Chase Hodges-Heilmann Title: None Abstract: None ============= email: RECEIVED ============= Group: Soren Nelson Title: Spotify's Machine Learning Models Abstract: If you wanted to get a leg up on your competition in the business world fifteen years ago, you would turn your business digital. Today, if you want to get a leg up on your competition, you use Artificial Intelligence to reduce the amount of friction between what your customers want/need and what you are giving them. One such company who has taken the leap to integrate machine learning, a subset of AI, to individualize their customer's experience is Spotify. There is a reason that Spotify is still around after three of the biggest companies in the world: Apple, Google, and Amazon; have all stepped into the music streaming industry. They are able to recommend better music to me than any of the other three. At first I thought I was biased in believing this, as I am a loyal Spotify user. However, in doing research, I have come to find that Spotify does in fact have a much better system than the other three. They use three styles of models to recommend music. First, they use what they call Collaboration Models. These compare your music against other users music. The next style is Natural Language Processing models. These models compare songs based on words used to describe the songs via articles on the web. The last, and my personal favorite, is used to recommend songs that are not as popular. This style looks at the actual music and uses similarities to recommend similar songs to you. Throughout this paper I will discuss how each of these models works and why Spotify's approach is the best in the industry. ============= email: RECEIVED ============= Group: Grant Keller and Kearsa Hodgson Title: cryptographic hashing and application to blockchain structures Abstract: Display step by step how the hash method works. ============= email: Missing Hodgson email ============= Group: Spencer Fajarado Title: Linear Algebra and some applications to cryptography: Hill cypher Abstract: Show how letters in the alphabet can be given numerical values, and using this, we will use matrices to create a hill-cypher to encript plaintext. In addition, we shall look at some of the applications of linear algebra to the WWII enigma machine. ============= email: RECEIVED ============= Group: Erik Martinez and Tim VanAusdal Title: Balancing vector diagrams using angle computations [changed in March 2018] Abstract: None ============= email: Missing Martinez ============= Group: Sean Johnson Title: linear transformations between reference frames in special relativity Abstract: Examples of how orientation of objects change with different motions and how time is warped linearly. ============= email: u0940249@utah.edu ============= Group: Jake Durham Title: 2D image manipulation in games using matrices Abstract: None ============= email: RECEIVED ============= Group: Tristan Bowler Abstract: The use of linear transformations such as dilation, contraction, rotation, reflection, shear, and projection in the creation and variance of videogame graphics. The ability to transform and duplicate game objects is an important part of creating a realistic game universe and the tools of linear algebra and linear transformations are a convenient tool for game designers and animators to accomplish this. ============= email: RECEIVED ============= Group: Inchul Pak Title: computer graphics Abstract: animation of a polygonal figure in computer graphics ============= email: RECEIVED ============= Group: Colin McNabb Title: reaction pathways using linear equations Abstract: None ============= email: RECEIVED ============= Group: Chase Stolworthy Title: Genetic Drift Modeled by a Markov Chain Abstract: Genetic drift is an evolutionary process responsible for the of organisms. The Wright-Fisher model of genetic drift can be modeled as a discrete-time Markov chain. My project will explore how this model works, use topics of linear algebra to show interesting properties of the model, and run computer simulations of the Markov chain on hypothetical populations with varying allele frequency distributions. ============= email: RECEIVED ============= Group: Stephanie Orgill Title: Image Translations, Rotations, and Scaling Abstract: Using maple, show how images can be displayed and manipulated by giving examples of images that are moved, rotated, and scaled after the appropriate matrices are applied to the image. ============= email: RECEIVED ============= Group: Colton Watson Title: Translations, Scaling, Rotations Abstract: Apply linear algebra to computer graphics by taking an image, scaling that image by an arbitrary amount, rotating it by an arbitrary angle, and placing that image at a different location on the screen. ============= email: RECEIVED ============= Group: Montana Throne Title: Fractal Computer Creations Abstract: Fractals are infinite patterns that look similar at all levels of magnification and exist between the normal dimensions. With the advent of the computer, we can generate these complex structures to model natural structures