• Jill Ellern, Finding the Good Stuff: Looking at the New Databases Now Available to You (IEEE Explore, ACM's Digital Library, and More...)
• Abstract: Jill Ellern will show off the new databases Hunter has added that are especially helpful for Math and CS. She wants to get some input on the reference web pages she has put up for CS and talk about what she would like to do for Math.  
  

•  Edward E Johnson, Math and Art, Some Common Questions 
  
• Abstract: There is an almost universal belief among those outside of mathematics that math is not a creative endeavor. Mathematicians, of course, know this to be patently false. This misconception may be primarily due to the unfamiliarity of the general public with not only the content but the processes of higher mathematics. For even those who attend college or graduate school, their terminal mathematics course is still quite fundamental and even mechanical in its approach. They never see the elegance of higher mathematics. This presentation attempts to dispel this notion with an example of the parallels between two disparate fields. In the arts we will examine the evolution of painting since the Renaissance and in mathematics the development of metric spaces and their kin. In these seemingly unrelated areas we will see that the “artists” have been asking the same questions of their medium. The general audience will be provided with a glimpse of the creative processes of higher mathematics while the mathematicians will be provided with a ready example that dispels this tired math myth.

• Greg Boudreaux, Which Came First – The Derivative or the Derivation?

• Abstract: A derivation on a ring R may be defined as an additive group homomorphism D such that D(rs) = rD(s) + D(r)s for all r,s in R (called the Leibniz rule). This concept, a generalization of the derivative from calculus, was devised in the 19^th Century and used successfully to prove that the indefinite integral of some functions cannot be expressed in terms of elementary functions. However, a little known Dutch mathematician by the name of Johann Hudde (1628-1704), devised a rule named after him, which can be viewed as a part-time derivation. Amazingly, he used it to drastically simplify Descartes’ method of finding tangents to algebraic functions, which, in turn, inspired Isaac Newton to develop the derivative. This talk will focus on Hudde’s Rule, its connection to derivations, and its classical use in computing tangents.

• <>Abstract: The Unification of Italy was proclaimed in 1861. This event marked a key turning point not only in the country's political life, but also in the development of mathematical studies and research. This talk will discuss the revival and renewal of Italian mathematics in the years following the Unification and will show that, parallel to a political unification, a mathematical unification also took place in Italy in the second half of the nineteenth century. In particular, in an institutional, historical, political, and mathematical context, this talk will focus on algebraic developments: by tracing the contributions of Italian mathematicians throughout the peninsula, it will show that, contrary to conventional wisdom, Italy supported a wide range of algebraic research.

• <>Abstract: We will discuss several matrix subgroups of the real general linear group GL(n), the set of all n by n matrices with real entries and nonzero determinants.  Of particular interest are some subgroups formed by partitioning the matrices.  These subgroups describe symmetries of real finite-dimensional vector spaces. As an application, we use these groups to generate conservation laws in the physics of particles and fields, such as the simultaneous conservation of linear and angular momentum in the free rigid body, or the Poincare symmetries of the four-dimensional spacetime of special relativity.
  

• Joe Rusinko, Tropical Geometry

• Adam Spiegler, The Motion of a Free Rigid Body
  

• Axelle Faughn, High School Trigonometry: The Beginning of a Transition

• Mark Sherriff, Analyzing Software Artifacts to Guide Development Decisions
  
  Abstract: During development, programming teams will produce numerous different types of software development artifacts. A software development artifact is an intermediate or final product that is the result or by-product of software development and can include anything from source code to change records in a source control system to defect records.  Sets of software development artifacts can help identify relationships between files that might not normally be apparent.  For example, source control records can be used to find out what files tend to change together.  This could be an indication that the files are functionally linked.
  
  The goal of this research is to build and investigate a methodology that uses software development artifacts to illuminate underlying relationships within a system and to use that information to drive development decisions.  For instance, information regarding how files tend to change together can improve impact analysis and regression test selection since there is empirical evidence as to how a change impacted these files in the past.  Software development artifacts can be gathered from tools within the development process, such as change management systems, source control systems, and defect tracking systems.  The associations between files are then highlighted using singular value decomposition.
  
  We performed a study on impact analysis and regression test seleciton based upon our technique with several releases of a software system from IBM.  Our results indicate that using software development artifacts can be a viable means to help drive development decisions.
  

• James Early, Association Rule Mining for Anomaly Detection
• Abstract: This presentation focuses on the systematic derivation of models used to identify attack behaviors. The technical challenge is to create models that can accurately differentiate normal from malicious events while keeping pace with the event stream. We will present our association rule mining techniques that produce compact, effective models. We will then demonstrate their utility in the network intrusion detection and database security domains.
  

• Yong Wei, Multimedia Personalization and Delivery System for Mobile Clients in Resource-Constrained Environment

• Abstract : The current proliferation of mobile computing devices and network technologies has created enormous opportunities for mobile device users to communicate with multimedia servers and with one another. One of the natural limitations of handheld computing devices is that they are constrained by their resources, such as battery power capacity, viewing time limit, amount of data received, and in many situations, by available network bandwidth connecting these devices with multimedia servers. Thus, the original videos often need to be personalized or adapted in order to fulfill the client’s request while simultaneously satisfying various client-side system-level constraints. We develop a mobile client-centered multimedia adaptation and delivery system which can optimally fulfill the client requests while simultaneously ensuring optimal utilization of the server-side and client-side system-level resources.

  <>

  The client-centered multimedia adaptation and delivery system consists of the following five subsystems: (1) the video preprocessing subsystem, (2) the multiple-level video summarization and hierarchical content representation subsystem, (3) the video personalization subsystem, (4) the multiple client request aggregation subsystem and (5) the client-side energy-aware multimedia streaming subsystem.

  The video preprocessing subsystem performs temporal video segmentation and indexing in the temporal domain. A data-driven stochastic modeling approach is proposed to perform both video segmentation and video indexing in a single pass automatically.  Indexed video segments are then fed to the multiple level video summarization and hierarchical content representation subsystem to build a visual content database. Each indexed video segment is summarized at multiple levels of abstraction. Content-aware key frame selection algorithm and motion panorama computation are used to generate video summaries for each indexed video segment. In the video personalization subsystem, the client video content preference is matched with the video summaries stored in the visual content database. In order to generate the personalized video summary, the client usage environment and the client-side system-level constraints are evaluated. The personalization engine selects the optimal subset of video contents that are most relevant to the clients’ preference(s) subject to the constraints imposed by the client. In order to utilize the server-end resources efficiently, a multiple-stage client request aggregation strategy is designed and implemented to aggregate similar client requests together such that the number of requests the multimedia server needs to process is reduced. The client-side statistical prediction-based multimedia streaming strategy reduces the wireless network interface card (WNIC) energy consumption to receive multimedia streams by judiciously transitioning the WNIC to a lower power consuming sleep state during the no-data intervals in the multimedia stream, without explicit support from the multimedia servers themselves.

• Jung-ha An, Variational Partial Differential   Equation (PDE) Models with an Application to Medical  Imaging

• Qiquing  Yu, A Survey of Statistics Used in Biology, Engineering and Economics

• Risto Atanasov, Introduction to 2 dimensional topology

  • Abstract: I will discuss simplicial complexes and their use in the proof of the Brouwer fixed point theorem. I will also talk about the idea of the Poincaré duality theorem.
• Sonal Dekhane, A Formal Specification and Analysis Framework for Object-Oriented Designs

May:  

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Last Modified: 23 August 2006