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It is necessary to accurately capture the growth trajectory of fluorescence where the best fit, precision, and relative efficiency are essential. Having this in mind, a new family of growth functions called TWW (Tabatabai, Wilus, Wallace) was introduced. This model is capable of accurately analyzing quantitative polymerase chain reaction (qPCR). This new family provides a reproducible quantitation of gene copies and is less labor-intensive than current quantitative methods. A new cycle threshold based on TWW that does not need the assumption of equal reaction efficiency was introduced. The performance of TWW was compared with 3 classical models (Gompertz, logistic, and Richard) using qPCR data. TWW models the relationship between the cycle number and fluorescence intensity, outperforming some state-of-the-art models in performance measures. The 3-parameter TWW model had the best model fit in 68.57% of all cases, followed by the Richard model (28.57%) and the logistic (2.86%). Gompertz had the worst fit in 88.57% of all cases. It had the best precision in 85.71% of all cases followed by Richard (14.29%). For all cases, Gompertz had the worst precision. TWW had the best relative efficiency in 54.29% of all cases, while the logistic model was best in 17.14% of all cases. Richard and Gompertz tied for the best relative efficiency in 14.29% of all cases. The results indicate that TWW is a good competitor when considering model fit, precision, and efficiency. The 3-parameter TWW model has fewer parameters when compared to the Richard model in analyzing qPCR data, which makes it less challenging to reach convergence. [ABSTRACT FROM AUTHOR]

The study of damage and failure in fractured rock masses is crucial. This study employs the representative volume element (RVE) method to develop a microscale rock model. The model simulates the propagation and rupture of fractures by integrating factors including actual mineralogical composition, the Weibull distribution function, the Mohr–Coulomb damage criterion, and strain softening. Results indicate that fractures reduce the uniaxial compressive strength of the rock and that peak strength is significantly correlated with crack geometries. Plastic damage in rocks was categorized into three stages: elastic, rapid growth, and postpeak softening. A logistic growth model describes the plastic volume change curves for rocks with various fracture geometries, establishing the relationship between plastic damage volume and damage variables. Constitutive models for rocks with varying fracture geometries under uniaxial compression were formulated. The accuracy and applicability of these models were validated, providing a theoretical basis for rock engineering applications. Highlights: A heterogeneous plastic damage model based on representative volume elements is developed.A logistic growth model was used to describe the plastic volume change curves for rocks containing different fracture geometries.The relationship between rock plastic damage volume and damage variables was established.Plastic damage constitutive models of rocks containing different fracture geometries under uniaxial compression were obtained and validated. [ABSTRACT FROM AUTHOR]

This paper presents numerical works on estimating some logistic models using particle swarm optimization (PSO). The considered models are the Verhulst model, Pearl and Reed generalization model, von Bertalanffy model, Richards model, Gompertz model, hyper-Gompertz model, Blumberg model, Turner et al. model, and Tsoularis model. We employ data on commercial and rural banking assets in Indonesia due to their tendency to correspond with logistic growth. Most banking asset forecasting uses statistical methods concentrating solely on short-term data forecasting. In banking asset forecasting, deterministic models are seldom employed, despite their capacity to predict data behavior for an extended time. Consequently, this paper employs logistic model forecasting. To improve the speed of the algorithm execution, we use the Cauchy criterion as one of the stopping criteria. For choosing the best model out of the nine models, we analyze several considerations such as the mean absolute percentage error, the root mean squared error, and the value of the carrying capacity in determining which models can be unselected. Consequently, we obtain the best-fitted model for each commercial and rural bank. We evaluate the performance of PSO against another metaheuristic algorithm known as spiral optimization for benchmarking purposes. We assess the robustness of the algorithm employing the Taguchi method. Ultimately, we present a novel logistic model which is a generalization of the existence model. We evaluate its parameters and compare the result with the best-obtained model. [ABSTRACT FROM AUTHOR]

Background: With the global spread of COVID-19, detecting high-risk countries/regions timely and dynamically is essential; therefore, we sought to develop automatic, quantitative and scalable analysis methods to observe and estimate COVID-19 spread worldwide and further generate reliable and timely decision-making support for public health management using a comprehensive modeling method based on multiple mathematical models. Methods: We collected global COVID-19 epidemic data reported from January 23 to September 30, 2020, to observe and estimate its possible spread trends. Countries were divided into three outbreak levels: high, middle, and low. Trends analysis was performed by calculating the growth rate, and then country grouping was implemented using group-based trajectory modeling on the three levels. Individual countries from each group were also chosen to further disclose the outbreak situations using two predicting models: the logistic growth model and the SEIR model. Results: All 187 observed countries' trajectory subgroups were identified using two grouping strategies: with and without population consideration. By measuring epidemic trends and predicting the epidemic size and peak of individual countries, our study found that the logistic growth model generally estimated a smaller epidemic size than the SEIR model. According to SEIR modeling, confirmed cases in each country would take an average of 9–12 months to reach the outbreak peak from the day the first case occurred. Additionally, the average number of cases at the peak time will reach approximately 10–20% of the countries' populations, and the countries with high trends and a high predicted size must pay special attention and implement public health interventions in a timely manner. Conclusions: We demonstrated comprehensive observations and predictions of the COVID-19 outbreak in 187 countries using a comprehensive modeling method. The methods proposed in this study can measure COVID-19 development from multiple perspectives and are generalizable to other epidemic diseases. Furthermore, the methods also provide reliable and timely decision-making support for public health management. [ABSTRACT FROM AUTHOR]

