S-shaped Growth Research Articles

English

Development of information technology has decreased the costs of processing information, and the internet has speeded up communication. Internet is a crucial technological innovation which has exceptional economic impact. Factual information confirms that developed countries possess higher concentrations of internet compared with undeveloped countries. For instance, in Albania for a long time, internet penetration levels have remained too low from 1995 to 2004, and have an impulse of increase in 2007. This study has the goal to analyze the diffusion process of Internet in Albania. The principal objective of this research is to model and forecast the values of Internet diffusion using the data of percentage of Internet users of World Bank database. In the first part, it was established that the diffusion of the Internet follows the S-shaped growth curve using Loglet Lab. The parameters of model give information on the Internet diffusion speed and the maximum potential percentage of Internet users. Growth projection informs providers of Internet products and service about the potential consumer base.

Diffusion of innovations in Axelrod’s model

.Axelrod’s model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e. individuals become more similar when they interact) and homophily (i.e. individuals interact preferentially with similar others). The strength of these factors is controlled by two parameters: F, the number of features that characterize the cultures, and q, the common number of states each feature can assume. For fixed F, a large value of q reduces the frequency of interactions between individuals because it makes their cultures more diverse. Here we assume that the innovation is a new state of a cultural feature of a single individual—the innovator—and study how the innovation spreads through the networks of the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially successful innovation spreads linearly with time t, but in the long-time limit it spreads diffusively (∼t1/2) in 1D and sub-diffusively (∼) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of t. For random graphs with a finite number of nodes N, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity K of the graph and the per-feature diversity q. A large q is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large K is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with t. In an infinite random graph we find that the number of adopters of a successful innovation scales with with for K > 2 and for K = 2. We suggest that the exponent γ may be a useful index to characterize the process of diffusion of successful innovations in diverse scenarios.

Determining the optimal allocation of testing resource for modular software system using dynamic programming

Reliability is a major concern in the process of software development because unreliable software can cause failure in the computer system that can be hazardous. A way to enhance the reliability of software is to detect and remove the faults during the testing phase, which begins with module testing wherein modules are tested independently to remove a substantial number of faults within a limited resource. Therefore, the available resource must be allocated among the modules in such a way that the number of faults is removed as much as possible from each of the modules to achieve higher software reliability. In this article, we discuss the problem of optimal resource allocation of the testing resource for a modular software system, which maximizes the number of faults removed subject to the conditions that the amount of testing-effort is fixed, a certain percentage of faults is to be removed and a desired level of reliability is to be achieved. The problem is formulated as a non linear programming problem (NLPP), which is modeled by the inflection S-shaped software reliability growth models (SRGM) based on a non homogeneous Poisson process (NHPP) which incorporates the exponentiated Weibull (EW) testing-effort functions. A solution procedure is then developed using a dynamic programming technique to solve the NLPP. Furthermore, three special cases of optimum resource allocations are also discussed. Finally, numerical examples using three sets of software failure data are presented to illustrate the procedure developed and to validate the performance of the strategies proposed in this article. Experimental results indicate that the proposed strategies may be helpful to software project managers for making the best decisions in allocating the testing resource. In addition, the results are compared with those of Kapur et al. (2004), Huang and Lyu (2005), and Jha et al. (2010) that are available in the literature to deal the similar problems addressed in this article. It reveals that the proposed dynamic programming method for the testing-resource allocation problem yields a gain in efficiency over other methods.

Properties and prediction accuracy of a sigmoid function of time-determinate growth

The properties and short-term prediction accuracy of mathematical model of sigmoid time-determinate growth, denoted as “KM-function”, are presented. Comparative mathematical analysis of the function revealed that it is a model of asymmetrical sigmoid growth, which starts at zero size of an organism and terminates when it reaches its final size. The function assumes a finite length of the growth period and includes a parameter interpretable as the expected lifespan of the organism. Moreover, the possibility for growth curve inflexion at any age is possible, so the function can be used for modelling of S-shaped growth trajectories with various degree of asymmetry. These good theoretical predispositions for realistic growth predictions were empirically evaluated. The KM-function used in three and four-parameter forms was compared with three classical (Richards, Korf and Weibull) growth functions employing two parameterisation methods - nonlinear least squares (NLS) and Bayesian method. The evaluation was conducted on the basis of the tree diameter series obtained from stem analyses. The main empirical findings are: (i) if the minimisation of the prediction bias is required, the KM-function in three-parameter form in connection with Bayes parameterisation can be recommended; (ii) if the minimisation of root square error (RMSE) is required, the best short-term prediction results for a particular dataset were obtained with four-parameter Weibull function employing NLS parameterisation; (iii) moreover, three-parameter functions parameterised by Bayesian methods show a considerably smaller RMSE by 15-25% as well as smaller biases by 40-60% than four-parameter functions employing NLS. Overall, all analyses confirmed relative usefulness of the KM-function in comparison with classical growth functions, especially in connection with Bayesian parameterisation.

