Digital Commons Network^™

The Planar Rook Monoid, Kathryn E. Herbig

Mathematics, Statistics, and Computer Science Honors Projects

Pascal's triangle is a very important structure in combinatorics: its entries, the binomial coefficients, answer a number of counting-related questions. I will define a set of functions, the Planar Rook monoid, whose structure is tied to Pascal's Triangle. Most of the connections between the monoid and Pascal's triangle are seen when we allow the functions to work as linear transformations on different vector spaces; I will show several examples which lead to algebraic proofs of famous binomial identities. These proofs give insight into the deep connection between the monoid and Pascal's Triangle.

Sound Source Localization And Separation, Biniyam Tesfaye Taddese

Mathematics, Statistics, and Computer Science Honors Projects

People face the problem of sound source localization and separation in situations where they attempt to localize and focus on a source of sound among a dissonance of conversations and background noise. This paper synthesizes a sound source localization routine. We utilize a general source separation technique, Independent Component Analysis.. Particularly, basic ICA was applied to separate mixtures of low frequency, narrow band, non-Gaussian signals by using closely spaced uni-directional microphones. The localization routine worked with an average condition number of 10. The routine was tested on data collected in a laboratory.

Probabilistic Robot Localization Using Visual Landmarks, Peter E. Anderson-Sprecher

Mathematics, Statistics, and Computer Science Honors Projects

Effective robot navigation and route planning is impossible unless the position of the robot within its environment is known. Motion sensors that track the relative movement of a robot are inherently unreliable, so it is necessary to use cues from the external environment to periodically localize the robot. There are many methods for accomplishing this, most of which either probabilistically estimate the robot's movement based on range sensors, or require having enough unique visual landmarks present to geometrically calculate the robot's position at any time.

In this project I examined the feasibility of using the probabilistic Monte Carlo localization algorithm …

Analysis Of Defenses Against Distributed Denial Of Service Attacks, D. Eric Chan-Tin

Mathematics, Statistics, and Computer Science Honors Projects

Distributed Denial of Service (DDoS) attacks are attempts to overwhelm a computer system in order to deny access by legitimate users. They are generally unstoppable, but there is a good deal of on-going research on methods to reduce their negative effects. This paper will deal with the design of a model that simulates such an attack. The simulation model is then used to study possible ways to defend against these attacks. Three experiments are run: 1) using a priority queue to sort messages from clients based on how many connections they have open on the server; 2) limiting the number …

A Model Representation For The Symmetric Group And The Partition Algebra, Michael D. Decker

Mathematics, Statistics, and Computer Science Honors Projects

Combinatorics is the art of counting, how many such objects are there. Algebra deals with how objects can interact. Representation theory sits between the two. In particular, it uses combinatorial techniques to prove algebraic questions. Herein I use it to derive information about the symmetric group, S_n, by proving a combinatorial identity. In mathematics though, we always seek the strongest possible theorem, the broadest result. Thus it is natural to consider here not only S_n, but also several other related diagram algebras. The conjecture and part, but not all, of the proof will generalize.

After introducing the necessary definitions, background, …