Brennan Benavidez Music. Abstract: I'll compare and contrast the data given, through Maple, of different instruments playing the same note in relation to the puretone through markov chains. Samuel Teare Image Compression Abstract: Using a few different image compression methods, compare the effectiveness and quality of the resulting images. Discover with methods and values produce the best compression without suffering too much quality loss. Methods have yet to be determined. Base images and compressed images will be shown along with the data and method explanations. Patrick Ekel Discrete Optimization I will be developing and solving a linear objective function using discrete optimization, possibly via fractional linear programming. The objective function represents agricultural yield. I am thinking about using cost, land, time, and other resources as the constraints. I am not yet sure which algorithm I will be using (simple, brewer's etc). Chris Billingsley Fractals: Starting From The Base The project will create fractals using linear transformations of matrices, trying to manipulate the column vectors to make art. Maple assist is expected. Ann Wilcox IMAGE COMPRESSION Abstract: I would like to do something with image compression. I don't quite understand how this works and I would like to do more research on the topic. I do not have a group and am willing to join another group or have others join me. Asher Sorensen Linear Algebra in Pattern Recognition Abstract: Linear algebra is useful finding patterns in data. From google searches to handwritten digit identification, vectors and matrices are ever-present in the modern data driven way of life. Linear algebra offers efficient methods to solve these common problems. [NOT AN ABSTRACT of a PROJECT] Josh Ulrich Enoch Sanz Statistics and Probability: Body Weight Abstract. Create a more accurate model for predicting body weight, assuming that individuals underestimate their weight randomly by 2-4%. Plot both the old and new models together, demonstrating the difference in prediction models between the old and new predictions. Discuss why our prediction model is more accurate and relevant for making predictions on a universal basis. Brady Jacobson The Effectiveness of Image Compression with Different Photos. Abstract. Compress digital photos by using different compression methods in order to see which method results in an image that retains its quality. Test our compression by using multiple photos of varying degrees of detail. This allows us to see what types of photos are more difficult to compress while also keeping the photo's original good quality. Jasper Slaff Translations, Scaling, and Rotations. Abstract: Investigate different types of image compression and how they differ, specifically with retaining image quality. I wanted to look into the two methods suggested on the website, but I also wanted to look into more common image compression styles and saving formats, such as JPEG, and GIF. Abstract. Transformations both linear and affine as related to robotics. Details forthcoming. Saleema Qazi Gabrielle Legaspi Encryption Using Hill Cyphers and Linear Algebra Abstract. Discuss the history of hill cyphers as well as their strength compared to other methods of cryptography. Explain the process and benefits of utilizing modular algebra in hill cyphers. Explore in detail how to encrypt a text using hill cyphers and the process of decryption with the inverse of the key matrix. Anthony Kounalis Traffic flow and electronic sales. Abstract. Use a variety of websites to set up a matrix model for sales, the year of those sales, etc. Try to find a general formula to describe these sales. My goal is to use electronic sales from the past and to do simple prediction like either the total sales in 2016, or even try to predict the totals this year. Tom Steinbrecher Demand Elasticity with Two Stage Least Squares Regression Abstract. Show how TSLS regression, as an iterative form of OLS can be utilized to calculate the demand elasticity of a product. The paper will present the procedure along with assumptions as a method to understand the linear algebra powering the statistical reasoning.Abstract: Investigate different types of image compression and how they differ, specifically with retaining image quality. I wanted to look into the two methods suggested on the website, but I also wanted to look into more common image compression styles and saving formats, such as JPEG, and GIF. Andy Krivanek Basketball Stats Abstract. Develop a model for inferring the amount of points, rebounds and assists per game an NBA player would average over an 82 game season using the players position and minutes played per game. Investigate a model that uses height instead of position to determine stats. Conner Elaine Schacherer Image Compression with SVD and DCT Abstract: Compare how images are compressed using two different methods, the Singular Value Decomposition (SVD) and the Discrete Cosine Transformation (DCT). Compare and contrast how the two methods do compression and their effectiveness. Veronika GribenkoAbstract: Investigate different types of image compression and how they differ, specifically with retaining image quality. I wanted to look into the two methods suggested on the website, but I also wanted to look into more common image compression styles and saving formats, such as JPEG, and GIF. 2008 Use of Commodities: How productive was the economy? Abstract. The data on 2008 use of commodities by industry will be used to construct a consumption matrix. Based on the results, the economy production level will be found and analyzed. Mark Lavelle Least-Squares multiple regression Abstract. Write a script in the statistical package R to perform Ordinary Least-Squares multiple regression on a data set provided in '.csv' format. The output of such a script would include the overall model