Prediction of Experimental Rainfall-Eroded Soil Area Based on S-Shaped Growth Curve Model Framework

Rainfall-induced soil erosion of a mountain area plays a significant role in supplying sediment and shaping the landscape. The related area of soil erosion, as an index of the changed landscape, is easier to calculate visually using some popular imaging tools. By image analysis, our work shows that the changing of the soil erosion area admits the structure of an S-growth curve. Therefore, we propose to establish an S-curve model, based on incremental learning, to predict the soil erosion area. In the process of incremental learning, we dynamically update the accumulative rainfall and rainfall intensity to train the parameters of our S-curve model. In order to verify our prediction model, the index of area is utilized to express the output of eroded soil in a series of experiments. The results show that the proposed S-growth curve model can be used to estimate the growth of the soil erosion area (average relative error 3%–9.7%) according to variable soil material and rainfall intensity. The original S-growth curve model can calculate the erosion areas of just one soil material and one rainfall condition whose average relative error is 7.5%–12.2%; compared to the simple time series analysis-moving average method (average relative error 5.7%–12.1%), our proposed S-growth curve model can reveal the physical mechanism and evolution of the research object.

Exponentiated Weibull distribution approach based inflection S-shaped software reliability growth model

Abstract The aim of this paper was to estimate the number of defects in software and remove them successfully. This paper incorporates Weibull distribution approach along with inflection S-shaped Software Reliability Growth Models (SRGM). In this combination two parameter Weibull distribution methodology is used. Relative Prediction Error (RPE) is calculated to predict the validity criterion of the developed model. Experimental results on actual data from five data sets are compared with two other existing models, which expose that the proposed software reliability growth model predicts better estimation to remove the defects. This paper presents best software reliability growth model with including feature of both Weibull distribution and inflection S-shaped SRGM to estimate the defects of software system, and provide help to researchers and software industries to develop highly reliable software products.

A white-box model of S-shaped and double S-shaped single-species population growth.

Complex systems may be mechanistically modelled by white-box modeling with using logical deterministic individual-based cellular automata. Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models). Most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka–Volterra models. In black-box models, the individual-based (mechanistic) mechanisms of population dynamics remain hidden. Here we mechanistically model the S-shaped and double S-shaped population growth of vegetatively propagated rhizomatous lawn grasses. Using purely logical deterministic individual-based cellular automata we create a white-box model. From a general physical standpoint, the vegetative propagation of plants is an analogue of excitation propagation in excitable media. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We have investigated mechanisms of the single-species population growth limited by habitat size, intraspecific competition, regeneration time and fecundity of individuals in two types of boundary conditions and at two types of fecundity. Besides that, we have compared the S-shaped and J-shaped population growth. We consider this white-box modeling approach as a method of artificial intelligence which works as automatic hyper-logical inference from the first principles of the studied subject. This approach is perspective for direct mechanistic insights into nature of any complex systems.

Metabolic acceleration in the pond snail Lymnaea stagnalis?

