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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., QC 20230130

[EN] 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.

[EN] 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.

The study elaborates the current publication trends in the field of telemedicine as well as the application of growth models to forecast future trends with the goal of determining the fitness of growth in publications using exponential, linear, and logistic growth models. The data for the study was downloaded from the Scopus database over a fifteen-year period, from 2005 to 2019. During the period, a total of 45719 publications were found with publication productivity showing an upward trend throughout the period. The results show that the growth of publications fits into the exponential model than linear or logistic models. This study also predicts that by 2025 there will a total of 108268 publications in the field of Telemedicine, as well as progressive research.

The present study demonstrates the growth of Crystallography literature for the period 1989-2013. A total of 45320 records were extracted from the Web of Science Database for twenty five years which is used as main source of primary data for the present study. The growth models were applied for the literature of Crystallography. The result of the study indicates that, the Relative Growth Rate (RGR) of Crystallography publication found to be decreasing trend and Doubling Time (Dt) found to be increasing trend. The growth of literature in the field of Crystallography does not follow eithers Exponential growth and Logistic models. However, it closely follows closely the Polynomial, Power and Linear growth models. The study concluded that there has been a consistent trend towards increased growth of literature in the field of Crystallography.

[EN] In this paper, we deal with the logistic growth model with a time-dependent carrying capacity that was proposed in the literature for the study of the total bacterial biomass during occlusion of healthy human skin. Accounting for data and model errors, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty is quantified by approximations of the solution stochastic process via truncated series solution together with the random variable transformation method. Numerical examples illustrate the theoretical results.

[EN] In this paper, we deal with the logistic growth model with a time-dependent carrying capacity that was proposed in the literature for the study of the total bacterial biomass during occlusion of healthy human skin. Accounting for data and model errors, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty is quantified by approximations of the solution stochastic process via truncated series solution together with the random variable transformation method. Numerical examples illustrate the theoretical results.

In vitro cell biology assays are routinely used to study cancer spreading, drug design and tissue repair. However, issues associated with reproducibility are reported in literature. In this thesis we investigate the overlooked source of variability that affects the reproducibility of cell biology assays, using a combined mathematical and experimental approach. By calibrating mathematical models to experimental data, we find that the initial degree of confluence significantly affects cell motility. Following the similar approach, we identify the two-phase growth in scratch assays. We then propose a proliferation mechanism for lattice-based, random walk models, which accounts for biologically more realistic crowding effects. At last, we use a lattice-based, random walk model to mimic the passaging process and find that the passage number could significantly affect the wound closure in scratch assays.

This paper discusses statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics addressed are mathematical model, statistical model and data assumptions, and some techniques (residual plots, sensitivity analysis, model comparison tests) for verifying these. The ideas are illustrated throughout with the popular logistic growth model of Verhulst and Pearl as well as with a recently developed population-level model of pneumococcal disease spread., Prepared in cooperation with the Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC and the Department of Mathematics and Statistics, Arizona State University, Tempe, AZ.