Browsing by Subject "School of Mathematics"

Now showing 1 - 11 of 11
  • Thumbnail Image
    Item
    3D Maps of the Supernova Remnant Cassiopeia A
    (2010-04-21) Olmschenk, Greg
    We studied the supernova remnant Cassiopeia A using NASA’s Spitzer Space Telescope. A supernova remnant is the debris of a supernova – the explosive death of a star in one of the most energetic events in the universe. Studying the supernova remnant gives us insight into the exotic physics of the explosion itself as well as the physics of the material affected by the powerful shock waves. We are especially interested in particle acceleration – the acceleration of particles to near the speed of light by magnetic fields in the shock waves. One eventual goal of our work is to create 3-dimensional density and temperature maps of the supernova debris. This will allow us to compare the debris before and after encountering a shock wave and potentially detect, for the first time, the energy lost to accelerated particles at this type of shock wave.
  • Thumbnail Image
    Item
  • Thumbnail Image
    Item
    China’s Vertical Integration Backward into Iron Ore
    (2011-04-13) Xue, Lu
    The rapid growth of China is one of the big economic events of recent years. China is increasingly sucking up raw materials throughout the world to feed its continually growing manufacturing sector. I particularly focus on the iron ore industry. Steel is the most basic manufacturing industry and China’s steel companies are not only importing the iron ore, it is “vertically integrating backward” into the iron ore business by going to Australia, Brazil and other part of world where are the sources of iron ore and buying up the iron ore and taking over the mining and production of it. Firstly, I made an assumption that China is following the ‘raising rivals’ price’ theory regarding vertical integrating behavior. In order to prove my hypothesis, I studied on China’s steel price and Brazil’s iron ore price. What is more, I compared China’s steel industry with the U.S, Japan and Korea to understand the differences and why China is doing this. During my research, I found out that Japan was raising the iron ore price while China’s steel price is also high. This is showing that China is indeed trying to vertically integrate. However, Japan is somehow hindering China from doing so. I also researched on 22 Australian iron ore miners and the cooperation relationship that they built with China and Korea trying to show which one of them is integrating backward more thoroughly into iron ore business overseas. The biggest difference is that rather than simply signing long-term contract with the iron ore companies China prefers buying stock from them and unlike Korea it is building relationships with relative smaller companies.
  • Thumbnail Image
    Item
    Compressive Sampling: The Future of Efficiency and Signal Processing
    (2009-04-08) Mueller, Peter
    The majority of data stored in a computer or in a signal are place-holding zeroes. Compressive sampling enables us to reduce the memory a set amount of data takes up until we need to use it again. Additionally, the limiting factor most people are worried about is time. Compressive sampling allows the sending of signals and data with less time and effort. The process is based on probability and the principles of random number generators which is built in to most computers. This makes the process of compressive sampling widely available.
  • Thumbnail Image
    Item
    Computation of Defects in Materials
    (2011-08-11) Veit, Max
    Abstract The purpose of this project is to investigate and assess, using the MATLAB computer language, some numerical methods used in several elds of computational molecular dynamics. First a theoretical model of a one-dimensional chain of atoms was studied. The atoms in this chain would interact based on the Lennard-Jones potential energy function. Several algorithms were investigated that found con gurations of the chain where the total potential energy was lowest. Aspects of the one-dimensional chain were then carried over into a model of a two-dimensional system of atoms. For this model a full simulation of the movement of the atoms in the system was used to study the system. It was found that one of the simplest atom con gurations, a square lattice pattern, was unstable. In the simulation, this structure evolved over time into several disconnected regions, called grains," of a more stable triangular-hexagonal lat- tice pattern. These structures are similar to crystal grains in real-world polycrystalline materials. Some basic computational thermodynamics (more specically, Langevin dynamics) was also used in the simulation. It was found that by regulating the temperature, or average kinetic energy, of the system, the formation of grains could be controlled to some degree.