There is a 'coffee ring' in the Bacillus subtilis biofilm center, and the colony biofilm morphologies are distinct inside and outside the 'coffee ring'. In this paper, we study this morphological difference and explain the reasons of the 'coffee ring' formation and further the causes to the morphological variation. We developed a quantitative method to characterize the surface morphology, the outer area is thicker than the inner area of the 'coffee ring', and the thickness amplitude in outer area is larger than inner area of the 'coffee ring'. We adopt a logistic growth model to obtain how the environmental resistance influence the colony biofilm thickness. Dead cells provide gaps for stress release and make folds formation in colony biofilm. we developed a technique for optical imaging and matching cells with the BRISK algorithm to capture the distribution and movement of motile cells and matrix producing cells in the colony biofilm. Matrix producing cells are mainly distribute in the outside of the 'coffee ring', and the extracellular matrix (ECM) prevents the motile cells moving outward from center. Motile cells mainly locate inside the ring, a small amount of dead motile cells outside the 'coffee ring' give rise to radial folds formation. There are no ECM blocking cell movements inside the ring, which result in uniform folds formation. The distribution of ECM and different phenotypes lead to the formation of the 'coffee ring', which is verified by using eps and flagellar mutants. [ABSTRACT FROM AUTHOR]

In response to significant shifts in dietary and lifestyle preferences, the global demand for fruits has increased dramatically, especially for apples, which are consumed worldwide. Growing apple orchards of more productive and higher quality with limited land resources is the way forward. Precise planting age identification and yield prediction are indispensable for the apple market in terms of sustainable supply, price regulation, and planting management. The planting age of apple trees significantly determines productivity, quality, and yield. Therefore, we integrated the time-series spectral endmember and logistic growth model (LGM) to accurately identify the planting age of apple orchard, and we conducted planting age-driven yield prediction using a neural network model. Firstly, we fitted the time-series spectral endmember of green photosynthetic vegetation (GV) with the LGM. By using the four-points method, the environmental carrying capacity (ECC) in the LGM was available, which serves as a crucial parameter to determine the planting age. Secondly, we combined annual planting age with historical apple yield to train the back propagation (BP) neural network model and obtained the predicted apple yields for 12 counties. The results show that the LGM method can accurately estimate the orchard planting age, with Mean Absolute Error (MAE) being 1.76 and the Root Mean Square Error (RMSE) being 2.24. The strong correlation between orchard planting age and apple yield was proved. The results of planting age-driven yield prediction have high accuracy, with the MAE up to 2.95% and the RMSE up to 3.71%. This study provides a novel method to accurately estimate apple orchard planting age and yields, which can support policy formulation and orchard planning in the future. [ABSTRACT FROM AUTHOR]

A highly efficient and convenient mapping can greatly contribute to access the plantation year in a large-scale orchard using remote sensing. Limited studies on the mapping orchard plantation age can be divided into two categories, namely: 1) using the spectral feature differences, and 2) using the vegetation phenology represented by remote sensing images. However, current studies cannot avoid the influence of mixed image elements on the spectral information of features. Alternatively, the linear hybrid decomposition model can be expected to effectively estimate the orchard plantation age in a large scale. The complex hybrid image can further be decomposed into different pure end elements for the physical information. This study aims to integrate the surface standard end element space using Landsat series images, in order to mapping the orchard plantation information. The following parts were included: 1) The area of apple orchard was firstly mapped to incorporate four standard end elements of substrate (SL, rock and soil), vegetation (GV, photosynthetic foliage), dark matter (DA, shadows), and water (WA, water bodies) into the original image, particularly with the random forest for the land use classification. 2) The Landsat8-OLI, Landsat7-ETM+, and Landsat5-TM sensor images were used to conduct the linear spectral mixture decomposition. Then, the time series curves of vegetation end element were constructed to determine the slow growth interval of apple orchard. The four-point method was applied to explore the maximum environmental carrying capacity of apple orchard in the study area. 3) The starting point of apple orchard plantation was found to fit the logistic growth model for the subsequent mapping of the orchard plantation information. The main findings were as follows. 1) Four end elements from the linear spectral mixture decomposition were used to better represent the surface component information in the orchard. The accuracy of feature extraction was also effectively improved after the fusion of the standard end element space and the random forest. Specifically, the overall accuracy of classification mapping reached up to 88.80% than before, with the Kappa coefficient of 0.86. Besides, there was a better interpretation of the orchard, with the accuracy of 92% than before. 2) An excellent stability was obtained to relatively present the vegetation end element time series curves. Among them, three Landsat series sensor images were used to extract the feature information during operation. The variation of land cover/use was easily used to capture the vegetation end member time series curves. Thus, the Logistic growth model better performed on the biological processes of vegetation growth. The fruit tree growth model was also fitted for the higher accuracy and stability, particularly with the overall fit of 0.751, and the mean error of 1.86 years. The finding can provide a strong reference to determine the plantation information and plantation year of fruit trees with the higher accuracy than before. [ABSTRACT FROM AUTHOR]

