PubMed

    Daelman, Jeff; Vermeulen, An; Willemyns, Tine; Ongenaert, Rebecca; Jacxsens, Liesbeth; Uyttendaele, Mieke; Devlieghere, Frank

    2013-01-15

    The microbiological safety of refrigerated and processed foods of extended durability (REPFED) is linked to spore-forming pathogens, more specifically Clostridium botulinum and Bacillus cereus. In this study two sets of growth/no growth (GNG) models are presented for the spores of two B. cereus strains. The models incorporate both product (water activity (a(w)) and pH) and process parameters (pasteurization value at 90 °C (P(90)) or heating temperature). The first model evaluates the effect of four different P(90)-values (P(90)=0, 4, 7 or 10 min, all applied at 90 °C) on the germination and subsequent growth of B. cereus spores under different conditions of pH and a(w) at 10 °C. These models show that a heat treatment not only increases the time to growth (TTG), but also significantly increases the minimal a(w) and pH necessary for germination and subsequent growth: e.g. at a(w) 0.995 and without heat treatment (P(90)=0), strain FF355 B. cereus spores were predicted to germinate and grow at pH 5.3. With a P(90) of 10 min, the minimal pH increased to 5.7. The second set of models for B. cereus spores compares the effect of three heat treatments with the same P(90)-value (10 min) but applied at different temperatures (85, 87 and 90 °C), on the germination and subsequent growth at 10 °C. The second model shows that lower heating temperatures (85 and 87 °C) had less effect on the TTG and minimal a(w) and pH than a higher temperature (90 °C). Finally, the first set of models was validated in broth using spores of seven psychrotrophic B. cereus strains, to evaluate the effect of strain variability on the model predictions. The results of the validation (% growth) were compared to the predicted growth probability. The results showed that the models were prone to fail-dangerous results (i.e. predicting no growth when growth was observed: 17%-34%). Using a very low threshold for growth (0.1% predicted chance of growth was considered to be complete growth), the models

  4. A Stochastic Super-Exponential Growth Model for Population Dynamics

    NASA Astrophysics Data System (ADS)

    Avila, P.; Rekker, A.

    2010-11-01

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

  5. A von Bertalanffy growth model with a seasonally varying coefficient

    USGS Publications Warehouse

    Cloern, James E.; Nichols, Frederic H.

    1978-01-01

    The von Bertalanffy model of body growth is inappropriate for organisms whose growth is restricted to a seasonal period because it assumes that growth rate is invariant with time. Incorporation of a time-varying coefficient significantly improves the capability of the von Bertalanffy equation to describe changing body size of both the bivalve mollusc Macoma balthicain San Francisco Bay and the flathead sole, Hippoglossoides elassodon, in Washington state. This simple modification of the von Bertalanffy model should offer improved predictions of body growth for a variety of other aquatic animals.

  6. Growth dynamics of geographically different arbuscular mycorrhizal fungal isolates belonging to the 'Rhizophagus clade' under monoxenic conditions.

    PubMed

    Silvani, Vanesa Analía; Bidondo, Laura Fernández; Bompadre, María Josefina; Colombo, Roxana Paula; Pérgola, Mariana; Bompadre, Agustín; Fracchia, Sebastián; Godeas, Alicia

    2014-01-01

    The growth dynamics of extraradical mycelium and spore formation of 14 "Rhizophagus" isolates from different sites in Argentina were evaluated under monoxenic conditions. A modified Gompertz model was used to characterize the development of mycelium and spores for each isolate under the same conditions. The lag time, maximal growth rate and total quantity of both extraradical hyphae and spores were determined. Wide variability among isolates was detected, and all growth parameters were significantly altered by fungal isolate. Discriminant analysis differentiated isolates primarily based on the extent of extraradical hyphae produced, yet such differences did not conclusively correspond to phylogenetic relationships among closely related isolates based on partial SSU sequences. Given that the "Rhizophagus" isolates were grown under controlled conditions for many generations, the expression of phenotypic variability could be attributed to genetic differences that are not completely resolved by phylogenetic analysis employing the small ribosomal gene.

  7. 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...

  8. 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…

  9. 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.

  10. 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

  11. Calcite growth kinetics: Modeling the effect of solution stoichiometry

    NASA Astrophysics Data System (ADS)

    Wolthers, Mariëtte; Nehrke, Gernot; Gustafsson, Jon Petter; Van Cappellen, Philippe

    2012-01-01

    Until recently the influence of solution stoichiometry on calcite crystal growth kinetics has attracted little attention, despite the fact that in most aqueous environments calcite precipitates from non-stoichiometric solution. In order to account for the dependence of the calcite crystal growth rate on the cation to anion ratio in solution, we extend the growth model for binary symmetrical electrolyte crystals of Zhang and Nancollas (1998) by combining it with the surface complexation model for the chemical structure of the calcite-aqueous solution interface of Wolthers et al. (2008). To maintain crystal stoichiometry, the rate of attachment of calcium ions to step edges is assumed to equal the rate of attachment of carbonate plus bicarbonate ions. The model parameters are optimized by fitting the model to the step velocities obtained previously by atomic force microscopy (AFM, Teng et al., 2000; Stack and Grantham, 2010). A variable surface roughness factor is introduced in order to reconcile the new process-based growth model with bulk precipitation rates measured in seeded calcite growth experiments. For practical applications, we further present empirical parabolic rate equations fitted to bulk growth rates of calcite in common background electrolytes and in artificial seawater-type solutions. Both the process-based and empirical growth rate equations agree with measured calcite growth rates over broad ranges of ionic strength, pH, solution stoichiometry and degree of supersaturation.

  12. 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.

  13. 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.

  14. Uneven Futures of Human Lifespans: Reckonings from Gompertz Mortality Rates, Climate Change, and Air Pollution

    PubMed Central

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

    2014-01-01

    The past 200 years have enabled remarkable increases in human lifespans thru improvements of 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 Jean 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 C cohorts would require 50% slower mortality rate accelerations, which would be a fundamental change in the rate of human aging. Looking into the 21st C, 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 to favor the spread of pathogens. We anticipate continuing socio-economic disparities of life expectancy. PMID:24401556

  15. 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. PMID:24401556

  16. [Models of economic theory of population growth].

    PubMed

    Von Zameck, W

    1987-01-01

    "The economic theory of population growth applies the opportunity cost approach to the fertility decision. Variations and differentials in fertility are caused by the available resources and relative prices or by the relative production costs of child services. Pure changes in real income raise the demand for children or the total amount spent on children. If relative prices or production costs and real income are affected together the effect on fertility requires separate consideration." (SUMMARY IN ENG)

  17. 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.…

  18. 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.

  19. 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.

  20. Recent advances in crop growth modeling

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Crop simulation models and model-based decision support systems are increasingly used to assist agricultural research and development. The systems approach and modelling tools have been linked down to scales of functional genomics and up to regional scales of natural resource management. Although cr...

  1. Modeling the Growth of Infrarenal Abdominal Aortic Aneurysms

    PubMed Central

    Bailey, Marc A.; Baxter, Paul D.; Jiang, Tao; Charnell, Aimee M.; Griffin, Kathryn J.; Johnson, Anne B.; Bridge, Katherine I.; Sohrabi, Soroush; Scott, D. Julian A.

    2013-01-01

    Background: Abdominal aortic aneurysm (AAA) growth is a complex process that is incompletely understood. Significant heterogeneity in growth trajectories between patients has led to difficulties in accurately modeling aneurysm growth across cohorts of patients. We set out to compare four models of aneurysm growth commonly used in the literature and confirm which best fits the patient data of our AAA cohort. Methods: Patients with AAA were included in the study if they had two or more abdominal ultrasound scans greater than 3 months apart. Patients were censored from analysis once their AAA exceeded 5.5 cm. Four models were applied using the R environment for statistical computing. Growth estimates and goodness of fit (using the Akaike Information Criterion, AIC) were compared, with p-values based on likelihood ratio testing. Results: Of 510 enrolled patients, 264 met the inclusion criteria, yielding a total of 1861 imaging studies during 932 cumulative years of surveillance. Overall, growth rates were: (1) 0.35 (0.31,0.39) cm/yr in the growth/time calculation, (2) 0.056 (0.042,0.068) cm/yr in the linear regression model, (3) 0.19 (0.17,0.21) cm/yr in the linear multilevel model, and (4) 0.21 (0.18,0.24) cm/yr in the quadratic multilevel model at time 0, slowing to 0.15 (0.12,0.17) cm/yr at 10 years. AIC was lowest in the quadratic multilevel model (1508) compared to other models (P < 0.0001). Conclusion: AAA growth was heterogeneous between patients; the nested nature of the data is most appropriately modeled by multilevel modeling techniques. PMID:26798704

  2. Crystal growth kinetics of the two-step model

    NASA Astrophysics Data System (ADS)

    Tai, Clifford Y.; Lin, Chiu-Hsiung

    1987-03-01

    The single crystal technique was used to measure the growth rate of the potassium alum (111) face and the magnesium sulfate (110) face. The two-step model was found appropriate to describe the growth kinetics with the surface integration order of two for potassium alum crystal and of one for magnesium sulfate crystal. The individual rate constants, Kd and Kr, were determined accordingly.

  3. Models and Determinants of Vocabulary Growth from Kindergarten to Adulthood

    ERIC Educational Resources Information Center

    Beitchman, Joseph H.; Jiang, Hedy; Koyama, Emiko; Johnson, Carla J.; Escobar, Michael; Atkinson, Leslie; Brownlie, E. B.; Vida, Ron

    2008-01-01

    Background: Increasing evidence suggests that childhood language problems persist into early adulthood. Nevertheless, little is known about how individual and environmental characteristics influence the language growth of individuals identified with speech/language problems. Method: Individual growth curve models were utilised to examine how…

  4. 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…

  5. 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

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. A new model for simulating growth in fish

    PubMed Central

    Hamre, Johannes; Johnsen, Espen

    2014-01-01

    A real dynamic population model calculates change in population sizes independent of time. The Beverton & Holt (B&H) model commonly used in fish assessment includes the von Bertalanffy growth function which has age or accumulated time as an independent variable. As a result the B&H model has to assume constant fish growth. However, growth in fish is highly variable depending on food availability and environmental conditions. We propose a new growth model where the length increment of fish living under constant conditions and unlimited food supply, decreases linearly with increasing fish length until it reaches zero at a maximal fish length. The model is independent of time and includes a term which accounts for the environmental variation. In the present study, the model was validated in zebrafish held at constant conditions. There was a good fit of the model to data on observed growth in Norwegian spring spawning herring, capelin from the Barents Sea, North Sea herring and in farmed coastal cod. Growth data from Walleye Pollock from the Eastern Bering Sea and blue whiting from the Norwegian Sea also fitted reasonably well to the model, whereas data from cod from the North Sea showed a good fit to the model only above a length of 70 cm. Cod from the Barents Sea did not grow according to the model. The last results can be explained by environmental factors and variable food availability in the time under study. The model implicates that the efficiency of energy conversion from food decreases as the individual animal approaches its maximal length and is postulated to represent a natural law of fish growth. PMID:24498574

  14. 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.

  15. 2D modeling of the regeneration surface growth on crystals

    NASA Astrophysics Data System (ADS)

    Thomas, V. G.; Gavryushkin, P. N.; Fursenko, D. A.

    2012-11-01

    A physical model is proposed to describe the growth of regeneration surfaces (flat crystal surfaces that are not parallel to any possible faces). According to this model, the change in the growth rate of a regeneration surface during its evolution and the decrease in the number of subindividuals forming the growth front can be explained by the implementation of two types of geometric selection: within each subindividual (the absorption of rapidly growing faces by slowly growing ones) and between subindividuals (when subindividuals absorb each other). A numerical modeling of the growth of the regeneration surface (30.30.19) of potassium alum crystals showed quantitative agreement between the model proposed and the experimental data.

  16. Connection between stochastic and deterministic modelling of microbial growth.

    PubMed

    Kutalik, Zoltán; Razaz, Moe; Baranyi, József

    2005-01-21

    We present in this paper various links between individual and population cell growth. Deterministic models of the lag and subsequent growth of a bacterial population and their connection with stochastic models for the lag and subsequent generation times of individual cells are analysed. We derived the individual lag time distribution inherent in population growth models, which shows that the Baranyi model allows a wide range of shapes for individual lag time distribution. We demonstrate that individual cell lag time distributions cannot be retrieved from population growth data. We also present the results of our investigation on the effect of the mean and variance of the individual lag time and the initial cell number on the mean and variance of the population lag time. These relationships are analysed theoretically, and their consequence for predictive microbiology research is discussed.

  17. 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

    2015-01-01

    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

  18. 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.

  19. 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)

  20. 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…

  1. Evaluating Latent Variable Growth Models through Ex Post Simulation.

    ERIC Educational Resources Information Center

    Kaplan, David; George, Rani

    1998-01-01

    The use of ex post (historical) simulation statistics as means of evaluating latent growth models is considered, and a variety of simulation quality statistics are applied to such models. Results illustrate the importance of using these measures as adjuncts to more traditional forms of model evaluation. (SLD)

  2. 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'…

  3. 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.

  4. A probabilistic growth model for partition polygons and related structures

    NASA Astrophysics Data System (ADS)

    Kearney, Michael J.

    2004-03-01

    A two-parameter, probabilistic growth model for partition polygon clusters is introduced and exact results obtained relating to the area moments and the area probability distribution. In particular, the scaling behaviour in the presence of asymmetry between growth along the two principal axes is discussed. Variants of the model are also examined, including the extension to rooted stack polygons. An interesting application relates to characterizing the asymptotic behaviour of the cumulative customer waiting time distribution in a particular discrete-time queue.

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

    NASA Astrophysics Data System (ADS)

    Shigeta, Masaya; Watanabe, Takayuki

    2010-08-01

    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.

  6. 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.

  7. Composite growth model applied to human oral and pharyngeal structures and identifying the contribution of growth types.

    PubMed

    Wang, Yuan; Chung, Moo K; Vorperian, Houri K

    2013-11-13

    The growth patterns of different anatomic structures in the human body vary in terms of growth amount over time, growth rate and growth periods. The oral and pharyngeal structures, also known as vocal tract structures, are housed in the craniofacial complex where the cranium/brain follows a distinct neural growth pattern, and the face follows a distinct somatic or skeletal growth pattern. Thus, it is reasonable to expect the oral and pharyngeal structures to follow a combined or mixed growth pattern. Existing parametric growth models are limited in that they are mainly focused on modeling one particular type of growth pattern. In this paper, we propose a novel composite growth model using neural and somatic baseline curves to fit the combined growth pattern of select vocal tract structures. The method can also determine the overall percent contribution of each of the growth types.

