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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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More Efficient Helicopter Blades Based on Whale Tubercles

Weitzman et al. | Dec 22, 2013

More Efficient Helicopter Blades Based on Whale Tubercles

Biomimicry is the practice of applying models and systems found in nature to improve the efficiency and usefulness of human technologies. In this study, the authors designed helicopter blades with tubercle structures similar to those found on the tails of humpback whales. The authors found that certain arrangements of these tubercle structures improved the windspeed and efficiency of a model helicopter.

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Model selection and optimization for poverty prediction on household data from Cambodia

Wong et al. | Sep 29, 2023

Model selection and optimization for poverty prediction on household data from Cambodia
Image credit: Paul Szewczyk

Here the authors sought to use three machine learning models to predict poverty levels in Cambodia based on available household data. They found teat multilayer perceptron outperformed the other models, with an accuracy of 87 %. They suggest that data-driven approaches such as these could be used more effectively target and alleviate poverty.

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Differential privacy in machine learning for traffic forecasting

Vinay et al. | Dec 21, 2022

Differential privacy in machine learning for traffic forecasting

In this paper, we measured the privacy budgets and utilities of different differentially private mechanisms combined with different machine learning models that forecast traffic congestion at future timestamps. We expected the ANNs combined with the Staircase mechanism to perform the best with every value in the privacy budget range, especially with the medium high values of the privacy budget. In this study, we used the Autoregressive Integrated Moving Average (ARIMA) and neural network models to forecast and then added differentially private Laplacian, Gaussian, and Staircase noise to our datasets. We tested two real traffic congestion datasets, experimented with the different models, and examined their utility for different privacy budgets. We found that a favorable combination for this application was neural networks with the Staircase mechanism. Our findings identify the optimal models when dealing with tricky time series forecasting and can be used in non-traffic applications like disease tracking and population growth.

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