around us such as blood vessels, heartbeat rhythms, trees, forests, and mountains, to name a few. I will begin by explaining how different linear transformations have been used to create fractals. Then I will explain how I have created fractals using linear transformations and include the computer-generated results. ============= email: RECEIVED ============= Group: August Masquelier and Rachel Brough Title: Comparing Lossy and Lossless Image Processing Techniques Using Linear Algebraic Methods Abstract: Commonly image processing is categorized into two distinct categories based on the "quality" of the end result. Lossless refers to images that when processed, have a result exactly the same in terms of quality to the original. On the other hand, lossy image processing refers to methods that output a result that is of different quality to the original, usually lower. In general, images are simply matrices of color information about each pixel. Because there are somewhere around 16.8 million different colors it can become quite complicated to represent them all in a single image and usually end up reserving large amounts of storage. As a result, computer scientists have developed methods, utilizing linear algebra and the idea of a matrix, to compress these images so that they take up less storage space. Both lossy and lossless methods, as discussed above, can be achieved using a process called SVD or singular value decomposition. The difference between the two is determined by the number of terms that the matrix color representation is reduced to utilizing the SVD process. In short, representing a large color range requires precise values, specifically 8-bits or 1-byte, for each color value RGB from 0-255. If we reduce the number of values that we are able to represent, we can significantly reduce the size of the file at the cost of some quality, which in the eyes of a computer scientist is a worthwhile trade. Our project will discuss the various methods of SVD image compression and possibly a few other methods on different file formats in an attempt to find the proper number of terms such that we reduce the file size but do not see too significant a drop in quality. ============= email: RECEIVED both ============= Group: Scott Hoge and Ricardo Sonsini Title: image compression Abstract: None ============= email: Sonsini not recieved ============= Group: Derek Miles Title: ecosystem represented as a flow network Abstract: None ============= email: RECEIVED ============= Group: Tyler Kroll Title: Using Linear Algebra to Rank the Men's Short Track Speedskating World Cup Relay Teams in the 2017-2018 Season Abstract: The goal of this paper will be to create a novel ranking of the men's short track speedskating World Cup relay teams based on the first four World Cups of the 2017-2018 season. Crucially, these are the four world-level competitions preceding the Olympic Games, and thus rank is vital for team goal-setting, seeding for future competitions, and predicting future outcomes, etc. Statistics to be factored into the ranking include placement in the A and B finals at each World Cup, strength of the relay team based on the aggregated ranks of each of its four members, difficulty of quarterfinal and semifinal placement (placement in a specific heat is randomly generated), margin of win/loss in terms of time, number of falls in a race, average speed of the race, top speed of the race, and number of passes made in a race, among others. Possible techniques include, but are certainly not limited to: the use of adjacency matrices, eigenvectors and eigenvalues, and the Perron-Frobenius theorem. Finally, a comparison between the resultant novel ranking and currently used World Cup ranking is of interest to this author, though the actual utility of such a comparison is unclear. ============= email: RECEIVED ============= Group: Will Stout and Tyler Hoskins Title: computer data structures and linear algebra. Abstract: None ============= email: RECEIVED both ============= Group: Peter Nelson Title: Applications of Linear Algebra in Genetics Abstract: how techniques of Linear Algebra can be used to predict heritability of some genetic trait(s). ============= email: RECEIVED ============= Group: Hayden Derk Strikwerda Title: Linear Regression Abstract: Why is it needed in this case? When dealing with defects in a business it is easy to quantify what percentage of your product is defective, it is not as easy to pinpoint where those defects come from. When various inputs are required to make a certain output it is harder to quantify how dependent a product is from one input. This is where simple linear regression plays a role in helping continuous improvement specialists eliminate defects in various products. How does it work? Simple Linear Regression works by plotting the data in a scatterplot and then running the linear regression line through the data points. Y = a + bX + e is the equation that is used in graphing the line. Y is the value of the output. A is the estimated Y intercept. b is the correlation from -1 to 1 which signifies the relationship form input to