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Investigation of the largest rigid shape that can be moved through a circular hallway of unit width with an arbitrary turn angle

Auto-Regressive Integrated Moving Average (ARIMA) models are known for their influence and application on time series data. This statistical analysis model uses time series data to depict future trends or values: a key contributor to crime mapping algorithms. However, the models may not function to their true potential when analyzing data with many different patterns. In order to determine the potential of ARIMA models, our research will test the model on irregularities in the data. Our team hypothesizes that the ARIMA model will be able to adapt to the different irregularities in the data that do not correspond to a certain trend or pattern. Using crime theft data and an ARIMA model, we determined the results of the ARIMA model’s forecast and how the accuracy differed on different days with irregularities in crime.

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.

People react to music by moving and dancing. This study examined if different types of music were correlated with higher heart rates and if this was at all affected by music preferences.

In this study the authors looked the trajectories of cosmic rays moving through a dipole field. They found that the trajectories of cosmic rays are determined by a particle's energy and interaction with Earth's B field.

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.

Smartphones are not only becoming an inseparable part of our daily lives, but also a low-cost, powerful optical imaging tool for more and more scientific research applications. In this work, smartphones were used as a low-cost, high-speed, photographic alternative to expensive equipment, such as those typically found in scientific research labs, to accurately perform motion tracking and analysis of fast-moving objects. By analyzing consecutive images, the speed and flight trajectory of water droplets in the air were obtained, thereby enabling us to estimate the area of the water droplets landing on the ground.

Racial inequality has been a major issue throughout the history of the United States. In recent years, however, especially with the election of America's first black president, many have claimed that we have made progress and are moving towards a post-racial society. The authors of this study sought to test that claim by evaluating whether high school age students still experience a phenomenon known as white guilt. White guilt is defined as remorse or shame felt by people of Caucasian descent about racial inequality.

Using the European Space Agency’s Gaia dataset, the authors analyzed the relationship between white dwarfs’ magnitudes and proper motions. They hypothesized that older white dwarf stars may have different velocities than younger ones, possibly that stars slow down as they age. They found that the white dwarfs in the dataset were substantially redder and higher magnitude (traits traditionally associated with older stars) as compared to their non-fast counterparts.

Did the COVID-19 pandemic and travel restrictions improve air quality? The authors investigate this question in New York City using existing pollution data and forecasting trends.