This paper aims to explore the transmission dynamics of COVID-19 with dengue co-infection using mathematical modeling. In this study, SIR model is developed that explains the trajectory of the epidemic to boost a plan for an effective control strategy for COVID-19 in Bangladesh. The model is extended to optimal control strategies. Pontryagin's Principle is used to establish the appropriate conditions for the existence of optimal control and the optimality system for the co-infection model. Coinfected cases were reduced with control greater than without control. Using Omicron incidence cases from 1st January – 13th April 2022, the maximum likelihood estimate of R0 with a 95% confidence interval is1.89 [ 95% CI: 1.88, 1.91]. The R0 estimated from the exponential growth method is 2.08 [95% CI: 2.07,2.09]and time-dependent estimate is 2.10[95% CI: 1.72,2.58]. The generalized logistic growth model predicted 19, 52,131 cumulative cases on day 103 (April 13, 2022), and a relatively flat curve of cumulative growth of COVID-19 cases implies a declining trend of new cases. The study also found from sensitivity analysis that, R0 is proportional to the mean generation time. This paper attempted to focus on suppressing the COVID-19 co-infections by preventing dengue and COVID-19. The results of the study show that by implementing optimal control spread of dengue and COVID-19 could be minimized. The logistic growth model suggests that the infection rate of COVID-19 is decreasing. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to deal with the randomness associated to ecological modelling. Data variability makes it necessary to analyse the impact of random perturbations on the fitted model parameters. We conduct such analysis for the logistic growth model with a certain sigmoid functional form of the carrying capacity, which was proposed in the literature for the study of parasite growth during infection. We show how the probability distributions of the parameters are set via the maximum entropy principle. Then the random variable transformation method allows for computing the density function of the population. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the non-autonomous logistic growth model with time-dependent intrinsic growth rate and carrying capacity. Accounting for errors in recorded data, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty of the model output is quantified by approximations of the first probability density function via the random variable transformation method. A numerical example illustrates the results. [ABSTRACT FROM AUTHOR]

As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly spreading in different parts of India, a reliable forecast for the cumulative confirmed cases and the number of deaths can be helpful for policymakers in making the decisions for utilizing available resources in the country. Recently, various mathematical models have been used to predict the outbreak of COVID-19 worldwide and also in India. In this article we use exponential, logistic, Gompertz growth and autoregressive integrated moving average (ARIMA) models to predict the spread of COVID-19 in India after the announcement of various unlock phases. The mean absolute percentage error and root mean square error comparative measures were used to check the goodness-of-fit of the growth models and Akaike information criterion for ARIMA model selection. Using COVID-19 pandemic data up to 20 December 2020 from India and its five most affected states (Maharashtra, Karnataka, Andhra Pradesh, Tamil Nadu and Kerala), we report 15-days-ahead forecasts for cumulative confirmed cases and the number of deaths. Based on available data, we found that the ARIMA model is the best-fitting model for COVID-19 cases in India and its most affected states. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population X (t). In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate r , carrying capacity K , intensity of Gaussian noise λ , noise intensity σ and stability index α vary. The MET from the interval (0 , 1) at the right boundary is finite if λ < 2 . For λ > 2 , the MET from (0 , 1) at this boundary is infinite. A larger stability index α is less likely leading to the extinction of the fish population. [ABSTRACT FROM AUTHOR]

In this study, in addition to classical Logistic and Gompertz models with three parameters, their growth models with four parameters were given. After that it is searched the effect of these growth models on the choice of appropriate growth model by using two separate data sets. For this purpose, classical Logistic and Gompertz growth models and their growth models with four parameters are compared with some model selection criteria such as such as error sum of squares, coefficient of determination, adjusted coefficient of determination and akaike information criteria. For the data set used in this study, it is found that the results of these growth models with four parameters are better than the results of these growth models. Thus, it is considered that these growth models with four parameters can be used in addition to these classical growth models. In addition, some other growth models with four parameters can be investigated for getting the best model choice. Even Logistic and Gompertz models with five and more parameters can be investigated for getting the best model choice. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic differential equation driven by multiplicative Gaussian noise. With the help of the associated Fokker–Planck equation, we analyze the population extinction probability and the probability of reaching a large population size before reaching a small one. We further study the impact of the harvest rate, noise intensity and the Allee effect on population evolution. The analysis and numerical experiments show that if the noise intensity and harvest rate are small, the population grows exponentially, and upon reaching the carrying capacity, the population size fluctuates around it. In the stochastic logistic-harvest model without the Allee effect, when noise intensity becomes small (or goes to zero), the stationary probability density becomes more acute and its maximum point approaches one. However, for large noise intensity and harvest rate, the population size fluctuates wildly and does not grow exponentially to the carrying capacity. So as far as biological meanings are concerned, we must catch at small values of noise intensity and harvest rate. Finally, we discuss the biological implications of our results. [ABSTRACT FROM AUTHOR]

