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Fractals: Exploring Mandelbrot Coordinates and qualitative characteristics of the corresponding Julia Set

Thomas et al. | Jul 07, 2022

Fractals: Exploring Mandelbrot Coordinates and qualitative characteristics of the corresponding Julia Set

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.

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Similarity Graph-Based Semi-supervised Methods for Multiclass Data Classification

Balaji et al. | Sep 11, 2021

Similarity Graph-Based Semi-supervised Methods for Multiclass Data Classification

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.

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Open Source RNN designed for text generation is capable of composing music similar to Baroque composers

Goel et al. | May 05, 2021

Open Source RNN designed for text generation is capable of composing music similar to Baroque composers

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.

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Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

Jain et al. | Jan 28, 2021

Analysis of Patterns in the Harmonics of a String with Artificially Enforced Nodes

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 2nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2nd, 3rd, and 4th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

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Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

Golla et al. | Dec 14, 2020

Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

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.

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Statistically Analyzing the Effect of Various Factors on the Absorbency of Paper Towels

Tao et al. | Dec 04, 2020

Statistically Analyzing the Effect of Various Factors on the Absorbency of Paper Towels

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.

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A Statistical Comparison of the Simultaneous Attack/ Persistent Pursuit Theory Against Current Methods in Counterterrorism Using a Stochastic Model

Tara et al. | Dec 01, 2020

A Statistical Comparison of the Simultaneous Attack/ Persistent Pursuit Theory Against Current Methods in Counterterrorism Using a Stochastic Model

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.

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