Under constant environmental conditions, most animals tend to grow following the von Bertalanffy growth curve. Deviations from this curve can point to changes in the environment that the animals experience, such as food limitation when the available food is not sufficient or suitable. However, such deviations can also point to a phenomenon called metabolic acceleration, which is receiving increasing attention in the field of Dynamic Energy Budget (DEB) modeling. Reasons for such an acceleration are usually changes in shape during ontogeny, which cause changes in the surface area to volume ratio of the organism. Those changes, in turn, lead to changes in some of the model parameters that have length in their dimension. The life-history consequences of metabolic acceleration as implemented in the DEB theory are an s-shaped growth curve (when body size is expressed as a length measure) and a prolongation of the hatching time. The great pond snail Lymnaea stagnalis was earlier found to be food limited during the juvenile phase in laboratory experiments conducted under classical ecotoxicity test protocols. The pond snail has isomorphic shell growth but yet does not exhibit the expected von Bertalanffy growth curve under food limitation. When applying the standard DEB model to data from such life-cycle experiments, we also found that the hatching time is consistently underestimated, which could be a sign of metabolic acceleration. We here present an application of the DEB model including metabolic acceleration to the great pond snail. We account for the simultaneous hermaphroditism of the snail by including a model extension that describes the relative investment into the male and female function. This model allowed us to adequately predict the life history of the snail over the entire life cycle. However, the pond snail does not change in shape substantially after birth, so the original explanation for the metabolic acceleration does not hold. Since the change in shape is not the only explanation for metabolic acceleration in animals, we discuss the possible other explanations for this pattern in L. stagnalis.

Isolation, culture, and induced multiple differentiation of Mongolian sheep bone marrow-derived mesenchymal stem cells

The aim of this paper was to explore the optimal method of isolating, purifying, and proliferating Mongolian sheep bone marrow-derived mesenchymal stem cells (BMSCs) and their multiple differentiation potentialities. Bone marrow (BM) was punctured from ∼1-year-old sheep, and BMSCs were harvested through gradient centrifuge and adherent cultures. Analysis of the growth of the passage 1, 5, and 10 cultures revealed an S-shaped growth curve with a population doubling time of 31.2h. Karyotyping indicated that the chromosome number in the Mongolian sheep was 2n = 54, comprising 26 pairs of autosomes and one pair of sex chromosomes (XY). RT-PCR demonstrated that OCT4, SOX2, and Nanog genes at passage 3 were positively expressed. The P3 BMSCs were cultured in vitro under inductive environments and induced into adipocytes, osteoblasts, chondrocytes, neural cells, and cardiomyocytes. Their differentiation properties were confirmed by histological staining, such as oil red, Alizarin red, hematoxylin-eosin, toluidine blue, and periodic acid schiff. RT-PCR showed that the specific genes to be induced were all expressed. This proves that the isolated cells are indeed the BMSCs and also provides valuable materials for somatic cell cloning and transgenic research.

Analyzing Macroscopic Demand Structure Based on New Model of S-shaped Growth

Analyzing Macroscopic Demand Structure Based on New Model of S-shaped Growth

Software Reliability Growth Models with Log-logistic Testing-Effort Function: A Comparative Study

Software reliability growth model is one of the basic techniques to assess software reliability quantitatively and it provides the essential information for software development activities. In this paper we compare the predictive capability of popular software reliability growth models (SRGM), such as exponential growth, delayed S-shaped growth and inflection S-shaped growth models. We first review the loglogistic testing-effort function and also discuss exponential type and S-shaped types SRGM with log-logistic testingeffort. We analyze the real data applications and compare the predictive capability of these SRGM. The experimental results reveal that inflection S-shaped type SRGM has better prediction capability as compare to exponential type SRGM.

Pure cultures and characterization of yak Sertoli cells

The culture of primary Sertoli cells has become an important resource in the study of their function. However, their use is limited because of contamination of isolated cells with other testicular cells, mainly germ cells. The aim was to establish technique to obtain pure yak Sertoli cells as well as to study the growth kinetics and biological characteristics of Sertoli cells in vitro. Two-step enzyme digestion was used to separate and culture yak Sertoli cells. Cultured using starvation method and the hypotonic treatment were also invented to get pure yak Sertoli cells. Furthermore, the purification of Yak Sertoli cells were identified according to their characteristics, such as bipolar corpuscular around the nucleus and expression of Fasl, in addition to their morphology. The average viability of the Sertoli cells was 97% before freezing and 94.5% after thawing, indicating that cryopreservation in liquid nitrogen had little influence on the viability of Sertoli cells. The growth tendency of yak Sertoli cells was similar to an S-shaped growth curve. Purified yak Sertoli cells frequently exhibited bipolar corpuscula in nucleus after Feulgen staining, and did have a positive reaction of Fasl by the immunocytochemical identification. After recovery chromosomal analysis of Sertoli cells had a normal chromosomal number of 60, comprising 29 pairs of autosomes and one pair of sex chromosomes. Assays for bacteria, fungi and mycoplasmas were negative. In conclusion, yak Sertoli cells have been successfully purified and cultured in vitro, and maintain stable biological characteristics after thawing. Therefore, it will not only preserve the genetic resources of yaks at the cellular level, but also provide valuable materials for transgenic research and feeder layer and nuclear donor cells in yak somatic cell cloning technology.