Background: The rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country.Methods: In this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period.Results: We observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551-26,702 cases in 5 days and an additional 47,449-57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145-437 COVID-19 deaths in 5 days and an additional 243-947 deaths in 10 days.Conclusions: By comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead. [ABSTRACT FROM AUTHOR]

Vegetation community plays a pivotal role in various geomorphic processes. The growth of vegetation intrinsically depends on the effective shear stresses exerted by the flow of material (e.g., water or soil) along the slope. We comparatively assess the growth and decay of vegetation using linear and logistic growth model coupled with a runoff erosion model. The linear growth model predicts a sharp decrease in the non-dimensional vegetation profile from the upper reach to the lower part along the slope. However, the logistic growth model delivers a smooth gradual decrease in the vegetation extent. Additionally, we propose a stochastic model to capture the role of internal and external factors in the dynamics of vegetation growth using two Gaussian noises. The steady probability distribution functions from the stochastic model provide insights about the role of different noises on the reaction of the system and suggest that bio-environmental factors are difficult to segregate from one another. Highlights: Comparative study between logistic and linear vegetation growth model coupled with a surface erosion model. Steady-state equilibrium vegetation profile along any slope suggests that the logistic growth model is more realistic. Effect of Gaussian noises in vegetation growth has been demonstrated with the aid of stationary probability distribution. [ABSTRACT FROM AUTHOR]

• This study applied a logistic growth model with parameters estimated by a non-linear least squares (NLS) method to daily new COVID-19 cases. • The model fitted time-series data exceedingly well for the whole of China, eleven selected Chinese provinces and municipalities, South Korea and Iran. • This study provided key estimates and a 95% confidence interval for parameters K , r, and P 0. • This study found that the growth rates of outbreaks differed between provinces in China and between South Korea and Iran. • As of March 13, 2020, this study's model suggested that countries such as the U.S.A., France, Italy, and Spain were still in the early stages of outbreaks. As the coronavirus disease 2019 (COVID-19) pandemic continues to proliferate globally, this paper shares the findings of modelling the outbreak in China at both provincial and national levels. This paper examines the applicability of the logistic growth model, with implications for the study of the COVID-19 pandemic and other infectious diseases. An NLS (Non-Linear Least Squares) method was employed to estimate the parameters of a differentiated logistic growth function using new daily COVID-19 cases in multiple regions in China and in other selected countries. The estimation was based upon training data from January 20, 2020 to March 13, 2020. A restriction test was subsequently implemented to examine whether a designated parameter was identical among regions or countries, and the diagnosis of residuals was also conducted. The model's goodness of fit was checked using testing data from March 14, 2020 to April 18, 2020. The model presented in this paper fitted time-series data exceedingly well for the whole of China, its eleven selected provinces and municipalities, and two other countries - South Korea and Iran - and provided estimates of key parameters. This study rejected the null hypothesis that the growth rates of outbreaks were the same among ten selected non-Hubei provinces in China, as well as between South Korea and Iran. The study found that the model did not provide reliable estimates for countries that were in the early stages of outbreaks. Furthermore, this study concured that the R 2 values might vary and mislead when compared between different portions of the same non-linear curve. In addition, the study identified the existence of heteroskedasticity and positive serial correlation within residuals in some provinces and countries. The findings suggest that there is potential for this model to contribute to better public health policy in combatting COVID-19. The model does so by providing a simple logistic framework for retrospectively analyzing outbreaks in regions that have already experienced a maximal proliferation in cases. Based upon statistical findings, this study also outlines certain challenges in modelling and their implications for the results. [ABSTRACT FROM AUTHOR]

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different (N , M) values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems. [ABSTRACT FROM AUTHOR]

The paper takes the industrial coupling symbiosis network (ICSN) of oil and gas resource-based urban eco-industrial parks (EIPs) as the research object. The purpose is to judge the stability of a symbiotic, one-way relying and two-way symbiosis model applied to oil and gas resource-based cities through constructing a logistic growth symbiotic network model. Through identifying and analyzing the stability model, the research concludes the stability conditions. The analytic results are as follows: In the symmetric ICSN system, it is important to maintain equal status and balanced benefit distribution among the coupled symbiotic enterprises. In the one-way-based ICSN system, the core enterprise significantly promotes the improvement of ecological efficiency the satellite enterprise while the satellite enterprise less effectively promotes the improvement of ecological efficiency of the core enterprise. In the two-way ICSN system, the core enterprise and the satellite enterprise are easily affected by the symbiotic enterprises within the network, and the stability is extremely poor. These conditions and analytic results will serve as a basis for constructing an efficient closed-loop system for ICSN of the oil and gas resource-based urban EIPs.Through the stability analysis of the industrial coupling symbiotic network of the oil and gas resource-based urban eco-industrial park, it can determine the stability conditions that affect the overall performance of the industrial park. Studies have shown that increasing network stability and improving energy efficiency in the park can improve the overall sustainability of the eco-industrial park and accelerate the effective transformation of resource-based cities. • Constructing an industrial coupling symbiotic network model. • Given stability conditions for three symbiotic modes. • Extremely poor stability of Two-way relying industry coupling symbiotic network. • Logistic growth model for network stability analysis. [ABSTRACT FROM AUTHOR]

