Intellectual property has gained more attention in recent decades because innovations have become one of the most important resources. This paper implements a probabilistic topic model using nonnegative matrix factorization (NMF) to discover some of the key elements in computer patent, as the industry grew from 1990 to 2009. This paper proposes a new “shrinking model” based on NMF and also performs a close examination of some variations of the base model. Note that rather than studying the strategy to pick the optimized number of topics (“rank”), this paper is particularly interested in which factorization (including different kinds of initiation) methods are able to construct “topics” with the best quality given the predetermined rank. Performing NMF to the description text of patent features, we observe key topics emerge such as “platform” and “display” with strong presence across all years but we also see other short-lived significant topics such as “power” and “heat” which signify the saturation of the industry.

From the agent-based, correlated random walk model presented, we observe the effects of varying the parameter values of maximum insect turning area, 𝛿max, density of trees, ω, maximum pollen carryover, 𝜅max, and probability of fertilization, P𝜅, on the distribution of pollen within a population of Cornus florida (flowering dogwood). We see that varying 𝛿max and 𝜅max changes the dispersal distance of pollen, which greatly affects many measures of connectivity. The clustering coefficient of fathers is maximized when 𝛿max is between 60° and 90°. Varying ω does not have a major effect on the clustering coefficient of fathers, but it does have a greater effect on other measures of genetic diversity. Lastly, we compare our simulations with randomly-placed trees with that of actual tree placement of C. florida at the VCU Rice Center, concluding that in order to truly understand how pollen is distributed within a specific ecosystem, specificity in describing tree locations is necessary.

The generalized inviscid Proudman-Johnson equation serves as a model for n-dimensional incompressible Euler flow, gas dynamics, high-frequency waves in shallow waters, and orientation of waves in a massive director field of a nematic liquid crystal. Furthermore, the equation also serves as a tool for studying the role that the natural fluid processes of convection and stretching play in the formation of spontaneous singularities, or of their absence. In this work, we study blow-up, and blow-up properties, in solutions to the generalized, inviscid Proudman-Johnson equation endowed with periodic or Dirichlet boundary conditions. More particularly,regularity of solutions in an Lp setting will be measured via a direct approach which involves the derivation of representation formulae for solutions to the problem. For a real parameter lambda, several classes of initial data are considered. These include the class of smooth functions with either zero or nonzero mean, a family of piecewise constant functions, and a large class of initial data with a bounded derivative that is, at least, continuous almost everywhere and satisfies Holder-type estimates near particular locations in the domain. Amongst other results, our analysis will indicate that for appropriate values of the parameter, the curvature of the data in a neighborhood of these locations is responsible for an eventual breakdown of solutions, or their persistence for all time. Additionally, we will establish a nontrivial connection between the qualitative properties of L-infinity blow-up in ux, and its Lp regularity. Finally, for smooth and non-smooth initial data, a special emphasis is made on the study of regularity of stagnation point-form solutions to the two and three dimensional incompressible Euler equations subject to periodic or Dirichlet boundary conditions.

Existing multi-echelon inventory optimization models and formulas were studied to get an understanding of how safety stock levels are determined. Because of the restrictive distribution assumptions of the existing safety stock formula, which are not necessarily realistic in practice, a method to analyze the performance of this formula in a more realistic setting was desired. A SimPy simulation model was designed and implemented for a simple two-stage supply chain as a way to test the performance of the safety stock formula. This implementation produced results which led to the conclusion that the safety stock formula tends to underestimate the level of safety stock needed to provide a certain service level when predicted standard deviation of demand is underestimated and the assumptions of normally distributed demand and normally distributed lead times are not fulfilled.

The structure of a protein molecule is highly correlated to its function. Some diseases such as cystic fibrosis are the result of a change in the structure of a protein so that this change interferes or inhibits its function. Often these changes in structure are caused by a misfolding of the protein molecule. To assist computational biologists, there is a database of proteins together with their misfolded versions, called decoys, that can be used to test the accuracy of protein structure prediction algorithms. In our work we use a nested graph model to quantify a selected set of proteins that have two single misfold decoys. The graph theoretic model used is a three tiered nested graph. Measures based on the vertex weights are calculated and we compare the quantification of the proteins with their decoys. Our method is able to separate the misfolded proteins from the correctly folded proteins.