fit, partial regression coefficients for all regressors, including all their interactions, significance tests and confidence intervals for each regressor, and multiple graphical depictions of the data. Miriam Galecki Abstract: Investigate different types of image compression and how they differ, specifically with retaining image quality. I wanted to look into the two methods suggested on the website, but I also wanted to look into more common image compression styles and saving formats, such as JPEG, and GIF. Principle Component Analysis Abstract. Demonstrate how PCA works. Explain the process using eigenvectors and an example. The example will be a large data set gathered from an analysis of the shape of barrier islands. Adam Lee Cryptology, AES encryption and Linear Algebra Abstract. The Advanced Encryption Standard (AES) is a modern day cipher that was endorsed by the U.S. National Institute of Standards and Technology (NIST). AES dates back to 1997 were it was created by two Belgian cryptographers, Joan Daemen and Vincent Rijmen. A variety of Linear Algebra techniques are used to perform the AES algorithm. The basic encryption process places 128 bits of text into a square matrix and then performs 4 operations. These operations are referred to as SubBytes, ShiftRows, MixColumns, and AddRoundKey. This project will take a closer look at some of these processes and the Linear Algebra behind them. Jonah Barber Discrete dynamic systems and continous approximations Abstract. Investigate discrete dynamic systems that are approximations of continuous ones. Focus on model accuracy and related velocity and acceleration vector fields. Alexandra Bertagnolli Joshua Rosen Markov Chain Text Generator Abstract. Program a Markov chain which generates statistically probable text based on its input. When the user gives it a text file, the program calculates the likelihood of which words follow each other. Each word is then assigned a transition matrix, in which each element of the matrix denotes the probability of which word occurs next. The program chooses and displays the most likely series of words to occur using the elements of these transition matrices. Rahul Ramkumar Samuel Bridge Using Convolutional Neural Networks to classify images of handwritten text Abstract: Convolutional Neural Networks are a type of neural network commonly used to identify objects in photos. This project will explore how a Convolutional Neural Net uses linear algebra to “learn” how to read handwritten numbers. Jeremy Jako Nathan Rogers Applications in genetics Abstract. Linear algebra is used to model certain genetics problems. One such problem is the issue of heritability and how genes are passed down through the three types of genes: AA, Aa, and aa. We can model these instances of inheritance using vector equations and transition matrices. Group: Belle Barnes Productivity of the 2008 Market Crash Abstract. Construct a consumption matrix in conjunction with section 2.6 of our textbook. The consumption matrix will be used to determine the productivity of the 2008 US economy. The data set is taken from the United States Bureau of Economic Analysis. The year 2008 is the year that the US market crashed and started to be rebuilt again. A consumption matrix will show if the market was profitable. This will be a beneficial examination of the market to determine patterns and the depth of the issues within the economy. Dylan Johnson Graphs and Adjacency Matrices Abstract. Graphs are an incredibly versatile structure insofar as they can model everything from the modernity of computer science and complexity of geography, to the intricacy of linguistic relationships and the universality of chemical structures. Representing such graphs as matrices only enhances the computational aspects of this modeling. Ultimately, this necessitates linear algebra. This paper will explore the relationships between graph theory, their associated matrix representations, and the matrix properties found in linear algebra. It will explore not only the adjacency matrices of graphs, but also the more interesting examples found in Laplacian matrices and distance matrices. Investigations may discuss the utility, or lack thereof, of such matrix representations for various classes of graphs, including disconnected graphs, complete graphs, and trees. Joseph Pugliano Brandon Sehestedt Cryptography: Matrices and Encryption Abstract. Study hill ciphers and how they are used to generate keys to encrypt words. The effectiveness of encryption keys will be investigated. Mark Van der Merwe Andrew Haas Image Compression Abstract. A bitmap image is compressed using singular value decomposition (SVD). Using Principal Component Analysis (PCA), we can throw out certain terms within a storage matrix, which will lower image quality but allow it to be stored for a fraction of the file size. Using compression algorithm Discrete Cosine Transform (DCT), we can separate an image into its frequencies and only keep "important" frequencies, again allowing us to shave off file size by sacrificing image quality. Julia Vonessen An investigation into the Hill Cipher Abstract. The Hill cipher uses matrices and their inverses to encrypt and decrypt messages. This project seeks to investigate Hill ciphers in three ways: (1) encrypting a message, (2) decrypting a message, and (3) breaking the cipher with a sample. Bria Linza Creating Fractals Abstract. Create fractal designs in Maple by using iterated contractions. A map is used to define the translations performing the generation of the fractal. Joe Narus Image Compression Abstract: Investigate different types of image compression and how they differ, specifically with retaining image quality. I wanted to look into the two methods suggested on the website, but I also wanted to look into more common image compression styles and saving formats, such as JPEG, and GIF.