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An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

Grewal et al. | Oct 05, 2020

An Analysis of the Density and Patterns of the Solutions of Diophantine Equations of the Third Power

In this study, the authors sought to find out how many mathematical solutions there were to the Indian mathematician Ramanujan's formula, which is a3 + b3 + c3 = d3, and also quantify the densities its solutions. They wrote their own computer program to do so and kept values of a, b, and c less than 10,000. While conducting the analysis, they were also looking for perfect power taxicab numbers and their frequency. They were able to find solutions and densities for the equation. Additionally, while they found that most perfect cube taxicab numbers had a frequency of 2 or 3, they also found on number with a frequency of 42!

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Comparing the Dietary Preference of Caenorhabditis elegans for Bacterial Probiotics vs. Escherichia coli.

Lulla et al. | Dec 18, 2020

Comparing the Dietary Preference of <i>Caenorhabditis elegans</i> for Bacterial Probiotics vs. <i>Escherichia coli</i>.

In this experiment, the authors used C. elegans as a simple model organism to observe the impact of probiotics on the human digestive system. The results of the experiments showed that the C. elegans were, on average, most present in Chobani cultures over other tested yogurts. While not statistically significant, these results still demonstrated that C. elegans might prefer Chobani cultures over other probiotic yogurts, which may also indicate greater gut benefits from Chobani over the other yogurt brands tested.

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A novel approach for early detection of Alzheimer’s disease using deep neural networks with magnetic resonance imaging

Ganesh et al. | Mar 20, 2022

A novel approach for early detection of Alzheimer’s disease using deep neural networks with magnetic resonance imaging

In the battle against Alzheimer's disease, early detection is critical to mitigating symptoms in patients. Here, the authors use a collection of MRI scans, layering with deep learning computer modeling, to investigate early stages of AD which can be hard to catch by human eye. Their model is successful, able to outperform previous models, and detected regions of interest in the brain for further consideration.

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