  8. An Integrated Model of Posttraumatic Stress and Growth.

    PubMed

    Lancaster, Steven L; Klein, Keith R; Nadia, Cyrus; Szabo, Lisa; Mogerman, Ben

    2015-01-01

    A number of recent models have examined cognitive predictors of posttraumatic stress and posttraumatic growth (S. Barton, A. Boals, & L. Knowles, 2013; J. Groleau, L. Calhoun, A. Cann, & G. Tedeschi, 2013; K. N. Triplett, R. G. Tedeschi, A. Cann, L. G. Calhoun, & C. L. Reeve, 2012). The current study examined an integrated model of predictors of distress and perceived growth in 194 college undergraduates. Domains covered included the roles of core belief challenge, event centrality, posttrauma cognitions, and event-related rumination. Negative cognitions about the self and the centrality of the event directly predicted both growth and distress, although intrusive rumination predicted only posttraumatic stress disorder symptoms, and deliberate rumination predicted only posttraumatic growth. Future research should continue to examine the shared and unique predictors of postevent growth and distress. PMID:26011515

  9. An Integrated Model of Posttraumatic Stress and Growth.

    PubMed

    Lancaster, Steven L; Klein, Keith R; Nadia, Cyrus; Szabo, Lisa; Mogerman, Ben

    2015-01-01

    A number of recent models have examined cognitive predictors of posttraumatic stress and posttraumatic growth (S. Barton, A. Boals, & L. Knowles, 2013; J. Groleau, L. Calhoun, A. Cann, & G. Tedeschi, 2013; K. N. Triplett, R. G. Tedeschi, A. Cann, L. G. Calhoun, & C. L. Reeve, 2012). The current study examined an integrated model of predictors of distress and perceived growth in 194 college undergraduates. Domains covered included the roles of core belief challenge, event centrality, posttrauma cognitions, and event-related rumination. Negative cognitions about the self and the centrality of the event directly predicted both growth and distress, although intrusive rumination predicted only posttraumatic stress disorder symptoms, and deliberate rumination predicted only posttraumatic growth. Future research should continue to examine the shared and unique predictors of postevent growth and distress.

  10. Lattice Boltzmann models for the grain growth in polycrystalline systems

    NASA Astrophysics Data System (ADS)

    Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu

    2016-08-01

    In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  11. 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.

  12. A Phase-Field Model for Grain Growth

    SciTech Connect

    Chen, L.Q.; Fan, D.N.; Tikare, V.

    1998-12-23

    A phase-field model for grain growth is briefly described. In this model, a poly-crystalline microstructure is represented by multiple structural order parameter fields whose temporal and spatial evolutions follow the time-dependent Ginzburg-Landau (TDGL) equations. Results from phase-field simulations of two-dimensional (2D) grain growth will be summarized and preliminary results on three-dimensional (3D) grain growth will be presented. The physical interpretation of the structural order parameter fields and the efficient and accurate semi-implicit Fourier spectral method for solving the TDGL equations will be briefly discussed.

  13. 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.

  14. 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.

  15. 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. PMID:24066142

  16. 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

  17. 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.

  18. 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

  19. The deviation of growth model for transparent conductive graphene

    NASA Astrophysics Data System (ADS)

    Chan, Shih-Hao; Chen, Jia-Wei; Chen, Hung-Pin; Wei, Hung-Sen; Li, Meng-Chi; Chen, Sheng-Hui; Lee, Cheng-Chung; Kuo, Chien-Cheng

    2014-10-01

    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.

  20. The deviation of growth model for transparent conductive graphene.

    PubMed

    Chan, Shih-Hao; Chen, Jia-Wei; Chen, Hung-Pin; Wei, Hung-Sen; Li, Meng-Chi; Chen, Sheng-Hui; Lee, Cheng-Chung; Kuo, Chien-Cheng

    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

  1. 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. PMID:25499055

  2. A ``Hydrogen partitioning'' model for hydrogen assisted crack growth

    NASA Astrophysics Data System (ADS)

    Gao, M.; Wei, R. P.

    1985-11-01

    A “hydrogen partitioning” model has been developed to account for the pressure and temperature dependence for hydrogen-assisted crack growth. The model gives explicit recognition to the role of hydr en-microstructure interactions in determining the distribution (or partitioning) of hydrogen among the various microstructural elements (principally between the prior-austenite grain boundaries and the matrix) and the rate of crack growth along the elements. It also takes into account the role of various rate controlling processes in determining the rate that hydrogen is being supplied to the fracture process (or embrittlement) zone. Quantitative assessment of the model indicates very good agreements between the model predictions and the observed crack growth responses for AISI 4340 and 4130 steels tested in hydrogen and for AISI 4340 steel tested in hydrogen sulfide. This model accurately characterizes the reduction in crack growth rate and the concomitant change in fracture mode at “high” temperatures. Through its integration with the earlier models, based on rate controlling processes, the model predicts the pressure and temperature dependence for K-independent crack growth over the entire range of environmental conditions.

  3. 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.

  4. A mathematical model of the growth of uterine myomas.

    PubMed

    Chen, C Y; Ward, J P

    2014-12-01

    Uterine myomas or fibroids are common, benign smooth muscle tumours that can grow to 10  cm or more in diameter and are routinely removed surgically. They are typically slow- growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material, based on a linear stress-strain relationship, and Darcy's law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of nonlinear partial differential equations with two moving boundaries. Numerical solutions of the model successfully reproduce qualitatively the clinically observed three-phase "fast-slow-fast" growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch-like cell growth response to stress. Analysis of large-time solutions reveal that while there is a functioning vasculature throughout the myoma, exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is also presented, and in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model.

  5. 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…

  6. Modeling photosynthesis and the growth of marine phytoplankton

    NASA Astrophysics Data System (ADS)

    Zvalinsky, V. I.; Tishchenko, P. Ya.

    2016-07-01

    The paper analyzes the most popular models of photosynthesis and growth of marine phytoplankton in the literature and demonstrates their limitations. A new approach to modeling is proposed and used to obtain new models of marine phytoplankton photosynthesis and growth. An important feature of the proposed models is their ability to describe coupled multisubstrate cyclical interactions typical of biochemical and physiological processes. As a first approximation, the mathematical models are represented by equations of nonrectangular hyperbolas. The models describe the stoichiometry of extraction of elements from the medium, whatever the degree of their limitation, an important feature in describing biogeochemical cycles of elements. This stoichiometry is governed by measurable internal parameters of an organism (substrate parameters) and can be a key cause of stoichiometric formation of elements in the ambient medium, described, for example, by the Redfield ratio. The substrate constants are fundamental characteristics of the models, which form "automatically" in the construction of model equations in arbitrary units.

  7. Characterization of crystal growth using a spiral nucleation model

    NASA Astrophysics Data System (ADS)

    Martins, P. M.; Rocha, F.

    2007-08-01

    Classical concepts of two-dimensional nucleation and spiral growth are used together with recent findings on the dynamics of dislocation spirals to derive a new crystal growth model. Initial growth nuclei result from the organization of adsorbed molecules in spirals around surface dislocations. The energetic barrier for the activation of the spiral nuclei is considerably lower than the admitted by classical two dimensional nucleation models. Stable nuclei evolve into bigger growth hillocks in supersaturated media through the incorporation of adsorbed units into their steps. The displacement velocity of steps during solution and vapour growth is calculated by different kinetic approaches, taking into consideration the distinct role of surface diffusion in each process, and avoiding known limitations of conventional theories. A generalized expression is obtained relating the crystal growth rate with main variables such as supersaturation, temperature, crystal size, surface topology and interfacial properties. At the end of the paper, the crystallization kinetics of sucrose measured at 40 °C is interpreted in the light of the new perspectives resulting from the proposed model. The application example illustrates how to estimate interfacial and topological properties from the experimental crystal growth results.

  8. 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.

  9. 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.

  10. 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

  11. Physcomitrella patens: a model for tip cell growth and differentiation.

    PubMed

    Vidali, Luis; Bezanilla, Magdalena

    2012-12-01

    The moss Physcomitrella patens has emerged as an excellent model system owing to its amenability to reverse genetics. The moss gametophyte has three filamentous tissues that grow by tip growth: chloronemata, caulonemata, and rhizoids. Because establishment of the moss plant relies on this form of growth, it is particularly suited for dissecting the molecular basis of tip growth. Recent studies demonstrate that a core set of actin cytoskeletal proteins is essential for tip growth. Additional actin cytoskeletal components are required for modulating growth to produce caulonemata and rhizoids. Differentiation into these cell types has previously been linked to auxin, light and nutrients. Recent studies have identified that core auxin signaling components as well as transcription factors that respond to auxin or nutrient levels are required for tip-growing cell differentiation. Future studies may establish a connection between the actin cytoskeleton and auxin or nutrient-induced cell differentiation.

  12. A stoichiometrically derived algal growth model and its global analysis.

    PubMed

    Li, Xiong; Wang, Hao

    2010-10-01

    Organisms are composed of multiple chemical elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can severely restrict organismal and population growth. However, many trophic interaction models only consider carbon limitation via energy flow. In this paper, we construct an algal growth model with the explicit incorporation of light and nutrient availability to characterize both carbon and phosphorus limitations. We provide a global analysis of this model to illustrate how light and nutrient availability regulate algal dynamics. PMID:21077710

  13. Modeling gas exchange in a closed plant growth chamber

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  14. Modeling Gas Exchange in a Closed Plant Growth Chamber

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  15. 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.

  16. 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.

  17. 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…

  18. 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…

  19. 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…

  20. Sensitivity of Fit Indices to Misspecification in Growth Curve Models

    ERIC Educational Resources Information Center

    Wu, Wei; West, Stephen G.

    2010-01-01

    This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

  1. 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…

  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. 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

  4. A thermodynamic model for growth mechanisms of multiwall carbon nanotubes.

    SciTech Connect

    Kaatz, Forrest H.; Overmyer, Donald L.; Siegal, Michael P.

    2006-02-01

    Multiwall carbon nanotubes are grown via thermal chemical vapor deposition between temperatures of 630 and 830 C using acetylene in nitrogen as the carbon source. This process is modeled using classical thermodynamics to explain the total carbon deposition as a function of time and temperature. An activation energy of 1.60 eV is inferred for nanotube growth after considering the carbon solubility term. Scanning electron microscopy shows growth with diameters increasing linearly with time. Transmission electron microscopy and Raman spectroscopy show multiwall nanotubes surrounded by a glassy-carbon sheath, which grows with increasing wall thickness as growth temperatures and times rise.

  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. Modeling the atomistic growth behavior of gold nanoparticles in solution

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  11. Modeling the atomistic growth behavior of gold nanoparticles in solution.

    PubMed

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

    2016-04-28

    The properties of gold nanoparticles strongly depend on their three-dimensional atomic structure, leading to an increased emphasis on controlling and predicting nanoparticle structural evolution during the synthesis process. In order to provide this atomistic-level insight and establish a link to the experimentally-observed growth behavior, a kinetic Monte Carlo simulation (KMC) approach is developed for capturing Au nanoparticle growth characteristics. The advantage of this approach is that, compared to traditional molecular dynamics simulations, the atomistic nanoparticle structural evolution can be tracked on time scales that approach the actual experiments. This has enabled several different comparisons against experimental benchmarks, and it has helped transition the KMC simulations from a hypothetical toy model into a more experimentally-relevant test-bed. The model is initially parameterized by performing a series of automated comparisons of Au nanoparticle growth curves versus the experimental observations, and then the refined model allows for detailed structural analysis of the nanoparticle growth behavior. Although the Au nanoparticles are roughly spherical, the maximum/minimum dimensions deviate from the average by approximately 12.5%, which is consistent with the corresponding experiments. Also, a surface texture analysis highlights the changes in the surface structure as a function of time. While the nanoparticles show similar surface structures throughout the growth process, there can be some significant differences during the initial growth at different synthesis conditions. PMID:27091290

  12. Using the Expolinear Growth Equation for Modelling Crop Growth in Year‐round Cut Chrysanthemum

    PubMed Central

    LEE, JEONG HYUN; GOUDRIAAN, JAN; CHALLA, HUGO

    2003-01-01

    The aim of this study was to predict crop growth of year‐round cut chrysanthemum (Chrysanthemum morifolium Ramat.) based on an empirical model of potential crop growth rate as a function of daily incident photosynthetically active radiation (PAR, MJ m–2 d–1), using generalized estimated parameters of the expolinear growth equation. For development of the model, chrysanthemum crops were grown in four experiments at different plant densities (32, 48, 64 and 80 plants m–2), during different seasons (planting in January, May–June and September) and under different light regimes [natural light, shading to 66 and 43 % of natural light, and supplementary assimilation light (ASS, 40–48 µmol m–2 s–1)]. The expolinear growth equation as a function of time (EXPOT) or as a function of incident PAR integral (EXPOPAR) effectively described periodically measured total dry mass of shoot (R2 > 0·98). However, growth parameter estimates for the fitted EXPOPAR were more suitable as they were not correlated to each other. Coefficients of EXPOPAR characterized the relative growth rate per incident PAR integral [rm,i (MJ m–2)–1] and light use efficiency (LUE, g MJ–1) at closed canopy. In all four experiments, no interaction effects between treatments on crop growth parameters were found. rm,i and LUE were not different between ASS and natural light treatments, but were increased significantly when light levels were reduced by shading in the summer experiments. There was no consistent effect of plant density on growth parameters. rm,i and LUE showed hyperbolic relationships to average daily incident PAR averaged over 10‐d periods after planting (rm,i) or before final harvest (LUE). Based on those relationships, maximum relative growth rate (rm, g g–1 d–1) and maximum crop growth rate (cm, g m–2 d–1) were described successfully by rectangular hyperbolic relationships to daily incident PAR. In model validation, total dry mass of shoot (Wshoot, g m

  13. Rock Physics Models of Biofilm Growth in Porous Media

    NASA Astrophysics Data System (ADS)

    Jaiswal, P.; alhadhrami, F. M.; Atekwana, E. A.