Scratch assays are in vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and proliferation by a logistic term. In a recent paper (Jin et al. in Bull Math Biol 79(5):1028–1050, 2017), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a nonlinear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations, we are able to show that the interplay between the resource concentration in the substrate and the cell subpopulations dynamics can explain the biphasic dynamics. [ABSTRACT FROM AUTHOR]

Company mergers can be considered as one of the ways for companies surviving in a situation if the sector population reaches to the end point. The aim of this study is to determine the key sectors in Turkey in which the merger strategies could be primarily needed. In this respect, the carrying capacities of 88 sectors according to the NACE (level 2) codes were calculated with the sector population, company founding and disbanding data during 2006-2016. It was determined that in 68 sectors, the sectors populations are above the carrying capacities of sectors. This shows that 77.3% of all sectors may face sectorial resource problems in the future. 10 sectors in which merger strategies could have a more critical importance for the continuity of companies are identified from 68 sectors. [ABSTRACT FROM AUTHOR]

Growth models are often used when modelling various processes in life sciences, ecology, demography, social sciences, etc. Dynamical growth models are usually formulated in terms of an ODE (system of ODS's) or by an explicit solution to an ODE, such as the logistic, Gompertz, and Richardson growth models. To choose a suitable growth model it is useful to know the physics‐chemical meaning of the model. In many situations this meaning is best expressed by means of a reaction network that possibly induces the dynamical growth model via mass action kinetics. Such reaction networks are well known for a number of growth models, such as the saturation‐decay and the logistic Verhulst models. However, no such reaction networks exist for the Gompertz growth model. In this work we propose some reaction networks using mass action kinetics that induce growth models that are (in certain sense) close to the Gompertz model. The discussion of these reaction networks aims to a better understanding of the chemical properties of the Gompertz model and "Gompertzian‐type" growth models. Our method can be considered as an extension of the work of previous authors who "recasted" the Gompertz differential equation into a dynamical system of two differential equations that, apart of the basic species variable, involve an additional variable that can be interpreted as a "resource." Two new growth models based on mass action kinetics are introduced and studied in comparison with the Gompertz model. Numerical computations are presented using some specialized software tools. [ABSTRACT FROM AUTHOR]

Growth models are often used when modelling various processes in life sciences, ecology, demography, social sciences, etc. Dynamical growth models are usually formulated in terms of an ODE (system of ODS's) or by an explicit solution to an ODE, such as the logistic, Gompertz, and Richardson growth models. To choose a suitable growth model it is useful to know the physics‐chemical meaning of the model. In many situations this meaning is best expressed by means of a reaction network that possibly induces the dynamical growth model via mass action kinetics. Such reaction networks are well known for a number of growth models, such as the saturation‐decay and the logistic Verhulst models. However, no such reaction networks exist for the Gompertz growth model. In this work we propose some reaction networks using mass action kinetics that induce growth models that are (in certain sense) close to the Gompertz model. The discussion of these reaction networks aims to a better understanding of the chemical properties of the Gompertz model and "Gompertzian‐type" growth models. Our method can be considered as an extension of the work of previous authors who "recasted" the Gompertz differential equation into a dynamical system of two differential equations that, apart of the basic species variable, involve an additional variable that can be interpreted as a "resource." Two new growth models based on mass action kinetics are introduced and studied in comparison with the Gompertz model. Numerical computations are presented using some specialized software tools. [ABSTRACT FROM AUTHOR]

Background Hepatitis B surface antigen (HBsAg)-seroconversion, or loss of HBsAg and acquisition of anti-hepatitis B surface (HBs) antibodies, defines functional cure of chronic hepatitis B virus (HBV) infection. After HBsAg-loss, little is known regarding the development of anti-HBs antibodies and even less so in individuals co-infected with HIV. Objectives To determine anti-HBs antibody kinetics after HBsAg-loss and explore determinants of HBsAg-seroconversion in HIV-HBV co-infected patients. Study design Patients enrolled in the French HIV-HBV cohort were included if they had >1 study visit after HBsAg-loss. Individual patient kinetics of anti-HBs antibody levels were modeled over time using mixed-effect non-linear regression, whereby maximum specific growth rate and maximal level of antibody production were estimated from a Gompertz growth equation. Results Fourteen (4.6%) of 308 co-infected patients followed in the cohort exhibited HBsAg-loss, all of whom were undergoing antiretroviral therapy. Nine (64.3%) of these patients achieved HBsAg-seroconversion during a median 3.0 years (IQR = 1.1–5.1) after HBsAg-loss. Across individuals with HBsAg-seroconversion, the fastest rates of antibody growth ranged between 0.57–1.93 year −1 (population maximum growth rate = 1.02) and antibody production plateaued between 2.09–3.66 log 10 mIU/mL at the end of follow-up (population maximal antibody levels = 2.66). Patients with HBsAg-seroconversion had substantial decreases in HBV DNA viral loads ( P = 0.03) and proportion with elevated ALT levels ( P = 0.02) and HBeAg-positive serology ( P = 0.08). No such differences were observed in those without HBsAg-seroconversion. Conclusions Most co-infected patients with HBsAg-seroconversion produced and maintained stable antibody levels, yet kinetics of anti-HBs production were much slower compared to those observed post-vaccination or after clearance of acute HBV-infection. [ABSTRACT FROM AUTHOR]