output. e is an error term representing the unexplained or residual variance. How does it relate to Linear Algebra When computing this line we use the least squares method. When using the least squares method there are techniques in linear algebra to find a, b, x, and e. What we are going to do? We will use these techniques to see if we can find causal relationships not just correlations in the defects we are seeing in our service. ============= email: RECEIVED ============= Group: Andre Watson Title: image compression Abstract: None ============= email: RECEIVED ============= Group: Valerie German Title: Linear Algebra in Error-Correcting Code Abstract: When sending information over a communication channel, some of the bits may become corrupted. Error-correcting code helps detect when these errors occur. Common types of error-correcting codes are repetition codes, hamming codes, Reed-Muller codes and low-density parity check codes, which use matrix algebra to find errors in transmitted code. I will examine the different ways linear algebra is applied in error detection and correction methods. ============= email: RECEIVED ============= Group: Sean Johnson Title: linear transformations between frames of reference Abstract: None ============= email: RECEIVED ============= Group: Corrin Krogh Title: Nutrition and Diet Abstract: Analysis of nutrition and ways to complete a well rounded diet from a list of food data. Collect nutritional information from common foods and putting them in an excel chart. Then I plan on finding things like what combinations that equal a standard healthy diet (will be defined) are the lowest cost, most nutrient dense. Topic Nutrition/ the Diet Problem Summary For my Semester Project, I plan on working on an analysis of nutrition and ways to complete a well-rounded diet from a list of food data. I plan on collecting nutritional information from common foods and putting them in an excel chart. This is a great example of using optimization and linear algebra. I plan on finding things like what combinations that equal a standard healthy diet (will be defined) are the lowest cost, most nutrient dense, etc. This of course will be done using linear algebra. Specifics: Food Groups Protein, Fruit, Grains, Vegetables For this analysis, we are excluding dairy 1500 Kcal diet. Protein = 4 Kcal per gram 150 grams Carbohydrates = 4 Kcal per gram 149 grams Fats = 9 Kcal per gram 34 grams Will need to specify a limit of portions per day when itemizing food products Narrowed down to following food list: Fruits: Orange, Strawberry, Raspberry, banana Vegetables: Spinach, Celery, Cauliflower, Broccoli, Tomato Meat: Salmon, Chicken, Ground Beef 96/4, Tilapia Grains: Oats, Jasmine Rice, Brown Rice, Quinoa ============= email: RECEIVED ============= Group: Anthony Calacino and Monica Moynihan Title: Applications of Linear Algebra in Political Science: Candidate Preferences in Elections Abstract: In democratic states with liberal elections, voters almost always have multiple candidates to choose from. These candidates typically represent different political parties, ideologies, or voting pacts. Voters have transitive preferences for these multiple candidates. Due to a variety of factors, an individual's most preferred candidate may not be elected. Electoral rules are often responsible for diverging voting preferences from actual votes cast. Individuals often know that their vote actually counting is contingent on how others vote and electoral rules. As a result, individuals anticipate such electoral rules and potential for certain candidates and adjust their actual vote (which may depart from the individual's true preference). Linear algebra has been applied to the problem of voting preferences in the past to determine ways that a voter (or group of voters) can change their behavior to elect certain preferred candidates. This project will investigate and report on the mathematics used to analyze the preferences of voters for candidates in elections. ============= email: RECEIVED both ============= Group: Mitch Mcaffee Title: Abstract: None ============= email: RECEIVED ============= Group: Nathan Taylor Title: Linear Algebra in the Google Page Rank Algorithm Abstract: To prioritize and provide information concerning the relevance of any given web page, Google calculates a value called a Page Rank for each web page in its network. The algorithm to calculate the Page rank is based off of a stochastic matrix and eigenvectors. This project will explore the principles behind the Google Page Rank and the use of linear algebra in performing its calculations. ============= email: RECEIVED ============= Group: Ariel Baughman Title: Electrical Circuits Abstract: I will use the applications of linear algebra to find the current and voltage along with the relationship in complex electrical circuits. By using Ohm's law and Kirchoff's Law, a matrix can be created to find voltage and currents. Linear Algebra can be a useful tool in simplifying several Physics equations into one simple matrix, showing the input currents and final voltages. ============= email: RECEIVED