    2013-12-01

    Recent studies suggest the potential to use acoustic techniques to image biofilm growth in porous media. Nonetheless the interpretation of the seismic response to biofilm growth and development remains speculative because of the lack of quantitative petrophysical models that can relate changes in biofilm saturation to changes in seismic attributes. Here, we report our efforts in developing quantitative rock physics models to biofilm saturation with increasing and decreasing P-wave velocity (VP) and amplitudes recorded in the Davis et al. [2010] physical scale experiment. We adapted rock physics models developed for modeling gas hydrates in unconsolidated sediments. Two distinct growth models, which appear to be a function of pore throat size, are needed to explain the experimental data. First, introduction of biofilm as an additional mineral grain in the sediment matrix (load-bearing mode) is needed to explain the increasing time-lapse VP. Second, introduction of biofilm as part of the pore fluid (pore-filling mode) is required to explain the decreasing time-lapse VP. To explain the time-lapse VP, up to 15% of the pore volume was required to be saturated with biofilm. The recorded seismic amplitudes, which can be expressed as a function of porosity, permeability and grain size, showed a monotonic time-lapse decay except on Day 3 at a few selected locations, where it increased. Since porosity changes are constrained by VP, amplitude increase could be modeled by increasing hydraulic conductivity. Time lapse VP at locations with increasing amplitudes suggest that these locations have a load-bearing growth style. We conclude that permeability can increase by up to 10% at low (~2%) biofilm saturation in load-bearing growth style due to the development of channels within the biofilm structure. Developing a rock physics model for the biofilm growth in general may help create a field guide for interpreting porosity and permeability changes in bioremediation, MEOR and

  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. 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

  16. 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.

  17. Modeling sugarcane growth in response to age, insolation, and temperature

    SciTech Connect

    How, K.T.S.

    1986-01-01

    Modeling sugarcane growth in response to age of cane, insolation and air temperature using first-order multiple regression analysis and a nonlinear approach is investigated. Data are restricted to one variety from irrigated fields to eliminate the impact of varietal response and rainfall. Ten first-order models are investigated. The predictant is cane yield from 600 field tests. The predictors are cumulative values of insolation, maximum temperature, and minimum temperature for 3, 6, 12, and 18 months, or for each crop period derived from weather observations near the test plots. The low R-square values indicate that the selected predictor variables could not account for a substantial proportion of the variations of cane yield and the models have limited predictive values. The nonlinear model is based on known functional relationships between growth and age, growth and insolation, and growth and maximum temperature. A mathematical expression that integrates the effect of age, insolation and maximum temperature is developed. The constant terms and coefficients of the equation are determined from the requirement that the model must produce results that are reasonable when compared with observed monthly elongation data. The nonlinear model is validated and tested using another set of data.

  18. Differential Growth Trajectories for Achievement among Children Retained in First Grade: A Growth Mixture Model

    ERIC Educational Resources Information Center

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

    2014-01-01

    The authors investigated the differential effect of retention on the development of academic achievement from grades 1 to 5 on children retained in grade 1 over 6 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…

  19. 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.

  20. Von Neumann's growth model: Statistical mechanics and biological applications

    NASA Astrophysics Data System (ADS)

    De Martino, A.; Marinari, E.; Romualdi, A.

    2012-09-01

    We review recent work on the statistical mechanics of Von Neumann's growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann's model can be helpful in uncovering functional organization principles of cell energetics.

  1. Analyzing Quasi-Experiments: Some Implications of Assuming Continuous Growth Models.

    ERIC Educational Resources Information Center

    Blumberg, Carol Joyce; Porter, Andrew C.

    1983-01-01

    The general class of continuous growth models are described and examples representative of growth models suggested for various types of academic and/or physical growth are given. The fan spread hypothesis is discussed in relationship to natural growth models, as well as differential linear growth. (PN)

  2. 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.

  3. 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

  4. Thermal-capillary model for Czochralski growth of semiconductor materials

    NASA Technical Reports Server (NTRS)

    Derby, J. J.; Brown, R. A.

    1985-01-01

    The success of efficiently calculating the temperature field, crystal radius, melt mensicus, and melt/solid interface in the Czochralski crystal growth system by full finite-element solution of the government thermal-capillary model is demonstrated. The model predicts realistic response to changes in pull rate, melt volume, and the thermal field. The experimentally observed phenomena of interface flipping, bumping, and the difficulty maintaining steady-state growth as the melt depth decreases are explained by model results. These calculations will form the basis for the first quantitative picture of Cz crystal growth. The accurate depiction of the melt meniscus is important in calculating the crystal radius and solidification interface. The sensitivity of the results to the equilibrium growth angle place doubt on less sophisticated attempts to model the process without inclusion of the meniscus. Quantitative comparison with experiments should be possible once more representation of the radiation and view factors in the thermal system and the crucible are included. Extensions of the model in these directions are underway.

  5. 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.

  6. An Eden model for the growth of adaptive networks

    NASA Astrophysics Data System (ADS)

    Meakin, Paul

    1991-12-01

    An adaptive growth model based on the Eden model has been investigated using computer simulations. In this model a “score” associated with all the sites along the shortest path from the newly added site to the initial seed or growth site is incremented by an amount δ 1 ( δ1=1/( l+1) η where l is the path length) and the score associated with all the sites in the cluster is decreased by a fixed amount δ2 ( δ2=1/ Nm) after each growth event. If the score associated with a site falls below zero it is removed from the cluster. In the asymptotic limit ( t→∞ where t is the number of growth events) the cluster size fluctuates about a constant value proportional to N vm where the exponent v is given by the empirical relationship v=2/(2+ η), which is supported by simple theoretical considerations. The growth of the number of occupied sites, s( t), can be represented by the scaling form s( t) = N vm ƒ(t/N vm) .

  7. Effects of growth hormone and insulin-like growth factor I on muscle in mouse models of human growth disorders.

    PubMed

    Clark, Ryan P; Schuenke, Mark; Keeton, Stephanie M; Staron, Robert S; Kopchick, John J

    2006-01-01

    The precise effects of growth hormone (GH) and insulin-like growth factor I (IGF-I) on muscle development and physiology are relatively unknown. Furthermore, there have been conflicting reports on the effects of GH/IGF-I on muscle. Distinguishing the direct effects of GH versus those of IGF-I is problematic, but animal models with altered GH/IGF-I action could help to alleviate some of the conflicting results and help to determine the independent actions of GH and IGF-I. The phenotypes of several mouse models, namely the GH receptor-gene-disrupted (GHR -/-) mouse and a variety of IGF-I -/- mice, are summarized, which ultimately will aid our understanding of this complex area. PMID:17259718

  8. 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

  9. 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

  10. Multiscale models for the growth of avascular tumors

    NASA Astrophysics Data System (ADS)

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

    2007-06-01

    In the past 30 years we have witnessed an extraordinary progress on the research in the molecular biology of cancer, but its medical treatment, widely based on empirically established protocols, still has many limitations. One of the reasons for that is the limited quantitative understanding of the dynamics of tumor growth and drug response in the organism. In this review we shall discuss in general terms the use of mathematical modeling and computer simulations related to cancer growth and its applications to improve tumor therapy. Particular emphasis is devoted to multiscale models which permit integration of the rapidly expanding knowledge concerning the molecular basis of cancer and the complex, nonlinear interactions among tumor cells and their microenvironment that will determine the neoplastic growth at the tissue level.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  13. Cinder cone growth modeled after Northeast crater, Mount Etna, Sicily

    NASA Technical Reports Server (NTRS)

    Mcgetchin, T. R.; Settle, M.; Chouet, B. A.

    1974-01-01

    The structure, physical properties of ejecta, ballistics, and growth of Northeast crater, a young pyroclastic cone that originated in 1911 near the summit of Mount Etna, Sicily, were studied in order to form a model of volcano cinder cone growth. Four stages of growth were discerned: (1) a simple cone; (2) a cone with an outward-dipping talus slope; (3) destruction of rounded rim by the inward migration of the upper edge of the talus pile; and (4) extension of limits of talus pile beyond the ballistic limit of ejecta trajectories. The model is used to predict the features of lunar and Martian cones, assuming that they erupted under conditions qualitatively similar to Etna's Northeast crater.

  14. 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.

  15. 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.

  16. A Model of Chloroplast Growth Regulation in Mesophyll Cells.

    PubMed

    Paton, Kelly M; Anderson, Lisa; Flottat, Pauline; Cytrynbaum, Eric N

    2015-09-01

    Chloroplasts regulate their growth to optimize photosynthesis. Quantitative data show that the ratio of total chloroplast area to mesophyll cell area is constant across different cells within a single species and also across species. Wild-type chloroplasts exhibit little scatter around this trend; highly irregularly shaped mutant chloroplasts exhibit more scatter. Here we propose a model motivated by a bacterial quorum-sensing model consisting of a switch-like signaling network that turns off chloroplast growth. We calculated the dependence of the location of the relevant saddle-node bifurcation on the geometry of the chloroplasts. Our model exhibits a linear trend, with linearly growing scatter dependent on chloroplast shape, consistent with the data. When modeled chloroplasts are of a shape that grows with a constant area-to-volume ratio (disks, cylinders), we find a linear trend with minimal scatter. Chloroplasts with area and volume that do not grow proportionally (spheres) exhibit a linear trend with additional scatter.

  17. 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.

  18. Optimization of a new mathematical model for bacterial growth

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

  19. Modelling of root growth and bending in two dimensions.

    PubMed

    Zieschang, H E; Brain, P; Barlow, P W

    1997-02-01

    A special co-ordinate system is developed for modelling the gravitropic bending of plant roots. It is based on the Local Theory of Curves in differential geometry and describes, in one dimension, growth events that may actually occur in two, or even three, dimensions. With knowledge of the spatial distributions of relative elemental growth rates (RELELs) for the upper and lower flanks of a gravistimulated root, and also their temporal dependencies, it is possible to compute the development of curvature along the root and hence describe the time-course of gravitropic bending. In addition, the RELEL distributions give information about the velocity field and the basipetal displacement of points along the root's surface. According to the Fundamental Theorem of Local Curve Theory, the x and y co-ordinates of the root in its bending plane are then determined from the associated values of local curvature and local velocity. With the aid of this model, possible mathematical growth functions that correspond to biological mechanisms involved in differential growth can be tested. Hence, the model can help not only to distinguish the role of various physiological or biophysical parameters in the bending process, but also to validate hypotheses that make assumptions concerning their relative importance. However, since the model is constructed at the level of the organ and treats the root as a fluid continuum, none of the parameters relate to cellular behaviour; the parameters must instead necessarily apply to properties that impinge on the behaviour of the external boundary of the root. PMID:11536796

  20. 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…

  1. 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 (TILSA)…

  2. 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,…

  3. 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…

  4. 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…

  5. 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

  6. The dynamics of error growth in a quasigeostrophic channel model

    NASA Technical Reports Server (NTRS)

    Straus, David M.

    1988-01-01

    The objective of the paper is to determine the extent to which baroclinic instability contributes to the growth of errors in simple, yet realistic models of atmospheric flow. The model used here is a two-level quasi-geostrophic channel model. Results of two predictability experiments are reported. In one experiment, the initial condition perturbation was confined to the highest wavenumbers and had an energy of 1 percent of the climatological energy of the model for these scales. In the other experiment, perturbations were put only in the planetary wave and had the same strength relative to climatology as in the first experiment, leading to much larger absolute errors.

  7. Network effects in a human capital based economic growth model

    NASA Astrophysics Data System (ADS)

    Vaz Martins, Teresa; Araújo, Tanya; Augusta Santos, Maria; St Aubyn, Miguel

    2009-06-01

    We revisit a recently introduced agent model [ACS, 11, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents’ social network, both on an agent’s decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.

  8. Dimensions of Escherichia coli at various growth rates: model for envelope growth.

    PubMed Central

    Pierucci, O

    1978-01-01

    The duplication of Escherichia coli B/r is described based on two independent sequences, the replication of the genome and the growth of the envelope. It is proposed that (i) new envelope growth zones are activated coincident with the initiation of new rounds of chromosome replication; (ii) each zone is active in envelope synthesis from the time of its inauguration to the division which follows the completion of the round of chromosome replication (that is, for C + D min); and (iii) the rate of envelope synthesis at each site is constant, independent of the growth rate. Measurements of the surface areas of two E. coli B/r substrains growing at a variety of rates and during nutritional transitions are consistent with the predictions of the model. PMID:355233

  9. 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.

  10. 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

  11. A Predictive Model of High Shear Thrombus Growth.

    PubMed

    Mehrabadi, Marmar; Casa, Lauren D C; Aidun, Cyrus K; Ku, David N

    2016-08-01

    The ability to predict the timescale of thrombotic occlusion in stenotic vessels may improve patient risk assessment for thrombotic events. In blood contacting devices, thrombosis predictions can lead to improved designs to minimize thrombotic risks. We have developed and validated a model of high shear thrombosis based on empirical correlations between thrombus growth and shear rate. A mathematical model was developed to predict the growth of thrombus based on the hemodynamic shear rate. The model predicts thrombus deposition based on initial geometric and fluid mechanic conditions, which are updated throughout the simulation to reflect the changing lumen dimensions. The model was validated by comparing predictions against actual thrombus growth in six separate in vitro experiments: stenotic glass capillary tubes (diameter = 345 µm) at three shear rates, the PFA-100(®) system, two microfluidic channel dimensions (heights = 300 and 82 µm), and a stenotic aortic graft (diameter = 5.5 mm). Comparison of the predicted occlusion times to experimental results shows excellent agreement. The model is also applied to a clinical angiography image to illustrate the time course of thrombosis in a stenotic carotid artery after plaque cap rupture. Our model can accurately predict thrombotic occlusion time over a wide range of hemodynamic conditions.

  12. [Growth modeling of Albizia niopoides (Mimosaceae) using dendrochronological methods].

    PubMed

    Giraldo, Víctor David; del Valle, Jorge Ignacio

    2012-09-01

    The annual growth rings in tropical trees are fairly common, but their study is relatively recent. Growth rings were found in trees of Albizia niopoides from the Porce River Canyon, Central Cordillera of the Colombian Andes. A total of 33 cross-sections were collected from trees distributed throughout the study area from 664-870masl. Cross-dating, spaguetti plot and 14C analyses were used to demonstrate ring annuality, assuming as hypothesis that these are real annual growth rings. A combination of descriptive analysis of time series (smoothing and pre-whitening) to filter climate noise and nonlinear regression with weighted residuals was used to fit the diameter to Korfs growth model, in which the coefficient of determination reaches values close to 100%. The positive residual autocorrelation of order 1, although not significant, is explained by the existence of energy reserves in the stem and by the accumulation of diameter increments required for the construction of the diameter growth model. The current and mean annual maximum increment rates are 1.03 and 0.94cm/year at ages 18 and 46 years old, respectively. These trees are classified within the group of fast growing species which can reach a cut diameter of over 50cm in approximately 52 years.