In response to climate change, many countries have set renewable energy targets and implemented various policy tools. However, there are contrasting views on the effects of such policy tools, with many deeming international oil prices a potential factor driving renewable energy diffusion. Using an extended logistic growth model, this study aims to investigate this issue and predict the impact of policy tools and oil prices on renewable energy deployment in the electric power sector under various scenarios. The results show that the renewable portfolio standards more significantly influence the diffusion of renewable energy than the feed-in tariff in South Korea’s electric power sector and higher international oil prices have led to higher diffusion rates. The forecast indicates that South Korea will generate 40.4–85.9 TW h of renewable electricity by 2024 depending on the scenario. The results also indicate that the renewable electricity diffusion rate will continue to increase by 2024, proving that the current diffusion is in its initial stage. The study concludes with implications for the government, which has a crucial role in the initial phase. [ABSTRACT FROM AUTHOR]

We use the state-space approach to the logistic population growth model to update our knowledge of a population of marine shrimp off the Chilean coast. The unobserved state is the annual shrimp biomass, and the observation is the mean catch per unit effort. The observation equation is linear, and the state equation is nonlinear. The models include normal, student- t , skew-normal, and skew- t distributions for additive observation errors; and log-normal, log- t , log-skew-normal, and log-skew- t distributions for multiplicative observation errors. We use Bayesian approach to obtain inference, and the posterior distributions are approximated using Markov chain Monte Carlo methods. Deviance Information Criteria are lower in models considering log-skew-normal and log-skew- t observation errors. Furthermore, considering the posterior predictive distributions of the autocorrelations of the observation errors, these two models work best for the analyzed data set. [ABSTRACT FROM AUTHOR]

Virtual plant modelling is becoming a hot issue both in computer graphics and agricultural researches. However, high‐realistic plant modelling and plant animation is still a problem both in theory and applications. In this study, an interactive animation method for virtual maize dynamic simulation is presented, and an experimental system is developed by using C + + program language and OpenGL library. Firstly, true three‐dimensional data and structural parameters of maize plant are collected as the foundation of modelling and animation. Secondly, an accurate virtual maize model is constructed based on interactive parameterised modelling. Constrained by logistic growth model, a group of key parameters is generated and precise maize animation with high‐realistic visualisation is created according to the factual plant growth. Furthermore, an applied system is developed based on the proposed algorithm, and a set of simulation results are generated by use of the system. The results show that the proposed method is feasible for realistic dynamic simulation and animation of maize. Finally, main contributions and limitations of the authors work are discussed, and some problems are addressed as the future works. [ABSTRACT FROM AUTHOR]

Abstract: A three-parameter logistic growth model was modified to monitor the glucose uptake profile of yeast during very-high-gravity (VHG) ethanol fermentation. The modified model was used to define t50 as a quantifier to differentiate among various fermentation conditions. There are two types of t50; t50 g is the time required to convert 50% of the initial glucose, and t50 e is the time required to produce half of the final ethanol. A 24 factorial experimental design was implemented to illustrate the applicability of using t50 to isolate active ingredients in VHG growth media. The analytical results obtained from the experimental design and from a modified model were compared, which demonstrated that t50 could serve the proposed objectives. A shorter t50 implies a faster fermentation. A tailing of the ethanol profile after t50 e indicates that there is an inhibitory effect imposed on yeast, i.e., the stronger the tailing in the ethanol profile, the stronger the inhibitory effect. When t50 is equal to or near to the halftime of the total course of the fermentation, a bell-shaped curve was seen for the glucose uptake rate or for the ethanol production rate, indicating that the inhibitory effect exerted on yeast was evenly distributed. [Copyright &y& Elsevier]

Abstract: Photofermentative hydrogen production from olive mill wastewater by Rhodobacter sphaeroides O.U.001 was investigated under different regimes of illumination. The analysis included measurements of biomass accumulation, H2-production, high-value bio-product accumulation (polyhydroxybutyrate and carotenoid) and measurements of the medium pH as a function of growth and productivity. Batch cultures were grown under continuous light (CL) or 12 h light/12 h dark (12L/12D) diurnal cycles. Growth under CL or 12L/12D cycles yielded about the same amount of biomass (0.5 g dry cell weight per L culture) and volume of H2 gas (50 ml H2 per L culture). On the other hand, 12L/12D cultures showed a pronounced lag in biomass and H2 accumulation. Advances described in the work would find application in lowering operational costs for hydrogen production by better management of the energy source and cheap feedstock utilization. Compare to CL, equivalent amount of hydrogen gas accumulation within shorter time interval denoted to have two times higher hydrogen production rate and light conversion efficiencies via diurnal cycles, which can yield 50% savings on consumed energy source. [Copyright &y& Elsevier]

