In this experiment, the authors modify the heat equation to account for imperfect insulation during heat transfer and compare it to experimental data to determine which is more accurate.

This study aimed to predict and explain chaotic behavior in the Mandelbrot Set, one of the world’s most popular models of fractals and exhibitors of Chaos Theory. The authors hypothesized that repeatedly iterating the Mandelbrot Set’s characteristic function would give rise to a more intricate layout of the fractal and elliptical models that predict and highlight “hotspots” of chaos through their overlaps. The positive and negative results from this study may provide a new perspective on fractals and their chaotic nature, helping to solve problems involving chaotic phenomena.

Here the authors investigate whether there are mathematical inaccuracies of perspective in artists' paintings that are undetectable with our naked eyes. Using the cross-ratio method, they find that there are three significant errors in various famous paintings which increase as the structures in the paintings recede from the viewer.

In this work, the authors investigate the accuracy with which two different population growth models can predict population growth over time. They apply the Malthusian law or Logistic law to US population from 1951 until 2019. To assess how closely the growth model fits actual population data, a least-squared curve fit was applied and revealed that the Logistic law of population growth resulted in smaller sum of squared residuals. These findings are important for ensuring optimal population growth models are implemented to data as population forecasting affects a country's economic and social structure.

This study follows the process of single-cloning and the growth of a homogeneous cell population in a superficial environment over the course of six weeks with the end goal of showing which of five tumor growth models commonly used to predict heterogeneous cancer cell population growth (Exponential, Logistic, Gompertz, Linear, and Bertalanffy) would also best exemplify that of homogeneous cell populations.

In this study, the authors use existing mathematical models to how high school athletes pace 800 m, 1600 m, and 3200 m distance track events compared to elite athletes.

In this study, we developed an algorithm to estimate the contact rate and the average infectious period of influenza using a Susceptible, Infected, and Recovered (SIR) epidemic model. The parameters in this model were estimated using data on infected Greek individuals collected from the National Public Health Organization. Our model labeled influenza as an epidemic with a basic reproduction value greater than one.

Auto-Regressive Integrated Moving Average (ARIMA) models are known for their influence and application on time series data. This statistical analysis model uses time series data to depict future trends or values: a key contributor to crime mapping algorithms. However, the models may not function to their true potential when analyzing data with many different patterns. In order to determine the potential of ARIMA models, our research will test the model on irregularities in the data. Our team hypothesizes that the ARIMA model will be able to adapt to the different irregularities in the data that do not correspond to a certain trend or pattern. Using crime theft data and an ARIMA model, we determined the results of the ARIMA model’s forecast and how the accuracy differed on different days with irregularities in crime.

In this study, the authors test the effect that the tilt angle of a solar panel has on the amount of energy it generates. This investigation highlights a simple way that people can harvest renewable energy more efficiently and effectively.

This unique research study evaluated the potential use of the flatworm, brown planaria (Dugesia tigrine), as an alternative model for teratogenicity testing. In this study, we exposed amputated planaria to varying concentrations of a known teratogen, vitamin A (retinol), for approximately 2 weeks, and evaluated multiple parameters including the formation of blastema and eyes. The results from this study demonstrated that high concentrations of retinol caused defects in head and eye formation in regenerating planaria, with similarities to vitamin A related teratogenicity findings in mammals. Based on these results, regenerating brown planaria are a promising alternative model for teratogenicity testing, which can potentially be paradigm shifting as it can reduce cost, time, and pregnant animal use in research.