Decision-making Reliability Estimation Model based on Building Construction Project Participants' Experience

Generally, building construction projects have a complex decision-making process because of the participation of various agents. In this situation, a final decision is arrived at by relying on subjective judgments based on the experience of project participants. For this reason, a method of assessing the objectivity of opinions is needed. In previous studies, the multi-criteria decision making method was applied to arrive at a final decision objectively, but this method has a limitation, in that the experience of each decision maker is not considered differently in the decision making process. Therefore, this study proposed a theoretical model using the S-shaped growth curve and regression analysis by building construction project type to quantitatively estimate decision-making reliability according to the experience of individual project participant`s. The developed model could be added to the Multi-criteria decision making method, and secure the objectivity and reliability of project participants' final opinion.

Portland Cement Hydration by Electrical Resistivity Method and Computer Simulation

Abstract A non-contacting electrical resistivity measurement device has been adopted to measure the electrical resistivities, ρ(t), of Portland cement pastes with water cement (w/c) ratios of 0.35, 0.40, and 0.45. The electrical resistivity curves all exhibit the same type of s-shaped growth; however, the electrical resistivity curve of the cement paste with the lower w/c ratio is always above those of higher w/c ratios. The hydration process can be divided into the dissolution and precipitation period, the setting period, the acceleration period, and the deceleration period, according to the rate of electrical resistivity development. In order to gain insights on the evolution of the microstructure during hydration, this study includes a computer simulation of the hydration process, considering the influence of particle size, w/c ratio, temperature, and orientation on representative length scales in the microstructures. The visualization of the microstructure evolution in the paste can well interpret the hydration process, which is consistent with the theoretical analysis. The microstructure evolutions show that the lower the w/c ratio is, the more quickly the hydration products cluster; consequently, it is easier and takes less time to form clusters, making the porosity decrease more rapidly, offering reasonable explanation of the characteristics of the 24 h compressive strengths of the pastes with different w/c ratios. The porosity obtained can well explain the development of the electrical resistivities of cement pastes with different w/c ratios after the dissolution period.

An S-shaped software reliability model with imperfect debugging and improved testing learning process

In this paper, we propose a non-homogeneous Poisson process (NHPP) based S-shaped software reliability growth model (SRGM) in presence of imperfect debugging with a new exponentially increasing fault content function and S-shaped fault detection rate. We develop the fault content function considering learning capability of testing team during software development process. Fault content increases rapidly at the beginning of testing process while it grows gradually at the end of testing process due to increasing efficiency of testing team with testing time. We use maximum likelihood estimation (MLE) method to estimate model parameters. Applicability of the proposed model has been presented by comparing with established models in terms of goodness of fit and predictive validity using two software failure data sets. Experimental results show that the proposed model gives better fit to real failure data sets and predicts future failure behaviour of software development accurately than established models.

SPC for Software Reliability using Inflection S-Shaped Model

Traditional statistical analysis methods account for natural variation but require aggregation of measurements over time,which can delay decision making.Statistical process control (SPC) is a branch of statistics that combines rigorous time series analysis methods with graphical presentation of data,often yielding insights into the data more quickly and in a way more understandble to lay decision makers .SPC and its primary tool-the control chart-provide researchers and practitioners with a method of better understanding and communicating data from software reliability improvement process efforts .This paper provides an s-shaped software reliability growth model based on the Non-Homogenous Poisson Process (NHPP).The maximum likelihood approach is used to estimate the unknown parameters of the model.

Turkey's per Capita Income Conversion to Southern European Countries

In this paper we have estimated the number of years for Turkey’s per capita income to converge with those of Italy, Spain, Portugal and Greece. The estimate is based upon convergence theory of per capita income of laggard countries to that of advanced countries if (1) there exists a gap between the countries’ initial level of per capita income with the laggard country having the lower per capita income, (2) there exists a per capita productivity growth rate differential in favor of the laggard country and (3) sufficient time horizon considered to effectuate the convergence. In this instance all three conditions are met and assumed. According to our calculations, Turkey’s per capita income will converge with Portugal in 33 years, Greece in 39 years, Italy in 46 years and Spain in 62 Years, all within the 21st century time horizon. In addition the empirical and theoretical basis for conversion of per capita income is elucidated and verified. Using a wide cross section of countries we find evidence of unconditional income convergence looking at both the mean as well as at the entire income distribution via ordinary least squares and quintile regression respectively. We also analyzed the presence of an S-shaped growth curve for explaining the observed rapid progression of convergence and its impact on the expected future global income distribution.

