Predicting the Next US President by Simulating the Electoral College

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic modeling and computer simulations can solve real-world problems for which analytical solutions may be difficult to find

Limiting Forms of Iterated Circular Convolutions of Planar Polygons

We consider a complex representation of an arbitrary planar polygon P centered at the origin. Let P(1) be the normalized polygon obtained from P by connecting the midpoints of its sides and normalizing the complex vector of vertex coordinates. We say that P(1) is a normalized average of P. We identify this averaging process with a special case of a circular convolution. We show that if the convolution is repeated many times, then for a large class of polygons the vertices of the limiting polygon lie either on an ellipse or on a star-shaped polygon. We derive a complete and compact analytical description of the limiting elliptical envelope using discrete Fourier transforms and circular convolutions. One of the key insights of this approach is the realization that the repeated circular convolution removes all higher harmonic pairs leaving only the principal harmonic pair from the discrete Fourier transform of the original polygon to dominate the Fourier transform of the repeatedly convolved polygon thereby controlling the limiting behavior

Creating Art Patterns with Math and Code

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors. The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for data analysis and visualizations. Our hope is that familiarity with R could improve our students\u27 chances of getting internships and full-time jobs. This project is supported by the DOE MSEIP grant # P120A150063. Project Team: Sandie Han (PI), Pamela Brown, Janet Liou-Mark, Johann Thiel, Boyan Kostadinov, and Erin Small

Simulation Insights Using R

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of the functionality and unique simulation and visualization features that R offers

How Much Should You Pay For a Financial Derivative?

We explain some key mathematical ideas behind the no-arbitrage pricing of financial derivatives by replication, starting from a simple coin toss model and ending with the continuous-time limit of a multi-step coin-toss model using a geometric random walk model. In the limit, we obtain the classical Black-Scholes-Merton formula for pricing European call and put options

Computational Insight with Monte Carlo Simulations

We introduce Monte Carlo simulations for estimating areas by playing a game of darts . We also introduce simulations of random walks. We use compact, vectorized programming, based on the R language, for all computer simulations and visualizations, aimed at high school students. This presentation is based on the Invited, prime time lecture given at the summer camp for gifted high school students at City College of New York, July 13, 2011

Simulating and Animating the Spatial Dynamics of Interacting Species Living on a Torus

The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled by the weighted average of the current population density and the average inflow of migrating species from the nearest 8-neighbor migration zone, applied to any given cell in the inner core of the grid (inside the reflecting boundary layer). All simulations are coded using the high-level programming language R, which allows for very compact code that can be quickly developed by using functional, matrix-based, programing. This programming approach allows the entire model dynamics to be coded in less than 50 lines of code, making it ideal for student projects. The main goal of the student research project is to create a video, animating the spatial interactions between the two species living on a torus, based on the given population and migration dynamics, initial conditions and parameter values. The resulting beautiful spatial wave patterns, produced by the interfering waves of the spatial population density, visualize the fluctuating abundance of the species in their torus-shaped universe over time. This is an html presentation, as given at the MAA MathFest 2015. We also provide an additional pdf document that contains the model animation. The pdf must be opened in Adobe Acrobat Reader for the animation to run. Preview on the Mac will not run the animation since it is not JavaScript enabled

Discovering Kepler’s Third Law from Planetary Data

In this data-inspired project, we illustrate how Kepler’s Third Law of Planetary Motion can be discovered from fitting a power model to real planetary data obtained from NASA, using regression modeling. The power model can be linearized, thus we can use linear regression to fit the model parameters to the data, but we also show how a non-linear regression can be implemented, using the R programming language. Our work also illustrates how the linear least squares used for fitting the power model can be implemented in Desmos, which could serve as the computational foundation for this project at a lower course level. This paper is based on our ICTCM 2020 talk with the same title. We included two NASA inspired student projects at the calculus level that were developed with the support of the Opening Gateways grant at New York City College of Technology

Using Data Science Tools for Investigating Chat Logs from the Conti Ransomware Group

The main goal of this paper is to showcase some results from a comprehensive data analysis that we did on the cache of chat logs from the notorious ransomware group Conti. The chat logs were made publicly available on February 27, 2022. They were translated from Russian into English, and contain 393 json files with chat logs from the instant messaging service Jabber. We employ a variety of modern data science tools for text mining, natural language processing, network analysis and geospatial analysis to investigate the Conti chat logs so that we can understand the command and control structure of the network and discover any valuable information hidden in the data, such as Bitcoin, IP, email and web addresses, as well as any other information that can lead to further insights into the inner workings of the Conti group