  13. [Growth modeling of Albizia niopoides (Mimosaceae) using dendrochronological methods].

    PubMed

    Giraldo, Víctor David; del Valle, Jorge Ignacio

    2012-09-01

    The annual growth rings in tropical trees are fairly common, but their study is relatively recent. Growth rings were found in trees of Albizia niopoides from the Porce River Canyon, Central Cordillera of the Colombian Andes. A total of 33 cross-sections were collected from trees distributed throughout the study area from 664-870masl. Cross-dating, spaguetti plot and 14C analyses were used to demonstrate ring annuality, assuming as hypothesis that these are real annual growth rings. A combination of descriptive analysis of time series (smoothing and pre-whitening) to filter climate noise and nonlinear regression with weighted residuals was used to fit the diameter to Korfs growth model, in which the coefficient of determination reaches values close to 100%. The positive residual autocorrelation of order 1, although not significant, is explained by the existence of energy reserves in the stem and by the accumulation of diameter increments required for the construction of the diameter growth model. The current and mean annual maximum increment rates are 1.03 and 0.94cm/year at ages 18 and 46 years old, respectively. These trees are classified within the group of fast growing species which can reach a cut diameter of over 50cm in approximately 52 years. PMID:23025084

  14. 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.

  15. Zebrafish and giant danio as models for muscle growth: determinate vs. indeterminate growth as determined by morphometric analysis.

    PubMed

    Biga, P R; Goetz, F W

    2006-11-01

    The zebrafish has become an important genetic model, but their small size makes them impractical for traditional physiological studies. In contrast, the closely related giant danio is larger and can be utilized for physiological studies that can also make use of the extensive zebrafish genomic resources. In addition, the giant danio and zebrafish appear to exhibit different growth types, indicating the potential for developing a comparative muscle growth model system. Therefore, the present study was conducted to compare and characterize the muscle growth pattern of zebrafish and giant danio. Morphometric analyses demonstrated that giant danio exhibit an increased growth rate compared with zebrafish, starting as early as 2 wk posthatch. Total myotome area, mean fiber area, and total fiber number all exhibited positive correlations with larvae length in giant danio but not in zebrafish. Morphometric analysis of giant danio and zebrafish larvae demonstrated faster, more efficient growth in giant danio larvae. Similar to larger teleosts, adult giant danio exhibited increased growth rates in response to growth hormone, suggesting that giant danio exhibit indeterminate growth. In contrast, adult zebrafish do not exhibit mosaic hyperplasia, nor do they respond to growth hormone, suggesting they exhibit determinate growth like mammals. These results demonstrate that giant danio and zebrafish can be utilized as a direct comparative model system for muscle growth studies, with zebrafish serving as a model organism for determinate growth and giant danio for indeterminate growth.

  16. Advanced Finite Element Modeling of Low Cycle Fatigue Crack Growth

    NASA Technical Reports Server (NTRS)

    Gregg, Wayne; McGill, Preston; Swanson, Greg; Wells, Doug; Throckmorton, D. A. (Technical Monitor)

    2001-01-01

    This document (a viewgraph presentation) assumes a crack-like defect of a size which may be missed in inspection will exist in most critical location of any critical structure or component. Flaw existence assumption is usually, but not always, conservative based on past experiences in NASA and knowledge of manufacturing processes. Cyclic, environmental, and sustained loads used to generate stresses on models. Fracture Mechanics analysis used to predict crack growth and residual strength. Must show that defective structure will still provide four times required mission lifetime. Special exemptions cover redundant structures, low risk parts, etc. Assessments require specialized software tools, experienced analysts, and reliable material crack growth rate test database.

  17. 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.

  18. 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

  19. Emergent properties of a computational model of tumour growth.

    PubMed

    Pantziarka, Pan

    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

  20. 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.

  1. Microphysical fundamentals governing cirrus cloud growth: Modeling studies

    NASA Technical Reports Server (NTRS)

    Sassen, Kenneth; Dodd, Gregory C.; Starr, David

    1990-01-01

    For application to Global Climate Models, large scale numerical models of cirrus cloud formation and maintenance need to be refined to more reliably simulate the effects and feedbacks of high level clouds. A key aspect is how ice crystal growth is initiated in cirrus, which has started a cloud microphysical controversy between camps either believing that heterogeneous or homogeneous drop freezing is predominantly responsible for cold cirrus ice crystal nucleation. In view of convincing evidence for the existence of highly supercooled cloud droplets in the middle and upper troposphere, however, it is concluded that active ice nuclei are rather scarce at cirrus cloud altitudes, and so a new understanding of cirrus cloud formation is needed. This understanding is sought through an examination of cirrus cloud growth models.

  2. 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. PMID:25665006

  3. 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%.

  4. Predictive Models for Nanostructure Evolution during Epitaxial Thin Film Growth

    NASA Astrophysics Data System (ADS)

    Evans, Jim

    2004-03-01

    We describe the development of a realistic atomistic lattice-gas (LG) model for multilayer homoepitaxial growth of metal(100) films at higher deposition temperatures (T). The model is tailored to incorporate the essential physical processes underlying growth, and is thus efficiently simulated using KMC [1]. It is shown to reliably predict film morphologies up to 1000's layers for a broad range of deposition conditions (T, flux), in fact revealing quite unexpected behavior. Specifically, we consider the Ag/Ag(100) system - the perceived prototype for smooth quasi-layer-by-layer growth at higher T. We predict the formation of mounds (multilayer stacks of islands) above 150K due to a small non-uniform step edge barrier. Initial growth at 300K is indeed smooth, but subsequent growth is actually extremely rough, corresponding to prolonged mound steepening. Thin films grow rougher at lower T down to 200K, but thick films grow smoother. Experiments confirm these surprising predictions [1,2]. We also find that long-time mound dynamics is quite distinct from predictions of standard continuum theories. For Ag/Ag(100) growth below 150K in the absence of terrace diffusion, one finds self-affine growth of films containing bulk vacancies [3], the latter feature being confirmed by X-ray scattering studies [4]. This regime can be modeled by accelerated MD [5], generic self-teaching KMC [6], or tailored LG models (distinct from the above model for higher T) [3,7]. Using the latter, we identify the key processes controlling morphology from 0-150K as capture of deposited atoms on the sides of nanoprotrusions, and the activation of low-barrier interlayer thermal diffusion processes. [1] Caspersen et al. PRB 65 (2002) 193407. [2] Elliott et al. PRB 54 (1996) 17938. [3] Stoldt et al. PRL 85 (2000) 800. [4] Botez et al. PRB 66 (2002) 075418. [5] Montalenti et al. PRL 87 (2001) 126101. [6] Henkelman et al. PRL 90 (2003) 116101. [7] Caspersen et al. PRB 64 (2001) 075401.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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

  10. On the Theory of Reactive Mixtures for Modeling Biological Growth

    PubMed Central

    Ateshian, Gerard A.

    2013-01-01

    Mixture theory, which can combine continuum theories for the motion and deformation of solids and fluids with general principles of chemistry, is well suited for modeling the complex responses of biological tissues, including tissue growth and remodeling, tissue engineering, mechanobiology of cells and a variety of other active processes. A comprehensive presentation of the equations of reactive mixtures of charged solid and fluid constituents is lacking in the biomechanics literature. This study provides the conservation laws and entropy inequality, as well as interface jump conditions, for reactive mixtures consisting of a constrained solid mixture and multiple fluid constituents. The constituents are intrinsically incompressible and may carry an electrical charge. The interface jump condition on the mass flux of individual constituents is shown to define a surface growth equation, which predicts deposition or removal of material points from the solid matrix, complementing the description of volume growth described by the conservation of mass. A formu-lation is proposed for the reference configuration of a body whose material point set varies with time. State variables are defined which can account for solid matrix volume growth and remodeling. Constitutive constraints are provided on the stresses and momentum supplies of the various constituents, as well as the interface jump conditions for the electrochem cal potential of the fluids. Simplifications appropriate for biological tissues are also proposed, which help reduce the governing equations into a more practical format. It is shown that explicit mechanisms of growth-induced residual stresses can be predicted in this framework. PMID:17206407

  11. Model for acid-base chemistry in nanoparticle growth (MABNAG)

    NASA Astrophysics Data System (ADS)

    Yli-Juuti, T.; Barsanti, K.; Hildebrandt Ruiz, L.; Kieloaho, A.-J.; Makkonen, U.; Petäjä, T.; Ruuskanen, T.; Kulmala, M.; Riipinen, I.

    2013-12-01

    Climatic effects of newly-formed atmospheric secondary aerosol particles are to a large extent determined by their condensational growth rates. However, all the vapours condensing on atmospheric nanoparticles and growing them to climatically relevant sizes are not identified yet and the effects of particle phase processes on particle growth rates are poorly known. Besides sulfuric acid, organic compounds are known to contribute significantly to atmospheric nanoparticle growth. In this study a particle growth model MABNAG (Model for Acid-Base chemistry in NAnoparticle Growth) was developed to study the effect of salt formation on nanoparticle growth, which has been proposed as a potential mechanism lowering the equilibrium vapour pressures of organic compounds through dissociation in the particle phase and thus preventing their evaporation. MABNAG is a model for monodisperse aqueous particles and it couples dynamics of condensation to particle phase chemistry. Non-zero equilibrium vapour pressures, with both size and composition dependence, are considered for condensation. The model was applied for atmospherically relevant systems with sulfuric acid, one organic acid, ammonia, one amine and water in the gas phase allowed to condense on 3-20 nm particles. The effect of dissociation of the organic acid was found to be small under ambient conditions typical for a boreal forest site, but considerable for base-rich environments (gas phase concentrations of about 1010 cm-3 for the sum of the bases). The contribution of the bases to particle mass decreased as particle size increased, except at very high gas phase concentrations of the bases. The relative importance of amine versus ammonia did not change significantly as a function of particle size. While our results give a reasonable first estimate on the maximum contribution of salt formation to nanoparticle growth, further studies on, e.g. the thermodynamic properties of the atmospheric organics, concentrations of low

  12. Model for acid-base chemistry in nanoparticle growth (MABNAG)

    NASA Astrophysics Data System (ADS)

    Yli-Juuti, T.; Barsanti, K.; Hildebrandt Ruiz, L.; Kieloaho, A.-J.; Makkonen, U.; Petäjä, T.; Ruuskanen, T.; Kulmala, M.; Riipinen, I.

    2013-03-01

    Climatic effects of newly-formed atmospheric secondary aerosol particles are to a large extent determined by their condensational growth rates. However, all the vapors condensing on atmospheric nanoparticles and growing them to climatically relevant sizes are not identified yet and the effects of particle phase processes on particle growth rates are poorly known. Besides sulfuric acid, organic compounds are known to contribute significantly to atmospheric nanoparticle growth. In this study a particle growth model MABNAG (Model for Acid-Base chemistry in NAnoparticle Growth) was developed to study the effect of salt formation on nanoparticle growth, which has been proposed as a potential mechanism lowering the equilibrium vapor pressures of organic compounds through dissociation in the particle phase and thus preventing their evaporation. MABNAG is a model for monodisperse aqueous particles and it couples dynamics of condensation to particle phase chemistry. Non-zero equilibrium vapor pressures, with both size and composition dependence, are considered for condensation. The model was applied for atmospherically relevant systems with sulfuric acid, one organic acid, ammonia, one amine and water in the gas phase allowed to condense on 3-20 nm particles. The effect of dissociation of the organic acid was found to be small under ambient conditions typical for a boreal forest site, but considerable for base-rich environments (gas phase concentrations of about 1010 cm-3 for the sum of the bases). The contribution of the bases to particle mass decreased as particle size increased, except at very high gas phase concentrations of the bases. The relative importance of amine versus ammonia did not change significantly as a function of particle size. While our results give a reasonable first estimate on the maximum contribution of salt formation to nanoparticle growth, further studies on, e.g. the thermodynamic properties of the atmospheric organics, concentrations of low

  13. A mathematical model for pancreatic cancer growth and treatments.

    PubMed

    Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B; Friedman, Avner

    2014-06-21

    Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer.

  14. 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.

  15. A mathematical model for pancreatic cancer growth and treatments.

    PubMed

    Louzoun, Yoram; Xue, Chuan; Lesinski, Gregory B; Friedman, Avner

    2014-06-21

    Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer. PMID:24594371

  16. 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.

  17. 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.

  18. 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…

  19. Study on Growth Curves of Longissimus dorsi Muscle Area, Backfat Thickness and Body Conformation for Hanwoo (Korean Native) Cows

    PubMed Central

    Lee, J. H.; Oh, S.-H.; Lee, Y. M.; Kim, Y. S.; Son, H. J.; Jeong, D. J.; Whitley, N. C.; Kim, J. J.

    2014-01-01

    The objective of this study was to estimate the parameters of Gompertz growth curves with the measurements of body conformation, real-time ultrasound longissimus dorsi muscle area (LMA) and backfat thickness (BFT) in Hanwoo cows. The Hanwoo cows (n = 3,373) were born in 97 Hanwoo commercial farms in the 17 cities or counties of Gyeongbuk province, Korea, between 2000 and 2007. A total of 5,504 ultrasound measurements were collected for the cows at the age of 13 to 165 months in 2007 and 2008. Wither height (HW), rump height (HR), the horizontal distance between the top of the hips (WH), and girth of chest (GC) were also measured. Analysis of variance was conducted to investigate variables affecting LMA and BFT. The effect of farm nested in location was included in the statistical model, as well as the effects of HW, HR, WH, and GC as covariates. All of the effects were significant in the analysis of variance for LMA and BFT (p<0.01), except for the HR effect for LMA. The two ultrasound measures and the four body conformation traits were fitted to a Gompertz growth curve function to estimate parameters. Upper asymptotic weights were estimated as 54.0 cm2, 7.67 mm, 125.6 cm, 126.4 cm, 29.3 cm, and 184.1 cm, for LMA, BFT, HW, HR, WH, and GC, respectively. Results of ultrasound measurements showed that Hanwoo cows had smaller LMA and greater BFT than other western cattle breeds, suggesting that care must be taken to select for thick BFT rather than an increase of only beef yield. More ultrasound records per cow are needed to get accurate estimates of growth curve, which, thus, helps producers select animals with high accuracy. PMID:25178367

  20. Survival curve fitting using the Gompertz function: a methodology for conducting cost-effectiveness analyses on mortality data.