Abstract: A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value () and normalized variance of the tumor cell population and state transition rate () between two steady states are numerically calculated. The results indicate that: (i) The delay time () enhances the coherence resonance in as a function of the multiplicative noise intensity () and increases as a function of the additive noise intensity (), i.e., enhances fluctuation of the system, however, the strength () of correlations between multiplicative and additive noise plays a contrary role to on these; (ii) enhances the coherence resonance in as a function of and increases as a function of , i.e., speeds up the rate of state transition, however, also plays a contrary role to on these. [Copyright &y& Elsevier]

Interpolated twitch technique (ITT) is a non-invasive method for assessing the completeness of muscle activation in clinical settings. Voluntary activation level (VA), measured by ITT and estimated by a conventional linear model, was reported to have a non-linear relationship with true voluntary contraction force at higher activation levels. The relationship needs to be further clarified for the correct use by clinicians and researchers. This study was to established a modified voluntary activation (modified VA) and define a valid range by fitting a non-linear logistic growth model. Eight healthy male adults participated in this study. Each subject performed three sets of voluntary isometric ankle plantar flexions at 20, 40, 60, 80 and 100% maximal voluntary contraction (MVC) with real-time feedback on a computer screen. A supramaximal electrical stimulation was applied on tibia nerve at rest and during contractions. The estimated VA was calculated for each contraction. The relationship between the estimated VA and the actual voluntary contraction force was fitted by a logistic growth model. The result showed that according to the upper and lower limit points of the logistic curve, the valid range was between the 95.16% and 10.55% MVC. The modified VA estimated by this logistic growth model demonstrated less error than the conventional model. This study provided a transfer function for the voluntary activation level and defined the valid range which would provide useful information in clinical applications. [ABSTRACT FROM AUTHOR]

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data. [Copyright &y& Elsevier]

In this note we present a critical review of the some of the positive features as well as some of the shortcomings of the generalized sensitivity functions (GSF) of Thomaseth–Cobelli in comparison to traditional sensitivity functions (TSF). We do this from a computational perspective of ordinary least squares estimation or inverse problems using two illustrative examples: the Verhulst–Pearl logistic growth model and a recently developed agricultural production network model. Because GSF provide information on the relevance of data measurements for the identification of certain parameters in a typical parameter estimation problems, we argue that they provide the basis for new tools for investigators in design of inverse problem studies. [ABSTRACT FROM AUTHOR]

The logistic growth model was applied in the study to evaluate the impacts of assimilable organic carbon (AOC) concentration on the growth characteristics of biofilm and bulk bacteria under high flow velocity condition. The experimental results showed that there existed a growth and decline relation between biofilm and bulk bacteria at the low (0.05 mg/L) and medium (0.5 mg/L) AOC levels. Increasing the AOC concentration up to 1.0 mg/L, it resulted in high amounts of biofilm and bulk bacteria simultaneously. Although the carrying capacity of biofilm bacteria at the medium condition of AOC level was substantially reduced, the specific growth rate (GR) of biofilm bacteria was largest at this condition. It showed that the reduction of biofilm bacteria quantity did not represent the suppression of bacterial growth. The quantity of bulk water bacteria was obviously dependent with the quantity of biofilm bacteria and the increase of free bacteria with time in networks was mainly due to the growth and detachment of biofilm bacteria, not due to the growth of free bacteria themselves. The maximum growth rate of biofilm bacteria was increased upon increasing the AOC level. It indicated that the AOC level was an important factor affecting the growth of biofilm bacteria. [Copyright &y& Elsevier]

• Early life was an open chemical system of reversible reactions with branched autocatalytic cycles (ACs). • Individual ACs show logistic growth like a biological population. • Pairs of ACs can interact just like biological species, including competition, predation, etc. • Simple chemical ecosystems can exhibit successional dynamics and historical contingence, implying evolution. • A chemical ecosystem framework explains how adaptive evolution can precede genetic encoding. It is becoming widely accepted that very early in life's origin, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolution. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed compartments that are subject to constant dilution by a solution with a fixed concentration of input chemicals. Modelling all chemical reactions as fully reversible, we show that seeding an autocatalytic cycle with tiny amounts of one or more of its member chemicals results in logistic growth of all member chemicals in the cycle. This finding justifies drawing an instructive analogy between an autocatalytic cycle and a biological species. We extend this finding to show that pairs of autocatalytic cycles can exhibit competitive, predator-prey, or mutualistic associations just like biological species. Furthermore, when there is stochasticity in the environment, particularly in the seeding of autocatalytic cycles, chemical ecosystems can show complex dynamics that can resemble evolution. The evolutionary character is especially clear when the network architecture results in ecological precedence, which makes a system's trajectory historically contingent on the order in which cycles are seeded. For all its simplicity, the framework developed here helps explain the onset of adaptive evolution in prebiotic chemical reaction networks, and can shed light on the origin of key biological attributes such as thermodynamic irreversibility and genetic encoding. [ABSTRACT FROM AUTHOR]