  • Thumbnail Image
    Item
    Embracing Revenge by Embracing Gaps
    (2011-04-13) Tourville, Nicholas
    The Liar statement, “This statement is false”, is one of the oldest unresolved paradoxes. To see why it is paradoxical, consider whether it is true or false. On the one hand, if it is true, then since it says it is false, it must be false. But surely it cannot be both true and false! So, on the other hand, maybe it is false. But then, since it simply asserts its own falsity, it must be true. It seems that we are forced into a contradiction. On first glance, this may seem like a cute puzzle or a mere oddity, but the Liar paradox indicates that there is a deep flaw in our ordinary conception of truth. I’m interested in “gappy” solutions to the paradox– solutions that hold that some statements (like the Liar) are neither true nor false. The statements falling in this gap between truth and falsity might be called pathological. Introducing this new category of statements lets us deal with the Liar statement above, but the Liar gets its revenge in a strengthened form: “This statement is false or pathological”. This strengthened Liar statement cannot consistently be considered true, false, or pathological, so it seems that we need to introduce yet another category of statements. Introducing the new category leads to another paradoxical statement, which leads to another category, which leads to another paradoxical statement, and so on. The result is a theory of truth with infinitely many categories of statements. I’m working on developing the philosophical motivations for such a theory.
  • Thumbnail Image
    Item
    Graph-based Poisson learning for image co-segmentation
    (2021) Ke, Siqi
    This paper focuses on applying the state-of-the-art graph-based semi-supervised learning algorithm Poisson Learning to the task of image co-segmentation. The weighted matrix built based on the image texture is used as the feature to do the classification by Poisson learning. The results presented in the paper show that Poisson learning does a good job in segmentation and has high accuracy at very low label rates. Moreover, Poisson learning is tolerant with multi-weight metrics and simple to implement.
  • Thumbnail Image
    Item
    Liesegang Patterns
    (2009-08-06) Park, Jun Yong
    This project was concerned with the study of Liesegang patterns in a reaction tube. Liesegang patterns are formed by a simple reaction, typically in gels, when the reaction product precipitates in a recurrent fashion. They consist of bands where the reaction product precipitated, which are spaced at distances which increase at a geometric rate. While Liesegang patterns are ubiquitous and easy to generate in experiments, there is a vast number of different model equations proposed in the literature. My goal of this project was to find a model that is different from the models proposed in the literature and that has desirable smoothness properties and models the phenomena relatively close to the real world experiment.
  • Thumbnail Image
    Item
    Money Market Funds Under the Current Financial Crisis
    (2009-04-08) Sun, Fei
    Money market funds, a special kind of mutual funds regulated by Rule 2a-7 of SEC Investment Company Act of 1940, are one of the investments with lowest risk which has been deemed and used almost equivalently as savings accounts with a bit higher return. However, money market funds are not insured by FDIC as are savings accounts. Last September, two money market funds went below $1.00 net asset value, which is also known as "broke the buck." This resulted in many law suits filed against the failed fund companies on misleading information once investors, especially many municipalities who invested tax payers' money in them, realized that they could not get back 100% of their money. I reviewed related SEC regulations and investigated into money market funds' information about their risks. After the cases of failed funds, most money funds now have clear indications on that they are different from savings accounts and are not FDIC insured. Additionally, I investigated the portfolio holdings and other financial facts of popular money market funds and collected data from both before and after September to obtain comparisons. Many funds have significantly lowered their risk level by cutting the percentage of risky investments, such as commercial paper, in their portfolio. Furthermore, most of the popular funds that are highly rated now are the huge ones with relatively low risks and low expense ratio, as opposed to the ones with high risks and high expense, since investors are very risk averse nowadays.
  • Thumbnail Image
    Item
  • Thumbnail Image
    Item
    Reading Between the Tweets: Clustering and Topic Extraction on Micro-Blogs
    (2010-04-21) Wolf, Katie
    According to Java et al., some of the main intentions of users on Twitter are daily chatting, conversations, sharing information/URLs, and reporting news. Topic extraction has been used in large documents such as online news articles, emails, scientific literature, and blogs, but little has been done with short documents like micro-blogs. Objective: Apply clustering and topic extraction techniques to micro-blogs as a first step toward tracking popular topics dynamically as they vary by time or location, or to enhance topic-related searches of tweets. The results found using a hybrid PDDP and K-Means clustering technique, typically used for categorizing large documents, have shown success when working with micro-blogs with noisy dictionaries. The methods show potential to be a basis for [semi-]supervised topic tracking and extraction using methods previously used for larger text documents.