    PubMed

    Messori, A

    1997-03-01

    The analysis of published survival curves can be the basis for incremental cost-effectiveness evaluations in which two treatments are compared with each other in terms of cost per life-year saved. The typical case is when a new treatment becomes available which is more effective and more expensive than the corresponding standard treatment. When effectiveness is expressed using the end-point of mortality, cost-effectiveness analysis can compare the (incremental) cost associated with the new treatment with the (incremental) clinical benefit measured in terms of number of life-years gained. The (incremental) cost-effectiveness ratio is therefore quantified as cost per life-year gained. This pharmacoeconomic methodology requires that the total patients years for the treatment and the control groups are estimated from their respective survival curves. We describe herein a survival-curve fitting method which carries our this estimation and a computer program implementing the entire procedure. Our method is based on a non-linear least-squares analysis in which the experimental points of the survival curve are fitted to the Gompertz function. The availability of a commercial program (PCNONLIN) is needed to carry out matrix handling calculations. Our procedure performs the estimation of the best-fit parameters from the survival curve data and then integrates the Gompertz survival function from zero-time to infinity. This integration yields the value of the area under the survival curve (AUC) which is an estimate of the number of patients years totalled in the population examined. If this AUC estimation is performed separately for the two survival curves of two treatments being compared, the difference between the two AUCs permits to determine the incremental number of patient years gained using the more effective of the two treatments as opposed to the other. The cost-effectiveness analysis can consequently be carried out. An example of application of this methodology is

  1. Modeling of defect formation in silicon carbide during PVT growth

    NASA Astrophysics Data System (ADS)

    Drachev, Roman Victorovich

    2002-01-01

    The improvement of PVT grown SiC structural quality is crucial for the wide commercialization of SiC devices that feature superior characteristics for power conditioning and control. This is why, this dissertation is devoted to investigation and development of comprehensive models that can help to explain, understand and, then, suppress (eliminate) formation of various defects in SiC during PVT growth. The dissertation consists of six chapters. The first chapter is introductory. The second chapter considers in detail the general principles and physical bases of the SiC PVT growth technique along with the temperature dependence of pressure, composition and stoichiometry of the SiC gaseous phase. Questions related to the diffusive mass transport in the SiC growth cell are also discussed. The growth velocity as a function of the mass transport rate, the heat balance at the surface of crystallization and the growth front-crystal backside temperature difference is analyzed. Also the graphitization processes and instability of the sublimation temperature in the source material region are addressed. Chapter number three concerns generation of silicon and carbon second phase precipitates at the front of SiC crystallization. The comprehensive models concerning these phenomena are developed. The fourth chapter considers defect formation in SiC caused by the presence of carbon and/or silicon second phase particles at the growth front. Generation mechanisms of such structural defects as heterogeneous inclusions, point and planar defects, and filamentary voids are discussed in detail. Chapter number five deals with the defects caused by thermal stresses in the growing boule of SiC. Analytical estimations of the axially symmetric temperature field distribution and shear stress radial distribution in plane strain approximation are employed in order to estimate the extent to which such phenomena cause the generation of dislocations and micropipe formation in the growing ingot. The

  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. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. Percolation model for growth rates of aggregates and its application for business firm growth

    NASA Astrophysics Data System (ADS)

    Fu, Dongfeng; Buldyrev, Sergey V.; Salinger, Michael A.; Stanley, H. Eugene

    2006-09-01

    Motivated by recent empirical studies of business firm growth, we develop a dynamic percolation model which captures some of the features of the economical system—i.e., merging and splitting of business firms—represented as aggregates on a d -dimensional lattice. We find the steady-state distribution of the aggregate size and explore how this distribution depends on the model parameters. We find that at the critical threshold, the standard deviation of the aggregate growth rates, σ , increases with aggregate size S as σ˜Sβ , where β can be explained in terms of the connectedness length exponent ν and the fractal dimension df , with β=1/(2νdf)≈0.20 for d=2 and 0.125 for d→∞ . The distributions of aggregate growth rates have a sharp peak at the center and pronounced wings extending over many standard deviations, giving the distribution a tent-shape form—the Laplace distribution. The distributions for different aggregate sizes scaled by their standard deviations collapse onto the same curve.

  10. 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

  11. Modeling algae growth in an open-channel raceway.

    SciTech Connect

    James, Scott Carlton

    2010-09-01

    Cost-effective implementation of microalgae as a solar-to-chemical energy conversion platform requires extensive system optimization; computer modeling can bring this to bear. This work uses modified versions of the U.S. Environmental Protection Agency's (EPA's) Environmental Fluid Dynamics Code (EFDC) in conjunction with the U.S. Army Corp of Engineers water-quality code (CE-QUAL) to simulate hydrodynamics coupled to growth kinetics of algae (Phaeodactylum tricornutum) in open-channel raceways. The model allows the flexibility to manipulate a host of variables associated with raceway-design, algal-growth, water-quality, hydrodynamic, and atmospheric conditions. The model provides realistic results wherein growth rates follow the diurnal fluctuation of solar irradiation and temperature. The greatest benefit that numerical simulation of the flow system offers is the ability to design the raceway before construction, saving considerable cost and time. Moreover, experiment operators can evaluate the impacts of various changes to system conditions (e.g., depth, temperature, flow speeds) without risking the algal biomass under study.

  12. Modeling algae growth in an open-channel raceway.

    PubMed

    James, Scott C; Boriah, Varun

    2010-07-01

    Cost-effective implementation of microalgae as a solar-to-chemical energy conversion platform requires extensive system optimization; computer modeling can bring this to bear. This work uses modified versions of the U.S. Environmental Protection Agency's (EPA's) Environmental Fluid Dynamics Code (EFDC) in conjunction with the U.S. Army Corp of Engineers' water-quality code (CE-QUAL) to simulate hydrodynamics coupled to growth kinetics of algae (Phaeodactylum tricornutum) in open-channel raceways. The model allows the flexibility to manipulate a host of variables associated with raceway-design, algal-growth, water-quality, hydrodynamic, and atmospheric conditions. The model provides realistic results wherein growth rates follow the diurnal fluctuation of solar irradiation and temperature. The greatest benefit that numerical simulation of the flow system offers is the ability to design the raceway before construction, saving considerable cost and time. Moreover, experiment operators can evaluate the impacts of various changes to system conditions (e.g., depth, temperature, flow speeds) without risking the algal biomass under study.

  13. Kinetic model of impurity poisoning during growth of calcite

    SciTech Connect

    DeYoreo, J; Wasylenki, L; Dove, P; Wilson, D; Han, N

    2004-05-18

    The central role of the organic component in biologically controlled mineralization is widely recognized. These proteins are characterized by a high proportion of acidic amino acid residues, especially aspartate, Asp. At the same time, biomineralization takes place in the presence of a number of naturally-occurring, inorganic impurities, particularly Mg and Sr. In an attempt to decipher the controls on calcite growth imposed by both classes of modifiers, we have used in situ AFM to investigate the dependence of growth morphology and step kinetics on calcite in the presence of Sr{sup 2+}, as well as a wide suite of Aspartic acid-bearing polypeptides. In each case, we observe a distinct and step-specific modification. Most importantly, we find that the step speed exhibits a characteristic dependence on impurity concentration not predicted by existing crystal growth models. While all of the impurities clearly induce appearance of a 'dead zone,' neither the width of that dead zone nor the dependence of step speed on activity or impurity content can be explained by invoking the Gibbs-Thomson effect, which is the basis for the Cabrera-Vermilyea model of impurity poisoning. Common kink-blocking models also fail to explain the observed dependencies. Here we propose a kinetic model of inhibition based on a 'cooperative' effect of impurity adsorption at adjacent kink sites. The model is in qualitative agreement with the experimental results in that it predicts a non-linear dependence of dead zone width on impurity concentration, as well as a sharp drop in step speed above a certain impurity content. However, a detailed model of impurity adsorption kinetics that give quantitative agreement with the data has yet to be developed.

  14. Czochralski silicon crystal growth: Modeling and simulation study

    NASA Astrophysics Data System (ADS)

    Javidi, Massoud

    Czochralski (CZ) crystal growth process is a widely used technique in the manufacturing of silicon crystals and other semiconductor materials such as germanium (Ge) and gallium arsenide (GaAs). The ultimate goal for the Integrated Circuit (IC) industry is to have the highest quality substrate. There is a huge interest to manipulate the thermal field in both the melt and crystal and control the melt convection and crystal-annealing rate in order to reduce growth striations, impurity and dopant inhomogeneity concentrations, excess point defects generation at interface, and micro defects nucleation and growth within the growing crystal. The objective of this investigation has been to facilitate and spearhead the development of a simple/efficient simulation tool for the accurate prediction of global thermal and flow fields and the melt-crystal interface position in the CZ process. The numerical algorithm employs a rectangular (fixed or non-uniform) mesh for enhanced computational efficiency and an enthalpy-based technique for interface tracking. Turbulent flow in the melt is accounted for by utilizing a K-ε model. Radiative heat transfer is modeled in a lumped parameter sense without appreciably compromising on solution accuracy to further allow for CPU times savings. The simulation tool is validated in a number of benchmark flows such as Wheeler's problem. For the CZ crystal growth process, an entire growth cycle has been computed and reliable predictions for the evolution of interface position, and flow/thermal field characteristics have been obtained. The enhanced CPU efficiency of the approach developed here could help integrate it into on-line control strategies.

  15. Modelling of growth and product formation of Porphyridium purpureum.

    PubMed

    Fleck-Schneider, Pascale; Lehr, Florian; Posten, Clemens

    2007-10-31

    In this contribution experimental data and simulations of growth and product formation of the unicellular microalgae Porphyridium purpureum are presented. A mathematical model has been developed for a better understanding of growth and product formation in production plants. The model has been refined with the results of several cultivations in a new photobioreactor designed especially for the study of microalgal kinetics under highly defined illumination conditions. In this photobioreactor light is generated by an external light source and then distributed by means of optical fibres into an internal draft tube which also serves as irradiation element. All cultivations were performed in turbidostate mode. The influence of different light intensity changes, including stepwise change and light-dark cycles in the range from millisecond to second, has been investigated and the results were integrated into the mathematical model. The structured mathematical model consists of three levels: metabolic flux, control of macromolecules and the reactor level. A new linear optimization approach has been realized, enabling the model to describe even very different cultivation conditions. Output variables are among others the commercially interesting macromolecules of the microalgae, e.g. polysaccharides, pigments and polyunsaturated fatty acids. Thus, reliable predictions of the specific production rates of these products are possible for the production in a larger scale.

  16. 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.

  17. A new 'Jackson Hunt' model for monotectic composite growth

    NASA Astrophysics Data System (ADS)

    Stöcker, C.; Ratke, L.

    1999-06-01

    Directional solidification of monotectic alloys can lead under certain conditions of growth velocity and temperature gradient in the melt to composite microstructures with a rodlike appearance. For a theoretical description most researchers applied the Jackson and Hunt model of rod eutectic growth and predicted a relation between the mean rod distance R and the solidification velocity v0, as v0R2=const. similar to eutectics. The comparison between theory and experiments always led to discrepancies not yet resolved. In the approach presented here we propose an additional mode of mass transport in front of the zone coupled growth, since in our mind the main difference between monotectic and eutectic solidification is the liquid phase state of the (rod) L2 phase growing simultaneously within a nearly perfectly pure solid matrix. We assume that the thermocapillary effect causes convection at the surface of the liquid L2 phase. This Marangoni convection induces a flow field in front of the solidification front and has a strong influence on the solute transport, depending on the local temperature gradient and the Peclet number. We find a new relation between R and v0 in the case of small Peclet numbers and discuss some consequences on the stability of composite growth.

  18. 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)

  19. Microscopic modeling of confined crystal growth and dissolution.

    PubMed

    Høgberget, Jørgen; Røyne, Anja; Dysthe, Dag K; Jettestuen, Espen

    2016-08-01

    We extend the (1+1)-dimensional fluid solid-on-solid (SOS) model to include a confining flat surface opposite to the SOS surface subject to a constant load. This load is balanced by a repulsive surface-surface interaction given by an ansatz which agrees with known analytical solutions in the limit of two separated flat surfaces. Mechanical equilibrium is imposed at all times by repositioning the confining surface. By the use of kinetic Monte Carlo (KMC) we calculate how the equilibrium concentration (deposition rate) depends on the applied load, and find it to reproduce analytical thermodynamics independent of the parameters of the interaction ansatz. We also study the dependency between the surface roughness and the saturation level as we vary the surface tension, and expand on previous analyses of the asymmetry between growth and dissolution by parametrizing the linear growth rate constant for growth and dissolution separately. We find the presence of a confining surface to affect the speed of growth and dissolution equally. PMID:27627386

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

    PubMed

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

    2013-06-01

    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.

  1. Microscopic modeling of confined crystal growth and dissolution

    NASA Astrophysics Data System (ADS)

    Høgberget, Jørgen; Røyne, Anja; Dysthe, Dag K.; Jettestuen, Espen

    2016-08-01

    We extend the (1+1)-dimensional fluid solid-on-solid (SOS) model to include a confining flat surface opposite to the SOS surface subject to a constant load. This load is balanced by a repulsive surface-surface interaction given by an ansatz which agrees with known analytical solutions in the limit of two separated flat surfaces. Mechanical equilibrium is imposed at all times by repositioning the confining surface. By the use of kinetic Monte Carlo (KMC) we calculate how the equilibrium concentration (deposition rate) depends on the applied load, and find it to reproduce analytical thermodynamics independent of the parameters of the interaction ansatz. We also study the dependency between the surface roughness and the saturation level as we vary the surface tension, and expand on previous analyses of the asymmetry between growth and dissolution by parametrizing the linear growth rate constant for growth and dissolution separately. We find the presence of a confining surface to affect the speed of growth and dissolution equally.

  2. 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…

  3. 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.

  4. 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...

  5. Travelling wave analysis of a mathematical model of glioblastoma growth.

    PubMed

    Gerlee, Philip; Nelander, Sven

    2016-06-01

    In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.

  6. Travelling wave analysis of a mathematical model of glioblastoma growth.

    PubMed

    Gerlee, Philip; Nelander, Sven

    2016-06-01

    In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered. PMID:27021919

  7. Mechanistic models of biofilm growth in porous media

    NASA Astrophysics Data System (ADS)

    Jaiswal, Priyank; Al-Hadrami, Fathiya; Atekwana, Estella A.; Atekwana, Eliot A.

