Here based on an interest in fractals, the authors used a Julia Set Generator to consider a specific point on the Mandelbrot set with an associated coordinate. In this manner, they found that the complexity of the Mandelbrot and Julia Sets are governed by relatively simple rules, revealing that the intricate patterns of fractals can be defined by defined by simple rules and patterns.

In this article, the authors investigate whether stock selection across various sectors is efficient enough to outperform an overall market. Stocks from 2006 to 2020 were selected across sectors to calculate beta values using the Capital Asset Pricing Model.

The purpose of the study was to determine whether graph-based machine learning techniques, which have increased prevalence in the last few years, can accurately classify data into one of many clusters, while requiring less labeled training data and parameter tuning as opposed to traditional machine learning algorithms. The results determined that the accuracy of graph-based and traditional classification algorithms depends directly upon the number of features of each dataset, the number of classes in each dataset, and the amount of labeled training data used.

Recurrent neural networks (RNNs) are useful for text generation since they can generate outputs in the context of previous ones. Baroque music and language are similar, as every word or note exists in context with others, and they both follow strict rules. The authors hypothesized that if we represent music in a text format, an RNN designed to generate language could train on it and create music structurally similar to Bach’s. They found that the music generated by our RNN shared a similar structure with Bach’s music in the input dataset, while Bachbot’s outputs are significantly different from this experiment’s outputs and thus are less similar to Bach’s repertoire compared to our algorithm.

In this article, the authors use datasets of professional and youth soccer players' movements to map and statistically compare them. Analysis compared movements that led to goals or no-goals and differences between pros and youth.

This study examines the higher harmonics in an oscillating string by analyzing the sound produced by a guitar with a spectrum analyzer. The authors mathematically hypothesized that the higher harmonics in the series of the directly excited 2^nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3^rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2^nd, 3^rd, and 4^th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

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.

In this study, the authors investigate just how effectively paper towels can absorb different types of liquid and whether changing the properties of the towel (such as folding it) affects absorbance. Using variables of either different liquid types or the folded state of the paper towels, they used thorough approaches to make some important and very useful conclusions about optimal ways to use paper towels. This has important implications as we as a society continue to use more and more paper towels.

Though current strategies in counterterrorism are somewhat effective, the Simultaneous Attack/Persistent Pursuit (SAPP) Theory may be superior alternative to current methods. The authors simulated five attack strategies (1 SAPP and 4 non-SAPP), and concluded that the SAPP model was significantly more effective in reducing the final number of terrorist attacks. This demonstrates the comparative advantage of utilizing the SAPP model, which may prove to be critical in future efforts in counterterrorism.

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!