Companies continually seek to improve their business model through feedback and customer satisfaction surveys. Social media provides additional opportunities for this advanced exploration into the mind of the customer. By extracting customer feedback from social media platforms, companies may increase the sample size of their feedback and remove bias often found in questionnaires, resulting in better informed decision making. However, simply using personnel to analyze the thousands of relative social media content is financially expensive and time consuming. Thus, our study aims to establish a method to extract business intelligence from social media content by structuralizing opinionated textual data using text mining and classifying these reviews by the degree of customer satisfaction. By quantifying textual reviews, companies may perform statistical analysis to extract insight from the data as well as effectively address concerns. Specifically, we analyzed a subset of 56,000 Yelp reviews on fast food restaurants and attempt to predict a quantitative value reflecting the overall opinion of each review. We compare the use of two different predictive modeling techniques, bagged Decision Trees and Random Forest Classifiers. In order to simplify the problem, we train our model to accurately classify strongly negative and strongly positive reviews (1 and 5 stars) reviews. In addition, we identify drivers behind strongly positive or negative reviews allowing businesses to understand their strengths and weaknesses. This method provides companies an efficient and cost-effective method to process and understand customer satisfaction as it is discussed on social media.

The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate the likelihood of type I error and type II error by changing the values of parameters. In the first chapter, we discuss the motivation behind the work presented in this thesis. Also, we introduce the definitions used throughout the paper. In the second chapter, we derive test statistics for the likelihood ratio test and the score test for the geometric distribution. For the score test, we consider the score test using both the observed information matrix and the expected information matrix, and obtain the score test statistic zO and zI . Chapter 3 discusses the likelihood ratio test and the score test for the inflated binomial distribution. The main parameter of interest is w, so p is a nuisance parameter in this case. We derive the likelihood ratio test statistics and the score test statistics to test w. In both tests, the nuisance parameter p is estimated using maximum likelihood estimator pˆ. We also consider the score test using both the observed and the expected information matrices. Chapter 4 focuses on the score test in the inflated binomial distribution. We generate data to follow the zero inflated binomial distribution by using the package R. We plot the graph of the ratio of the two score test statistics for the sample data, zI /zO , in terms of different values of n0, the number of zero values in the sample. In chapter 5, we discuss and compare the use of the score test using two types of information matrices. We perform a simulation study to estimate the two types of errors when applying the test to the geometric distribution and the inflated binomial distribution. We plot the percentage of the two errors by fixing different parameters, such as the probability p and the number of trials m. Finally, we conclude by briefly summarizing the results in chapter 6.

Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion (AIM) model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior: the most noteworthy being the fingering of hopper bands. A Particle-in-Cell method is used to optimize simulations, allowing for trials of up to 106 particles over reasonable timescales. We analyze the shapes of these swarms, note the similarities between simulations of large and small swarms, and propose possible methods for analyzing simulation metrics.

Post-Earnings-Announcement Drift (PEAD) is commonly accepted in the fields of accounting and finance as evidence for stock market inefficiency. Less accepted are the numerous explanations for this anomaly. This project aims to investigate the cause for PEAD by harnessing the power of machine learning algorithms such as Principle Component Analysis (PCA) and a rule-based learning technique, applied to large stock market data sets. Based on the notion that the market is consumer driven, repeated occurrences of irrational behavior exhibited by traders in response to news events such as earnings reports are uncovered. The project produces findings in support of the PEAD anomaly using non-accounting nor financial methods. In particular, this project finds evidence for delayed price response exhibited in trader behavior, a common manifestation of the PEAD phenomenon.

Processing user requests quickly requires not only fast servers, but also demands methods to quickly locate idle servers to process those requests. Methods of finding idle servers are analogous to open addressing in hash tables, but with the key difference that servers may return to an idle state after having been busy rather than staying busy. Probing sequences for open addressing are well-studied, but algorithms for locating idle servers are less understood. We investigate sequential probing with a random start as a method for finding idle servers, especially in cases of heavy traffic. We present a procedure for finding the distribution of the number of probes required for finding an idle server by using a Markov chain and ideas from enumerative combinatorics, then present numerical simulation results in lieu of a general analytic solution.