    2014-07-01

    Nondestructive acoustics methods can be used to monitor in situ biofilm growth in porous media. In practice, however, acoustic methods remain underutilized due to the lack of models that can translate acoustic data into rock properties in the context of biofilm. In this paper we present mechanistic models of biofilm growth in porous media. The models are used to quantitatively interpret arrival times and amplitudes recorded in the 29 day long Davis et al. (2010) physical scale biostimulation experiment in terms of biofilm morphologies and saturation. The model pivots on addressing the sediment elastic behavior using the lower Hashin-Shtrikman bounds for grain mixing and Gassmann substitution for fluid saturation. The time-lapse P wave velocity (VP; a function of arrival times) is explained by a combination of two rock models (morphologies); "load bearing" which assumes the biofilm as an additional mineral in the rock matrix and "pore filling" which assumes the biofilm as an additional fluid phase in the pores. The time-lapse attenuation (QP-1; a function of amplitudes), on the other hand, can be explained adequately in two ways; first, through squirt flow where energy is lost from relative motion between rock matrix and pore fluid, and second, through an empirical function of porosity (φ), permeability (κ), and grain size. The squirt flow model-fitting results in higher internal φ (7% versus 5%) and more oblate pores (0.33 versus 0.67 aspect ratio) for the load-bearing morphology versus the pore-filling morphology. The empirical model-fitting results in up to 10% increase in κ at the initial stages of the load-bearing morphology. The two morphologies which exhibit distinct mechanical and hydraulic behavior could be a function of pore throat size. The biofilm mechanistic models developed in this study can be used for the interpretation of seismic data critical for the evaluation of biobarriers in bioremediation, microbial enhanced oil recovery, and CO2

  8. 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)

  9. Concentration-driven growth of model protocell membranes.

    PubMed

    Budin, Itay; Debnath, Anik; Szostak, Jack W

    2012-12-26

    The first protocell membranes may have assembled from fatty acids and related single-chain lipids available in the prebiotic environment. Prior to the evolution of complex cellular machinery, spontaneous protocell membrane growth and division had to result from the intrinsic physicochemical properties of these molecules, in the context of specific environmental conditions. Depending on the nature of the chemical and physical environment, fatty acids can partition between several different phases, including soluble monomers, micelles, and lamellar vesicles. Here we address the concentration dependence of fatty acid aggregation, which is dominated by entropic considerations. We quantitatively distinguish between fatty acid phases using a combination of physical and spectroscopic techniques, including the use of the fluorescent fatty acid analogue Laurdan, whose emission spectrum is sensitive to structural differences between micellar and lamellar aggregates. We find that the monomer-aggregate transition largely follows a characteristic pseudophase model of molecular aggregation but that the composition of the aggregate phase is also concentration dependent. At low amphiphile concentrations above the critical aggregate concentration, vesicles coexist with a significant proportion of micelles, while more concentrated solutions favor the lamellar vesicle phase. We subsequently show that the micelle-vesicle equilibrium can be used to drive the growth of pre-existing vesicles upon an increase in amphiphile concentration either through solvent evaporation or following the addition of excess lipids. We propose a simple model for a primitive environmentally driven cell cycle, in which protocell membrane growth results from evaporative concentration, followed by shear force or photochemically induced division. PMID:23198690

  10. 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. PMID:26436372

  11. Simulating Cancer Growth with Multiscale Agent-Based Modeling

    PubMed Central

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

    2014-01-01

    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. PMID:24793698

  12. 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.

  13. 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.

  14. A model of northern pintail productivity and population growth rate

    USGS Publications Warehouse

    Flint, P.L.; Grand, J.B.; Rockwell, R.F.

    1998-01-01

    Our objective was to synthesize individual components of reproductive ecology into a single estimate of productivity and to assess the relative effects of survival and productivity on population dynamics. We used information on nesting ecology, renesting potential, and duckling survival of northern pintails (Anas acuta) collected on the Yukon-Kuskokvim Delta (Y-K Delta), Alaska, 1991-95, to model the number of ducklings produced under a range of nest success and duckling survival probabilities. Using average values of 25% nest success, 11% duckling survival, and 56% renesting probability from our study population, we calculated that all young in our population were produced by 13% of the breeding females, and that early-nesting females produced more young than later-nesting females. Further, we calculated, on average, that each female produced only 0.16 young females/nesting season. We combined these results with estimates of first-year and adult survival to examine the growth rate (??) of the population and the relative contributions of these demographic parameters to that growth rate. Contrary to aerial survey data, the population projection model suggests our study population is declining rapidly (?? = 0.6969). The relative effects on population growth rate were 0.1175 for reproductive success, 0.1175 for first-year survival, and 0.8825 for adult survival. Adult survival had the greatest influence on ?? for our population, and this conclusion was robust over a range of survival and productivity estimates. Given published estimates of annual survival for adult females (61%), our model suggested nest success and duckling survival need to increase to approximately 40% to achieve population stability. We discuss reasons for the apparent discrepancy in population trends between our model and aerial surveys in terms of bias in productivity and survival estimates.

  15. Modeling and control of the Czochralski crystal growth process

    NASA Astrophysics Data System (ADS)

    Martinez, Denise Marie

    The Czochralski process is a method of pulling crystal from the melt that is widely used by the semiconductor industry. The current breadth of this industry makes the method indespensible. The International Technology Roadmap for Semiconductors forecasts the use of 35 nm technology on 64 Gbit DRAM and 10 GHz processor speeds by the end of this decade. This implies the need for higher quality crystals, and therefore improved growth systems. Furthermore, industry has noted a problem with rapid pull rate variation contributing to structural defects in the grown crystals. It was proposed by industry to investigate elimination of the pull rate as a control input. The current state of the system as well as the predicted path of the industry served to motivate development of a new control scheme. The first objective of this work was to develop or enhance a first-principles based model of the process. This model must be kept at a manageable order to accommodate online simulation while still capturing the dominant process physics. The model must also be formulated as a time differential equation in order to apply the desired control theories. The second objective of this work was to answer industry's question regarding elimination of pull rate as a manipulated input. The final objective of this work was to use the model to design a new control algorithm. The control development includes consideration of the time delay between heater and the crystal. The work is based on silicon growth, but the developments are kept as generic as possible for future application to other materials. Data from industry crystal growths as well as experimental results reported in literature will be used to gauge the effectiveness of the new designs.

  16. 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...

  17. 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

  18. 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

  19. Multilevel models for repeated measures research designs in psychophysiology: an introduction to growth curve modeling.

    PubMed

    Kristjansson, Sean D; Kircher, John C; Webb, Andrea K

    2007-09-01

    Psychophysiologists often use repeated measures analysis of variance (RMANOVA) and multivariate analysis of variance (MANOVA) to analyze data collected in repeated measures research designs. ANOVA and MANOVA are nomothetic approaches that focus on group means. Newer multilevel modeling techniques are more informative than ANOVA because they characterize both group-level (nomothetic) and individual-level (idiographic) effects, yielding a more complete understanding of the phenomena under study. This article was written as an introduction to growth curve modeling for applied researchers. A growth model is defined that can be used in place of RMANOVAs and MANOVAs for single-group and mixed repeated measures designs. The model is expanded to test and control for the effects of baseline levels of physiological activity on stimulus-specific responses. Practical, conceptual, and statistical advantages of growth curve modeling are discussed. PMID:17596179

  20. Stoichiometric growth model for riboflavin-producing Bacillus subtilis.

    PubMed

    Dauner, M; Sauer, U

    2001-09-01

    Rate equations for measured extracellular rates and macromolecular composition data were combined with a stoichiometric model to describe riboflavin production with an industrial Bacillus subtilis strain using errors in variables regression analysis. On the basis of this combined stoichiometric growth model, we explored the topological features of the B. subtilis metabolic reaction network that was assembled from a large amount of literature. More specifically, we simulated maximum theoretical yields of biomass and riboflavin, including the associated flux regimes. Based on the developed model, the importance of experimental data on building block requirements for maximum yield and flux calculations were investigated. These analyses clearly show that verification of macromolecular composition data is important for optimum flux calculations. PMID:11505383

  1. Growth exponents in surface models with non-active sites

    NASA Astrophysics Data System (ADS)

    Santos, M.; Figueiredo, W.; Aarão Reis, F. D. A.

    2006-11-01

    In this work, we studied the role played by the inactive sites present on the substrate of a growing surface. In our model, one particle sticks at the surface if the site where it falls is an active site. However, we allow the deposited particle to diffuse along the surface in accordance with some mechanism previously defined. Using Monte Carlo simulations, and some analytical results, we have investigated the model in (1+1) and (2+1) dimensions considering different relaxation mechanisms. We show that the consideration of non-active sites is a crucial point in the model. In fact, we have seen that the saturation regime is not observed for any value of the density of inactive sites. Besides, the growth exponent β turns to be one, at long times, whatever the mechanism of diffusion we consider in one and two dimensions.

  2. 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.

  3. Modeling of Intermetallic Compounds Growth Between Dissimilar Metals

    NASA Astrophysics Data System (ADS)

    Wang, Li; Wang, Yin; Prangnell, Philip; Robson, Joseph

    2015-09-01

    A model has been developed to predict growth kinetics of the intermetallic phases (IMCs) formed in a reactive diffusion couple between two metals for the case where multiple IMC phases are observed. The model explicitly accounts for the effect of grain boundary diffusion through the IMC layer, and can thus be used to explore the effect of IMC grain size on the thickening of the reaction layer. The model has been applied to the industrially important case of aluminum to magnesium alloy diffusion couples in which several different IMC phases are possible. It is demonstrated that there is a transition from grain boundary-dominated diffusion to lattice-dominated diffusion at a critical grain size, which is different for each IMC phase. The varying contribution of grain boundary diffusion to the overall thickening kinetics with changing grain size helps explain the large scatter in thickening kinetics reported for diffusion couples produced under different conditions.

  4. 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.

  5. 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.

  6. 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...

  7. A Big Bang model of human colorectal tumor growth

    PubMed Central

    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

    2015-01-01

    What happens in the early, still undetectable human malignancy 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 sub-clones 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 revealed the absence of selective sweeps, uniformly high intra-tumor heterogeneity (ITH), and sub-clone 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 sub-clone mixing indicative of early malignant potential. This new model provides a quantitative framework to interpret tumor growth dynamics and the origins of ITH with significant clinical implications. PMID:25665006

  8. 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.

  9. Stochastic contribution to the growth factor in the LCDM model

    SciTech Connect

    Ribeiro, A. L.B.; Andrade, A. P.A.; Letelier, P. S.

    2009-01-01

    We study the effect of noise on the evolution of the growth factor of density perturbations in the context of the LCDM model. Stochasticity is introduced as a Wiener process amplified by an intensity parameter alpha. By comparing the evolution of deterministic and stochastic cases for different values of alpha we estimate the intensity level necessary to make noise relevant for cosmological tests based on large-scale structure data. Our results indicate that the presence of random forces underlying the fluid description can lead to significant deviations from the nonstochastic solution at late times for alpha>0.001.

  10. Growth model of lantern-like amorphous silicon oxide nanowires

    NASA Astrophysics Data System (ADS)

    Wu, Ping; Zou, Xingquan; Chi, Lingfei; Li, Qiang; Xiao, Tan

    2007-03-01

    Silicon oxide nanowire assemblies with lantern-like morphology were synthesized by thermal evaporation of the mixed powder of SnO2 and active carbon at 1000 °C and using the silicon wafer as substrate and source. The nano-lanterns were characterized by a scanning electron microscope (SEM), high-resolution transmission electron microscope (HRTEM), energy-dispersive spectroscope (EDS) and selective area electron diffraction (SAED). The results show that the nano-lantern has symmetrical morphology, with one end connecting with the silicon wafer and the other end being the tin ball. The diameter of the nano-lantern is about 1.5-3.0 µm. Arc silicon oxide nanowire assemblies between the two ends have diameters ranging from 70 to 150 nm. One single catalyst tin ball catalyzes more than one amorphous nanowires' growth. In addition, the growth mechanism of the nano-lantern is discussed and a growth model is proposed. The multi-nucleation sites round the Sn droplet's perimeter are responsible for the formation of many SiOx nanowires. The growing direction of the nanowires is not in the same direction of the movement of the catalyst tin ball, resulting in the bending of the nanowires and forming the lantern-like silicon oxide morphology. The controllable synthesis of the lantern-like silicon oxide nanostructure may have potential applications in the photoelectronic devices field.

  11. 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. PMID:22444086

  12. 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. PMID:21036180

  13. Models of Jupiter's growth incorporating thermal and hydrodynamic constraints

    NASA Astrophysics Data System (ADS)

    Lissauer, Jack J.; Hubickyj, Olenka; D'Angelo, Gennaro; Bodenheimer, Peter

    2009-02-01

    We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, R. However, 3-D hydrodynamic simulations show that only gas within ˜0.25R remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ˜5%. 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. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ˜3 Myr. To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations

  14. 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…

  15. The Biasing Effects of Unmodeled ARMA Time Series Processes on Latent Growth Curve Model Estimates

    ERIC Educational Resources Information Center

    Sivo, Stephen; Fan, Xitao; Witta, Lea

    2005-01-01

    The purpose of this study was to evaluate the robustness of estimated growth curve models when there is stationary autocorrelation among manifest variable errors. The results suggest that when, in practice, growth curve models are fitted to longitudinal data, alternative rival hypotheses to consider would include growth models that also specify…

  16. 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

  17. Modelling population growth with delayed nonlocal reaction in 2-dimensions.

    PubMed

    Liang, Dong; Wu, Jianhong; Zhang, Fan

    2005-01-01

    In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-difusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining diferent boundary conditions. The important feature of the models is the reflection of the joint efect of the difusion dynamics and the nonlocal maturation delayed efect. We consider and ana- lyze numerical solutions of the mature population dynamics with some wellknown birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the efects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.

  18. 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

  19. 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.

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

    PubMed

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

    2006-01-01

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

  1. 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

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

    PubMed

    Hölttä, T; Vesala, T; Nikinmaa, E

    2007-11-01

    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.

  3. 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. PMID:26764747

  4. On a nonlinear model for tumour growth with drug application

    NASA Astrophysics Data System (ADS)

    Donatelli, Donatella; Trivisa, Konstantina

    2015-05-01

    We investigate the dynamics of a nonlinear system modelling tumour growth with drug application. The tumour is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumour is given by Brinkman's equation. The domain occupied by the tumour in this setting is a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behaviour, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research programme whose aim is the investigation of the effect of drug application in tumour growth.

