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Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation.

While some believe that ride-hailing services offer reduced CO₂ emissions compared to individual driving, studies have found that driving without passengers on ride-hailing trips or "deadheading" prevents this. Here, with a mathematical model, the authors investigated if the use of electric vehicles as ride-hailing vehicles could offer reduced CO₂ emissions. They found that the improved vehicle efficiency and cleaner generation could in fact lower emissions compared to the use of personal gas vehicles.

In this study, the authors test whether a gravity vehicle, which is a vehicle powered by its own gravity on a ramp, could be designed to move faster when mathematical calculations for optimal mass and center of gravity were applied in the design.

Bubbles! In this study, the authors investigate the effects that different materials, temperature, and distance have on the formation of water bubbles on the surface of copper and steel. They calculated mathematical relations based on the outcomes to better understand whether interstitial hydrogen present in the d-block metals form hydrogen bonds with the water bubbles to account for the structural and mechanical stability.

What type of motivation is more effective: reward or punishment? In this study, the authors assess the effects of positive or negative on the math scores of sixth graders.

Enzyme chemotaxis is a thermodynamic phenomenon in which enzymes move along a substrate concentration gradient towards regions with higher substrate concentrations and can be used to steer nanovehicles towards targets along natural substrate concentrations. In patients with Alzheimer’s disease, a gradient of tau protein forms in the bloodstream. Tau protein is a substrate of the enzyme CDK5, which catalyzes the phosphorylation of tau protein and can travel using chemotaxis along tau protein gradients to increasing concentrations of tau and amyloid-beta proteins. The authors hypothesized that CDK5 would be able to overcome these barriers of Brownian motion and developed a quantitative model using Michaelis-Menten kinetics to define the necessary parameters to confirm and characterize CDK5’s chemotactic behavior to establish its utility in drug delivery and other applications.

Machine learning algorithms are becoming increasingly popular for data crunching across a vast area of scientific disciplines. Here, the authors compare two machine learning algorithms with respect to accuracy and user-friendliness and find that random forest algorithms outperform logistic regression when applied to the same dataset.

Dust accumulation on solar panels can reduce electricity output by 20–50%, posing a major challenge for solar energy collection. Instead of altering panel design, we explored a simpler approach by modifying surface energy through nanotexturing, predicting that hydrophobic surfaces would repel both water and dust. This study found that treating glass and silicone surfaces with potassium hydroxide (KOH) for 13 and 10 minutes, respectively, created optimal nanotextures (445 nm for glass, 205 nm for silicone), significantly reducing dirt accumulation and improving solar energy capture.

Greenspaces (urban and wetland areas that contain vegetation) are beneficial to reducing pollution, while airplanes are a highly-polluting method of transportation. The authors examine the intersection of these two environmental factors by processing satellite images to reveal what percentage of flight paths go over greenspaces at major US airports.

The authors use the Lanczos algorithm to computationally solve the Schrodinger equation for 2D potentials with a Python program