Over the past decade, global sales of electric vehicles (EVs) have experienced significant growth. However, predictions of future sales developments, which are needed for the planning of EV production as well as supporting policies and a sufficient energy supply, are still sparse. In this study, a long-term forecast of the EV inventory in 26 countries across five continents is provided by means of a logistic growth model. Using actual sales data from 2010 to 2018, predictions were made for these countries until 2035. Findings indicate that, overall, 30% of the worldwide passenger vehicle fleet will be EVs in 2032. However, results also display vast differences between countries, which can particularly be attributed to divergences in governmental support. EV growth predictions were additionally analyzed in terms of sustainability impacts. The analysis showed that reductions in CO 2 emissions can be achieved with the predicted EV growth, given that countries invest heavily in renewable energy sources. Given the current energy mixes though, worldwide CO 2 emissions will continue to rise until 2035 despite a nearly 50% share of EVs. The paper further discusses the amount of energy that will be required to meet the growing demand and highlights that the production of EV batteries will be the key bottleneck in the development of EVs. Finally, important implications for policymakers, marketers and future research are derived. Image 1 • In 2032, 30% of all passenger cars worldwide are predicted to be EVs. • Despite an almost 50% share of EVs in 2035, CO 2 emissions will continue to rise. • EV growth reduces CO 2 emissions if countries adapt low emission electricity mixes. [ABSTRACT FROM AUTHOR]

Domestic energy policies destined to foster the use of end-use electric technologies could cause rapid penetration of new residential loads and, consequently, this could cause a significant increase in the demand for electricity in urban areas. This paper presents a spatial-temporal growth model for estimating the adoption of new end-use electric technologies encouraged by energy-efficiency policies. The proposed method consists of three modules: temporal, spatial and grouping. The temporal module calculates by districts or census tracts of a city, the percentage of homes in which residents are prospective buyers of a new end-use electric technology. Then, the spatial module adjusts the calculations made by the temporal module, considering the spatial interactions among the inhabitants of the districts. Finally, the grouping module discovers the low-voltage transformer where the prospective buyers are connected. The results of the proposed model are a spatial database with information related to the percentage of homes in which residents are prospective buyers of a new end-use electric technology, as well as the number of prospective buyers connected to each low-voltage transformer. The results can visualize through thematic maps to identify the districts where the new technology will have faster adoption. The proposed method was employed to estimate the adoption of induction heating cookers in a medium-sized Ecuadorian city. The Ecuadorian government has developed a program of economic subsidies to encourage its population to use this electrical appliance. The results from this application are an important tool to estimate the spatial increase in electricity demand, decide important issues related to the planning of distributed resources, and develop demand-side management programs. Furthermore, the results can be used to evaluate and manage energy policies formulated to achieve environmental and energy goals. • Spatial-temporal approach to estimate the adoption of new end-use technologies. • Procedure to generate new technologies adoption scenarios using different energy policies. • Method to discover the transformers that will supply electricity to adopters of new technologies. [ABSTRACT FROM AUTHOR]

• We introduced a family of logistic growth models that describe the fetch process of aeolian sand flux. • The logistic models best describe the observed sand flux data of wind tunnel and field. • The patterns of sand flux across a sand bed generally govern the goodness of fit of the fetch models. Soil loss and dust emissions due to wind erosion result in soil degradation. The fetch effect, referring to an increase in aeolian sand transport with downstream distance over an eroding surface, is important in modeling wind erosion and parameterizing sand dunes and ripples. Several fetch models have been developed to quantitatively depict the variation of sand flux over a sand bed. The present study first verifies that the family of logistic growth models extensively used in biological systems can be used to describe the fetch process of sand flux. The performances of Fryrear (Fryrear and Selah, 1996), Visser (Visser et al., 2004), Stout (Stout, 1990), Andreotti (Andreotti et al., 2010), and logistic fetch models are investigated using data for 39 wind tunnel experiments across six countries and 51 field measurements across four countries. Results reveal that the patterns of sand flux across a sand bed generally govern the goodness of fit of these fetch models. The logistic models best describe the observed sand flux data and well simulate the maximum sand flux (fmax) and corresponding critical fetch length (L sat). Generally, the Fryrear, Visser, and logistic models yielded similar fmax and L sat while the Stout, and Andreotti models overestimate fmax and L sat. The magnitudes of the L sat and saturation length (b) varied considerably under different environments. More studies are required to explore the domain of L sat across various environments and what factors affect these fitting coefficients (such as fmax and L sat) and how for the logistic models. [ABSTRACT FROM AUTHOR]

This paper proposed a new computing method to quantitatively and non-destructively determine the corrosion of steel strands by analyzing the self-magnetic flux leakage (SMFL) signals from them. The magnetic dipole model and three growth models (Logistic model, Exponential model, and Linear model) were proposed to theoretically analyze the characteristic value of SMFL. Then, the experimental study on the corrosion detection by the magnetic sensor was carried out. The setup of the magnetic scanning device and signal collection method were also introduced. The results show that the Logistic Growth model is verified as the optimal model for calculating the magnetic field with good fitting effects. Combined with the experimental data analysis, the amplitudes of the calculated values (BxL(x,z) curves) agree with the measured values in general. This method provides significant application prospects for the evaluation of the corrosion and the residual bearing capacity of steel strand. [ABSTRACT FROM AUTHOR]