  5. 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.

  6. 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.

  7. An Evolutionary Hybrid Cellular Automaton Model of Solid Tumour Growth

    PubMed Central

    Gerlee, P.; Anderson, A.R.A.

    2007-01-01

    We propose a cellular automaton model of solid tumour growth, in which each cell is equipped with a micro-environment response network. This network is modelled using a feed-forward artificial neural network, that takes environmental variables as an input and from these determines the cellular behaviour as the output. The response of the network is determined by connection weights and thresholds in the network, which are subject to mutations when the cells divide. As both available space and nutrients are limited resources for the tumour this gives rise to clonal evolution where only the fittest cells survive. Using this approach we have investigated the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. The results show that the oxygen concentration affects the selection pressure, cell population diversity and morphology of the tumour. A low oxygen concentration in the tissue gives rise to a tumour with a fingered morphology that contains aggressive phenotypes with a small apoptotic potential, while a high oxygen concentration in the tissue gives rise to a tumour with a round morphology containing less evolved phenotypes. The tissue oxygen concentration thus affects the tumour at both the morphological level and on the phenotype level. PMID:17374383

  8. 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

  9. Nutrient-controlled growth of Skeletonema costatum: an applied model

    NASA Astrophysics Data System (ADS)

    Sun, Ke; Qiu, Zhongfeng; He, Yijun; Yin, Baoshu

    2014-05-01

    To model Skeletonema costatum blooms and their relationship with environmental parameters in situ, a S. costatum-specific zero-dimensional box model based on the mechanistic model Eco3M was established using physiological features. The parameters were calibrated using experimental counterparts, and simulations were compared with published laboratory findings. The resulting normalized objective function (NOF) values are less than 1.0 (and in most cases less than 0.58) and the values for the slope γ (between 0.656 7-1.127 4) and R 2 (between 0.806 8-0.971) are close to 1.0 for most of the sub-figures. This indicates good agreement between simulated and measured data and suggests that the model reproduces the general characteristics of S. costatum growth and use of nutrients under different N- or P-limiting conditions. The model is appropriate for further applications and can be used to test more scenarios using other nutrients.

  10. 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.

  11. 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

  12. 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.

  13. 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,…

  14. 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…

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

    PubMed Central

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

    2015-01-01

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

  16. 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). PMID:24218303

  17. 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.

  18. Modeling microalgal growth in an airlift-driven raceway reactor.

    PubMed

    Ketheesan, Balachandran; Nirmalakhandan, Nagamany

    2013-05-01

    In previous proof-of-concept studies, feasibility of a new airlift-raceway configuration and its energetic advantage and improved CO2 utilization efficiency over the traditional raceways and photobioreactors have been documented. In the current study, a mathematical model for predicting biomass growth in the airlift-raceway reactor is presented, which includes supply and transfer of CO2 and the synergetic effects of light, CO2, nitrogen, and temperature. The model was calibrated and validated with data from prototype scale versions of the reactor on two test species: Nannochloropsis salina and Scenedesmus sp., cultivated under indoor and outdoor conditions. Predictions of biomass concentrations by the proposed model agreed well with the temporal trend of the experimental data, with r(2) ranging from 0.96 to 0.98, p<0.001. A sensitivity analysis of the 10 model parameters used in this study revealed that only three of them were significant, with sensitivity coefficients ranging from 0.08 to 0.13.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Genomic Heritability of Bovine Growth Using a Mixed Model

    PubMed Central

    Ryu, Jihye; Lee, Chaeyoung

    2014-01-01

    This study investigated heritability for bovine growth estimated with genomewide single nucleotide polymorphism (SNP) information obtained from a DNA microarray chip. Three hundred sixty seven Korean cattle were genotyped with the Illumina BovineSNP50 BeadChip, and 39,112 SNPs of 364 animals filtered by quality assurance were analyzed to estimate heritability of body weights at 6, 9, 12, 15, 18, 21, and 24 months of age. Restricted maximum likelihood estimate of heritability was obtained using covariance structure of genomic relationships among animals in a mixed model framework. Heritability estimates ranged from 0.58 to 0.76 for body weights at different ages. The heritability estimates using genomic information in this study were larger than those which had been estimated previously using pedigree information. The results revealed a trend that the heritability for body weight increased at a younger age (6 months). This suggests an early genetic evaluation for bovine growth using genomic information to increase genetic merits of animals. PMID:25358309

  4. 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.

  5. Temperature Dependence of Vegetative Growth and Dark Respiration: A Mathematical Model

    PubMed Central

    Gent, Martin P. N.; Enoch, Herbert Z.

    1983-01-01

    A mathematical model of the processes involved in carbon metabolism is described that predicts the influence of temperature on the growth of plants. The model assumes that the rate of production of dry matter depends both on the temperature and the level of nonstructural carbohydrate. The level of nonstructural carbohydrate is determined by the rates of photosynthesis, growth, and maintenance respiration. The model describes the rate of growth and dark respiration, and the levels of carbohydrate seen in vegetative growth of carnation and tomato. The model suggests that the growth of plants at low temperatures is limited by a shortage of respiratory energy, whereas at high temperatures growth is limited by the shortage of carbohydrate. Thermoperiodism, wherein a warm day and cool night results in faster growth than does constant temperature, is explained by the model as an increase in the level of nonstructural carbohydrate which promotes the rate of growth relative to the rate of maintenance respiration. PMID:16662867

  6. NE Ohio Urban Growth Monitoring and Modeling Prototype. Revised

    NASA Technical Reports Server (NTRS)

    Siebert, Loren; Klosterman, Richard E.

    2001-01-01

    At the University of Akron, Dr. Loren Siebert, Dr. Richard Klosterman, and their graduate research assistants (Jung-Wook Kim, Mohammed Hoque, Aziza Parveen, and Ben Stabler) worked on the integration of remote sensing and GIs-based planning support systems. The primary goal of the project was to develop methods that use remote sensing land cover mapping and GIs-based modeling to monitor and project urban growth and farmland loss in northeast Ohio. Another research goal has been to use only GIS data that are accessible via the World Wide Web, to determine whether Ohio's small counties and townships that do not currently have parcel-level GIS systems can apply these techniques. The project was jointly funded by NASA and USGS OhioView grants during the 2000-2001 academic year; the work is now being continued under a USGS grant.

  7. Growth of transition metals on cerium tungstate model catalyst layers

    NASA Astrophysics Data System (ADS)

    Skála, T.; Tsud, N.; Stetsovych, V.; Mysliveček, J.; Matolín, V.

    2016-10-01

    Two model catalytic metal/oxide systems were investigated by photoelectron spectroscopy and scanning tunneling microscopy. The mixed-oxide support was a cerium tungstate epitaxial thin layer grown in situ on the W(1 1 0) single crystal. Active particles consisted of palladium and platinum 3D islands deposited on the tungstate surface at 300 K. Both metals were found to interact weakly with the oxide support and the original chemical state of both support and metals was mostly preserved. Electronic and morphological changes are discussed during the metal growth and after post-annealing at temperatures up to 700 K. Partial transition-metal coalescence and self-cleaning from the CO and carbon impurities were observed.

  8. Growth of transition metals on cerium tungstate model catalyst layers.

    PubMed

    Skála, T; Tsud, N; Stetsovych, V; Mysliveček, J; Matolín, V

    2016-10-01

    Two model catalytic metal/oxide systems were investigated by photoelectron spectroscopy and scanning tunneling microscopy. The mixed-oxide support was a cerium tungstate epitaxial thin layer grown in situ on the W(1 1 0) single crystal. Active particles consisted of palladium and platinum 3D islands deposited on the tungstate surface at 300 K. Both metals were found to interact weakly with the oxide support and the original chemical state of both support and metals was mostly preserved. Electronic and morphological changes are discussed during the metal growth and after post-annealing at temperatures up to 700 K. Partial transition-metal coalescence and self-cleaning from the CO and carbon impurities were observed. PMID:27494195

  9. Mathematical Modeling of Interleukin-35 Promoting Tumor Growth and Angiogenesis

    PubMed Central

    Liao, Kang-Ling; Bai, Xue-Feng; Friedman, Avner

    2014-01-01

    Interleukin-35 (IL-35), a cytokine from the Interleukin-12 cytokine family, has been considered as an anti-inflammatory cytokine which promotes tumor progression and tumor immune evasion. It has also been demonstrated that IL-35 is secreted by regulatory T cells. Recent mouse experiments have shown that IL-35 produced by cancer cells promotes tumor growth via enhancing myeloid cell accumulation and angiogenesis, and reducing the infiltration of activated CD8 T cells into tumor microenvironment. In the present paper we develop a mathematical model based on these experimental results. We include in the model an anti-IL-35 drug as treatment. The extended model (with drug) is used to design protocols of anti-IL-35 injections for treatment of cancer. We find that with a fixed total amount of drug, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing. We also find that the percentage of tumor reduction under anti-IL-35 treatment improves when the production of IL-35 by cancer is increased. PMID:25356878

  10. Growth and division in a dynamic protocell model.

    PubMed

    Villani, Marco; Filisetti, Alessandro; Graudenzi, Alex; Damiani, Chiara; Carletti, Timoteo; Serra, Roberto

    2014-01-01

    In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of "genetic memory molecules" (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells. PMID:25479130

  11. Growth and Division in a Dynamic Protocell Model

    PubMed Central

    Villani, Marco; Filisetti, Alessandro; Graudenzi, Alex; Damiani, Chiara; Carletti, Timoteo; Serra, Roberto

    2014-01-01

    In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of “genetic memory molecules” (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells. PMID:25479130

  12. 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.

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

    PubMed

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

    2016-01-01

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

  14. 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

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

    PubMed

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

    2016-01-01

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

  16. Modeling pollen tube growth: feeling the pressure to deliver testifiable predictions.

    PubMed

    Kroeger, Jens; Geitmann, Anja

    2011-11-01

    The frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step towards understanding the dynamics of the growth behavior in walled cells.

  17. 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…

  18. 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…

  19. Model experiments for the Czochralski crystal growth technique

    NASA Astrophysics Data System (ADS)

    Cramer, A.; Pal, J.; Gerbeth, G.

    2013-03-01

    A lot of the physical and the numerical modeling of Czochralski crystal growth is done on the generic Rayleigh-Bénard system. To better approximate the conditions in a Czochralski puller, the influences of a rounded crucible bottom, deviations of the thermal boundary conditions from the generic case, crucible and/or crystal rotation, and the influence of magnetic fields are often studied separately. The present contribution reviews some of these topics while concentrating on studies of the flow and related temperature fluctuations in systems where a rotating magnetic field (RMF) was applied. The three-dimensional convective patterns and the resulting temperature fluctuations will be discussed both for the mere buoyant case and for the application of an RMF. It is shown that a system between a Rayleigh-Bénard and a more realistic configuration, which is still cylindrical but whose surface is partially covered by a crystal model, behaves much the same as a Rayleigh-Bénard system. An RMF can be used to damp the temperature fluctuations. Secondly, a more Czochralski-like system is examined. It turns out that the RMF does not provide the desired damping of the temperature fluctutions in the parameter range considered.

  20. Dimensions, maximal growth sites, and optimization in the dielectric breakdown model.

    PubMed

    Mathiesen, Joachim; Jensen, Mogens H; Bakke, Jan Oystein Haavig

    2008-06-01

    We study the growth of fractal clusters in the dielectric breakdown model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent alpha_{min} ) as a function of the growth exponent eta of the DBM model. We do not find evidence for a phase transition from fractal to nonfractal growth for a finite eta value. Simultaneously, we observe that the limit of nonfractal growth (D-->1) is consistent with alpha_{min}-->12 . Finally, using an optimization principle, we give a recipe on how to estimate the effective value of eta from temporal growth data of fractal aggregates.

  1. 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. PMID:26539483

  2. 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

  3. 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.

  4. Hepatocyte growth factor, hepatocyte growth factor activator and arginine in a rat fulminant colitis model

    PubMed Central

    Zwintscher, Nathan P.; Shah, Puja M.; Salgar, Shashikumar K.; Newton, Christopher R.; Maykel, Justin A.; Samy, Ahmed; Jabir, Murad; Steele, Scott R.

    2016-01-01

    Introduction Dextran sodium sulfate (DSS) is commonly used to induce a murine fulminant colitis model. Hepatocyte growth factor (HGF) has been shown to decrease the symptoms of inflammatory bowel disease (IBD) but the effect of its activator, HGFA, is not well characterized. Arginine reduces effects of oxidative stress but its effect on IBD is not well known. The primary aim is to determine whether HGF and HGFA, or arginine will decrease IBD symptoms such as pain and diarrhea in a DSS-induced fulminant colitis murine model. Methods A severe colitis was induced in young, male Fischer 344 rats with 4% (w/v) DSS oral solution for seven days; rats were sacrificed on day 10. Rats were divided into five groups of 8 animals: control, HGF (700 mcg/kg/dose), HGF and HGFA (10 mcg/dose), HGF and arginine, and high dose HGF (2800 mcg/kg/dose). Main clinical outcomes were pain, diarrhea and weight loss. Blinded pathologists scored the terminal ileum and distal colon. Results DSS reliably induced severe active colitis in 90% of animals (n = 36/40). There were no differences in injury scores between control and treatment animals. HGF led to 1.38 fewer days in pain (p = 0.036), while arginine led to 1.88 fewer days of diarrhea (P = 0.017) compared to controls. 88% of HGFA-treated rats started regaining weight (P < 0.001). Discussion/Conclusion Although treatment was unable to reverse fulminant disease, HGF and arginine were associated with decreased days of pain and diarrhea. These clinical interventions may reduce associated symptoms for severe IBD patients, even when urgent surgical intervention remains the only viable option. PMID:27144006

  5. Morphology and growth of murine cell lines on model biomaterials.

    PubMed

    Godek, Marisha L; Duchsherer, Nichole L; McElwee, Quinn; Grainger, David W

    2004-01-01

    All biomaterial implants are assaulted by the host "foreign body" immune response. Understanding the complex, dynamic relationship between cells, biomaterials and milieu is an important first step towards controlling this reaction. Material surface chemistry dictates protein adsorption, and thus subsequent cell interactions. The cell-implant is a microenvironment involving 1) proteins that coat the surface and 2) cells that interact with these proteins. Macrophages and fibroblasts are two cell types that interact with proteins on biomaterials surfaces and play different related, but equally important, roles in biomaterials rejection and implant failure. Growth characteristics of four murine cell lines on model biomaterials surfaces were examined. Murine monocyte-macrophages (RAW 264.7 and J774A.1), murine macrophage (IC-21) and murine fibroblast (NIH 3T3) cell lines were tested to determine whether differences exist in adhesion, proliferation, differentiation, spreading, and fusion (macrophage lineages only) on these surfaces. Differences were observed in the ability of cells to adhere to and subsequently proliferate on polymer surfaces. (Monocyte-) macrophages grew well on all surfaces tested and growth rates were measured on three representative polymer biomaterials surfaces: tissue culture polystyrene (TCPS), polystyrene, and Teflon-AF. J774A.1 cultures grown on TCPS and treated with exogenous cytokines IL-4 and GM-CSF were observed to contain multinucleate cells with unusual morphologies. Thus, (monocyte-) macrophage cell lines were found to effectively attach to and interrogate each surface presented, with evidence of extensive spreading on Teflon-AF surfaces, particularly in the IC-21 cultures. The J774A.1 line was able to proliferate and/or differentiate to more specialized cell types (multinucleate/dendritic-like cells) in the presence of soluble chemokine cues. PMID:15133927

  6. MODELING THE RED SEQUENCE: HIERARCHICAL GROWTH YET SLOW LUMINOSITY EVOLUTION

    SciTech Connect

    Skelton, Rosalind E.; Bell, Eric F.; Somerville, Rachel S.