Structure of S-shaped growth in innovation diffusion

A basic question on innovation diffusion is why the growth curve of the adopter population in a large society is often S shaped. From macroscopic, microscopic, and mesoscopic viewpoints, the growth of the adopter population is observed as the growth curve, individual adoptions, and differences among individual adoptions, respectively. The S shape can be explained if an empirical model of the growth curve can be deduced from models of microscopic and mesoscopic structures. However, even the structure of growth curve has not been revealed yet because long-term extrapolations by proposed models of S-shaped curves are unstable and it has been very difficult to predict the long-term growth and final adopter population. This paper studies the S-shaped growth from the viewpoint of social regularities. Simple methods to analyze power laws enable us to extract the structure of the growth curve directly from the growth data of recent basic telecommunication services. This empirical model of growth curve is singular at the inflection point and a logarithmic function of time after this point, which explains the unstable extrapolations obtained using previously proposed models and the difficulty in predicting the final adopter population. Because the empirical S curve can be expressed in terms of two power laws of the regularity found in social performances of individuals, we propose the hypothesis that the S shape represents the heterogeneity of the adopter population, and the heterogeneity parameter is distributed under the regularity in social performances of individuals. This hypothesis is so powerful as to yield models of microscopic and mesoscopic structures. In the microscopic model, each potential adopter adopts the innovation when the information accumulated by the learning about the innovation exceeds a threshold. The accumulation rate of information is heterogeneous among the adopter population, whereas the threshold is a constant, which is the opposite of previously proposed models. In the mesoscopic model, flows of innovation information incoming to individuals are organized as dimorphic and partially clustered. These microscopic and mesoscopic models yield the empirical model of the S curve and explain the S shape as representing the regularities of information flows generated through a social self-organization. To demonstrate the validity and importance of the hypothesis, the models of three level structures are applied to reveal the mechanism determining and differentiating diffusion speeds. The empirical model of S curves implies that the coefficient of variation of the flow rates determines the diffusion speed for later adopters. Based on this property, a model describing the inside of information flow clusters can be given, which provides a formula interconnecting the diffusion speed, cluster populations, and a network topological parameter of the flow clusters. For two recent basic telecommunication services in Japan, the formula represents the variety of speeds in different areas and enables us to explain speed gaps between urban and rural areas and between the two services. Furthermore, the formula provides a method to estimate the final adopter population.

Effect of the Volume-to-Surface Ratio of Cultures on Escherichia coli Growth: An Experimental and Theoretical Analysis

The growth dynamics of bacterial populations are usually represented by the classical S-shaped profiles composed of lag, exponential and stationary growth phases. Although exceptions to this classical behavior occur, they are normally produced under non-standard conditions such as supply of two carbohydrates as sole carbon source. However, we here report variations in the classic S-shaped growth profiles of Escherichia coli under standard culturing conditions; explicitly, we found growth during transition to the stationary phase wherein the bacterial growth rate inversely depended on the volume-to-surface ratio of cultures (V/S); the reasons for this behavior were experimentally explored. To complement our experimental analysis, a theoretical model that rationalizes the bacterial response was developed; simulations based on the developed model essentially reproduced experimental growth curves. We consequently conclude that the effect of V/S on E. coli growth reflects an interplay between auto-catalytic bacterial growth, bacterial growth auto-inhibition, and, the relief of that inhibition.

Parameter estimation of S-shaped growth model: A modified particle swarm algorithm

Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others. In this paper, a modified particle swarm optimization algorithm based on the diffusion phenomenon (DPPSO) was employed to estimate the parameters for this model. Under the sense of least squares, the parameter estimation problem of S-shaped growth model, taking the Gompertz and Logistic models for example, is transformed into a multi-dimensional function optimization problem. The results show that the DPPSO algorithm can effectively estimate the parameters of the S-shaped growth model.