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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Geographic Distribution of Scripps National Spelling Bee Spellers Resembles Geographic Distribution of Child Population in US States upon Implementation of the RSVBee “Wildcard” Program
The Scripps National Spelling Bee (SNSB) is an iconic academic competition for United States (US) schoolchildren, held annually since 1925. However, the sizes and geographic distributions of sponsored regions are uneven. One state may send more than twice as many spellers as another state, despite similar numbers in child population. In 2018, the SNSB introduced a wildcard program known as RSVBee, which allowed students to apply to compete as a national finalist, even if they did not win their regional spelling bee. In this study, the authors tested the hypothesis that the geographic distribution of SNSB national finalists more closely matched the child population of the US after RSVBee was implemented.
Read More...The Effect of Varying Training on Neural Network Weights and Visualizations
Neural networks are used throughout modern society to solve many problems commonly thought of as impossible for computers. Fountain and Rasmus designed a convolutional neural network and ran it with varying levels of training to see if consistent, accurate, and precise changes or patterns could be observed. They found that training introduced and strengthened patterns in the weights and visualizations, the patterns observed may not be consistent between all neural networks.
Read More...Artificial Intelligence Networks Towards Learning Without Forgetting
In their paper, Kreiman et al. examined what it takes for an artificial neural network to be able to perform well on a new task without forgetting its previous knowledge. By comparing methods that stop task forgetting, they found that longer training times and maintenance of the most important connections in a particular task while training on a new one helped the neural network maintain its performance on both tasks. The authors hope that this proof-of-principle research will someday contribute to artificial intelligence that better mimics natural human intelligence.
Read More...Ant Colony Optimization Algorithms with Multiple Simulated Colonies Offer Potential Advantages for Solving the Traveling Salesman Problem and, by Extension, Other Optimization Problems
Ant colony optimization algorithms simulate ants moving from point to point on a graph and coordinate their actions, similar to ants laying down pheromones to strengthen a path as it is used more frequently. These ACO algorithms can be applied to the classic traveling salesman problem, which aims to determine the lowest-cost path through a given set of points on a graph. In this study, a novel multiple-colony system was developed that uses multiple simulated ant colonies to generate improved solutions to the traveling salesman problem.
Read More...Mathematical modeling of plant community composition for urban greenery plans
Here recognizing the importance of urban green space for the health of humans and other organisms, the authors investigated if mathematical modeling can be used to develop an urban greenery management plan with high eco-sustainability by calculating the composition of a plant community. They optimized and tested their model against green fields in a Beijing city park. Although the compositions predicted by their models differed somewhat from the composition of testing fields, they conclude that by using a mathematical model such as this urban green space can be finely designed to be ecologically and economically sustainable.
Read More...Heat conduction: Mathematical modeling and experimental data
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.
Read More...Estimating the liquid jet breakdown height using dimensional analysis with experimental evidence
These authors mathematically deduce a model that explains the interesting (and unintuitive) physical phenomenon that occurs when water falls.
Read More...Enhancing the quantum efficiency of a silicon solar cell using one dimensional thin film interferometry
Here, recognizing the need to improve the efficiency of the conversion of solar energy to electrical energy, the authors used MATLAB to mathematically simulate a multi-layered thin film with an without an antireflective coating. They found that the use of alternating ZnO-SiO2 multilayers enhanced the transmission of light into the solar cell, increasing its efficiency and reducing the reflectivity of the Si-Air interface.
Read More...Comparison of three large language models as middle school math tutoring assistants
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.
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