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!

Intelligent vehicles utilize a combination of video-enabled object detection and radar data to traverse safely through surrounding environments. However, since the most momentary missteps in these systems can cause devastating collisions, the margin of error in the software for these systems is small. In this paper, we hypothesized that a novel object detection system that improves detection accuracy and speed of detection during adverse weather conditions would outperform industry alternatives in an average comparison.

Engineered bacteria that degrade oil are currently being considered as a safe option for the treatment of oil spills. For this approach to be successful, the bacteria must effectively express oil-degrading genes they uptake as part of an external genoming vehicle called a "plasmid". Using a computational approach, the authors investigate plasmid-bacterium compatibility to find pairs that ensure high levels of gene expression.

The Environmental Protection Agency (EPA) reports a significant number of heavy metal-contaminated sites across the United States. To address this public health concern, rhizoremediation using microbes has emerged as a promising solution. Here, a combination of soil microbes were inoculated in the rhizosphere in soil contaminated with 500 parts per million (ppm) of lead. Results showed rhizoremediation is an effective bioremediation strategy and may increase crop productivity by converting nonarable lands into arable lands.

The authors test the durability of synthetic versus non-synthetic fabrics though loose thread counts, color fade over time, and shrinkage tests.

Cystic fibrosis is a genetic disease caused by mutations in the CFTR gene. In this paper, the authors attempt to identify variations in stretches of up to 8 nucleotides in the protein-coding portions of the CFTR gene that are associated with disease development. This would allow screening of newborns or even fetuses in utero to determine the likelihood they develop cystic fibrosis.

Osteosarcoma is a type of bone cancer that affects young adults and children. Early diagnosis of osteosarcoma is crucial to successful treatment. The current methods of diagnosis, which include imaging tests and biopsy, are time consuming and prone to human error. Hence, we used deep learning to extract patterns and detect osteosarcoma from histological images. We hypothesized that the combination of two different technologies (transfer learning and data augmentation) would improve the efficacy of osteosarcoma detection in histological images. The dataset used for the study consisted of histological images for osteosarcoma and was quite imbalanced as it contained very few images with tumors. Since transfer learning uses existing knowledge for the purpose of classification and detection, we hypothesized it would be proficient on such an imbalanced dataset. To further improve our learning, we used data augmentation to include variations in the dataset. We further evaluated the efficacy of different convolutional neural network models on this task. We obtained an accuracy of 91.18% using the transfer learning model MobileNetV2 as the base model with various geometric transformations, outperforming the state-of-the-art convolutional neural network based approach.

The Human Immunodeficiency Virus (HIV) infects approximately 40 million people globally, and one million people die every year from Acquired Immune Deficiency Syndrome (AIDS)-related illnesses. This study examined the interactions between the HIV-1 envelope glycoprotein gp120 and the human lymphocyte receptor integrin α4β7, the putative first long-range receptor for the envelope glycoprotein of the virus in mucosal tissues. Presented data support the claim that the V1 loop is involved in the binding between α4β7 and the HIV-1 envelope glycoprotein through molecular dockings.

The authors analyzed biosolids from five Wisconsin wastewater treatment plants and suggest using KBr pellet FTIR as a simple and rapid method to start characterizing P species in biosolids.

People are quick to accept the assumption that a light will appear dimmer the farther away they are, citing the inverse square relationship that illuminance obeys as rationale. However, repeated observations of light sources maintaining their brightness over large distances prompted us to explore how the brightness, or perceived illuminance of a light varies with the viewing distance from the object. We hypothesized that since both the illuminance of the light source and image size decrease at the same rate, then the concentration, or intensity of the image remains unchanged, and subsequently the perceived illuminance.