    2012-07-01

    We explore the effects of mergers on the evolution of massive early-type galaxies by modeling the evolution of their stellar populations in a hierarchical context. We investigate how a realistic red sequence population set up by z {approx} 1 evolves under different assumptions for the merger and star formation histories, comparing changes in color, luminosity, and mass. The purely passive fading of existing red sequence galaxies, with no further mergers or star formation, results in dramatic changes at the bright end of the luminosity function and color-magnitude relation. Without mergers there is too much evolution in luminosity at a fixed space density compared to observations. The change in color and magnitude at a fixed mass resembles that of a passively evolving population that formed relatively recently, at z {approx} 2. Mergers among the red sequence population ('dry mergers') occurring after z = 1 build up mass, counteracting the fading of the existing stellar populations to give smaller changes in both color and luminosity for massive galaxies. By allowing some galaxies to migrate from the blue cloud onto the red sequence after z = 1 through gas-rich mergers, younger stellar populations are added to the red sequence. This manifestation of the progenitor bias increases the scatter in age and results in even smaller changes in color and luminosity between z = 1 and z = 0 at a fixed mass. The resultant evolution appears much slower, resembling the passive evolution of a population that formed at high redshift (z {approx} 3-5), and is in closer agreement with observations. We conclude that measurements of the luminosity and color evolution alone are not sufficient to distinguish between the purely passive evolution of an old population and cosmologically motivated hierarchical growth, although these scenarios have very different implications for the mass growth of early-type galaxies over the last half of cosmic history.

  7. 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…

  8. THE INFLUENCE OF MODEL TIME STEP ON THE RELATIVE SENSITIVITY OF POPULATION GROWTH TO SURVIVAL, GROWTH AND REPRODUCTION

    EPA Science Inventory

    Matrix population models are often used to extrapolate from life stage-specific stressor effects on survival and reproduction to population-level effects. Demographic elasticity analysis of a matrix model allows an evaluation of the relative sensitivity of population growth rate ...

  9. Characterization of commercial and biological growth curves in the Segureña sheep breed.

    PubMed

    Lupi, T M; Nogales, S; León, J M; Barba, C; Delgado, J V

    2015-08-01

    Non-linear models were analysed to describe both the biological and commercial growth curves of the Segureña sheep, one of the most important Spanish breeds. We evaluated Brody, von Bertalanffy, Verhulst, logistic and Gompertz models, using historical data from the National Association of Segureña Sheep Breeders (ANCOS). These records were collected between 2000 and 2013, from a total of 129 610 weight observations ranging from birth to adulthood. The aim of this research was to establish the mathematical behaviour of body development throughout this breed's commercial life (birth to slaughter) and biological life (birth to adulthood); comparison between both slopes gives important information regarding the best time for slaughter, informs dietary advice according to animals' needs, permits economical predictions of productions and, by using the curve parameters as selection criteria, enables improvements in growth characteristics of the breed. Models were fitted according to the non-linear regression procedure of statistical package SPSS version19. Model parameters were estimated using the Levenberg-Marquardt algorithm. Candidate models were compared using the determinative coefficient, mean square error, number of iterations, Akaike information coefficient and biological coherence of the estimated parameters. The von Bertalanffy and logistic models were found to be best suited to the biological and commercial growth curves, respectively, for both sexes. The Brody equation was found to be unsuitable for studying the commercial growth curve. Differences between the parameters in both sexes indicate a strong impact of sexual dimorphism on growth. This can emphasize the value of the highest growth rate for females, indicating that they reach maturity earlier.

  10. A bifactor model of the Posttraumatic Growth Inventory

    PubMed Central

    Konkolÿ Thege, Barna; Kovács, Éva; Balog, Piroska

    2014-01-01

    Purpose: The Posttraumatic Growth Inventory (PTGI) is a self-administered measurement instrument designed to provide information concerning positive psychological changes after a traumatic life event. The aim of the present study was to examine the psychometric properties of the PTGI in a Hungarian sample. By examining a bifactor model of the instrument, we also wanted to contribute to the establishment of an evidence-based practice concerning the use of different score types (total score versus subscale scores). Methods: Altogether, 691 Hungarian respondents (82.2% female; M age = 33.0 ± 13.4 years), who experienced some kind of trauma or loss, participated in this study. Results: A series of confirmatory factor analyses revealed that among the tested first- and second-order models, a bifactor model provided the best-fit to our data (χ 2/df = 4.32, Comparative Fit Index = .91, root mean square error of approximation = .07, standardized root mean square residual = .04). Further, the Hungarian version of the PTGI showed high internal consistency (Cronbach's alpha = .93, omega total = .95, omega hierarchical = .87) and test–retest reliability (r = .90; p < .01) coefficients. However, omega hierarchical coefficients (.14–.40) and explained variance values (.05–.10) for the subscales were low. Conclusions: The present study provided empirical support for the psychometric adequacy of the Hungarian adaptation of the PTGI and suggests that only the total and not the subscale scores of the inventory should be used. PMID:25750800

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

    NASA Astrophysics Data System (ADS)

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

    2013-04-01

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

  12. Multiscale study of bacterial growth: Experiments and model to understand the impact of gas exchange on global growth.

    PubMed

    Lalanne-Aulet, David; Piacentini, Adalberto; Guillot, Pierre; Marchal, Philippe; Moreau, Gilles; Colin, Annie

    2015-01-01

    Using a millifluidics and macroscale setup, we study quantitatively the impact of gas exchange on bacterial growth. In millifluidic environments, the permeability of the incubator materials allows an unlimited oxygen supply by diffusion. Moreover, the efficiency of diffusion at small scales makes the supply instantaneous in comparison with the cell division time. In hermetic closed vials, the amount of available oxygen is low. The growth curve has the same trend but is quantitatively different from the millifluidic situation. The analysis of all the data allows us to write a quantitative modeling enabling us to capture the entire growth process.

  13. Assessment of improved root growth representation in a 1-D, field scale crop model

    NASA Astrophysics Data System (ADS)

    Miltin Mboh, Cho; Gaiser, Thomas; Ewert, Frank

    2015-04-01

    Many 1-D, field scale crop models over-simplify root growth. The over-simplification of this "hidden half" of the crop may have significant consequences on simulated root water and nutrient uptake with a corresponding reflection on the simulated crop yields. Poor representation of root growth in crop models may therefore constitute a major source of uncertainty propagation. In this study we assess the effect of an improved representation of root growth in a model solution of the model framework SIMPLACE (Scientific Impact assessment and Modeling PLatform for Advanced Crop and Ecosystem management) compared to conventional 1-D approaches. The LINTUL5 crop growth model is coupled to the Hillflow soil water balance model within the SIMPLACE modeling framework (Gaiser et al, 2013). Root water uptake scenarios in the soil hydrological simulator Hillflow (Bronstert, 1995) together with an improved representation of root growth is compared to scenarios for which root growth is simplified. The improvement of root growth is achieved by integrating root growth solutions from R-SWMS (Javaux et al., 2008) into the SIMPLACE model solution. R-SWMS is a three dimensional model for simultaneous modeling of root growth, soil water fluxes and solute transport and uptake. These scenarios are tested by comparing how well the simulated water contents match with the observed soil water dynamics. The impacts of the scenarios on above ground biomass and wheat grain are assessed

  14. A computational model that predicts reverse growth in response to mechanical unloading

    PubMed Central

    Genet, M.; Acevedo-Bolton, G.; Ordovas, K.; Guccione, J. M.; Kuhl, E.

    2014-01-01

    Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure–volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry. PMID:24888270

  15. Colorado Growth Model--Brief Report: Student Growth Percentiles and FRL Status. Accountability & Data Analysis Unit

    ERIC Educational Resources Information Center

    Colorado Department of Education, 2013

    2013-01-01

    This report examines the relationship between socioeconomic status, as defined by a free-and-reduced lunch proxy variable, and student growth percentiles by elementary, middle, and high school grade levels for math, reading, and writing. Comparisons were made between median growth percentiles for each educational level by free and reduced lunch…

  16. A bioreaction-diffusion model for growth of marine sponge explants in bioreactors.

    PubMed

    Garcia Camacho, F; Chileh, T; Cerón García, M C; Sánchez Mirón, A; Belarbi, E H; Chisti, Y; Molina Grima, E

    2006-12-01

    Marine sponges are sources of high-value bioactives. Engineering aspects of in vitro culture of sponges from cuttings (explants) are poorly understood. This work develops a diffusion-controlled growth model for sponge explants. The model assumes that the explant growth is controlled by diffusive transport of at least some nutrients from the surrounding medium into the explant that generally has a poorly developed aquiferous system for internal irrigation during early stages of growth. Growth is assumed to obey Monod-type kinetics. The model is shown to satisfactorily explain the measured growth behavior of the marine sponge Crambe crambe in two different growth media. In addition, the model is generally consistent with published data for growth of explants of the sponges Disidea avara and Hemimycale columella. The model predicted that nutrient concentration profiles for nutrients, such as dissolved oxygen within the explant, are consistent with data published by independent researchers. In view of the proposed model's ability to explain available data for growth of several species of sponge explants, diffusive transport does play a controlling role in explant growth at least until a fully developed aquiferous system has become established. According to the model and experimental observations, the instantaneous growth rate depends on the size of the explant and all those factors that influence the diffusion of critical nutrients within the explant. Growth follows a hyperbolic profile that is consistent with the Monod kinetics.

  17. NADH-Regulated metabolic model for growth of Methylosinus trichosporium OB3b. Model presentation, parameter estimation, and model validation.

    PubMed

    Sipkema, E M; de Koning, W; Ganzeveld, K J; Janssen, D B; Beenackers, A A

    2000-01-01

    A biochemical model is presented that describes growth of Methylosinus trichosporium OB3b on methane. The model, which was developed to compare strategies to alleviate NADH limitation resulting from cometabolic contaminant conversion, includes (1) catabolism of methane via methanol, formaldehyde, and formate to carbon dioxide; (2) growth as formaldehyde assimilation; and (3) storage material (poly-beta-hydroxybutyric acid, PHB) metabolism. To integrate the three processes, the cofactor NADH is used as central intermediate and controlling factor-instead of the commonly applied energy carrier ATP. This way a stable and well-regulated growth model is obtained that gives a realistic description of a variety of steady-state and transient-state experimental data. An analysis of the cells' physiological properties is given to illustrate the applicability of the model. Steady-state model calculations showed that in strain OB3b flux control is located primarily at the first enzyme of the metabolic pathway. Since no adaptation in V(MAX) values is necessary to describe growth at different dilution rates, the organism seems to have a "rigid enzyme system", the activity of which is not regulated in response to continued growth at low rates. During transient periods of excess carbon and energy source availability, PHB is found to accumulate, serving as a sink for transiently available excess reducing power. PMID:10753442

  18. Antifungal activity evaluation of Mexican oregano (Lippia berlandieri Schauer) essential oil on the growth of Aspergillus flavus by gaseous contact.

    PubMed

    Gómez-Sánchez, Aída; Palou, Enrique; López-Malo, Aurelio

    2011-12-01

    The antifungal activity of Mexican oregano (Lippia berlandieri Schauer) essential oil by gaseous contact on the growth of Aspergillus flavus at selected essential oil concentrations (14.7, 29.4, 58.8, or 117.6 μl of essential oil per liter of air) and temperatures (25, 30, or 35°C) was evaluated in potato dextrose agar formulated at water activity of 0.98 and pH 4.0. Mold growth curves were adequately fitted (0.984 < R(2) < 0.999) by the modified Gompertz model. The effect of the independent variables (concentration of essential oil and temperature) on the estimated model parameters (reciprocal of growth rate [1/ν(m)] and lag time [λ]) were evaluated through polynomial equations. Both ν(m) and λ were significantly (P < 0.05) affected by the independent variables; ν(m) decreased and λ increased as essential oil concentration increased and temperature decreased, which suggests that Mexican oregano essential oil retards or inhibits mold germination stage. Further, minimum fungistatic and fungicide essential oil concentrations at 30 and 35°C were determined. Mexican oregano essential oil applied in gas phase exerts important antifungal activity on the growth of A. flavus, suggesting its potential to inhibit other food spoilage molds. PMID:22186064

  19. Coherent states of Gompertzian growth

    NASA Astrophysics Data System (ADS)

    Molski, Marcin; Konarski, Jerzy

    2003-08-01

    The origin of the Gompertz function G(t)=G0eb/a(1-e-at) widely applied to fit the biological and medical data, particularly growth of organisms, organs, and tumors is analyzed. It is shown that this function is a solution of a time-dependent counterpart of the Schrödinger equation for the Morse oscillator with anharmonicity constant equal to 1. The coherent states of the Gompertzian systems, which minimize the time-energy uncertainty relation, have been found. These are eigenstates of the annihilation operator identified with the operator of growth, whereas eigenstates of the creation operator represent the Gompertzian states of regression. The coherent formation of the specific growth patterns in the Gompertzian systems appears as a result of the nonlocal long-range cooperation between the microlevel (the individual cell) and the macrolevel (the system as a whole).

  20. A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.

    PubMed

    Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M

    2014-04-01

    A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications.