[Specific room for each seminar is indicated]
Fiber products and exceptional sets
VaR optimal portfolios a global optimization approach
Abstract: Value at Risk is defined as the maximum loss of a portfolio given a future time horizon within high confidence (or probability, typical values used are 95% or 99%). In our work we devise novel techniques to minimize the non-convex Value-at-Risk function. VaR has the following properties:
1. VaR is a non-coherent measure of risk; in particular, it is not sub-additive.
2. VaR also happens to be a non-convex (multiple local solutions).
3. VaR is a piece-wise non-linear function and thus a non-differentiable function of the independent variables, which are the weights of different securities in a portfolio.
4. The number of linear pieces is proportional to number of scenarios.
The above properties make search for a global minimum of VaR a very diffcult problem, in fact an NP-hard problem. We outline efficient algorithms for this hard problems using continuation methods for global minimum search. The results show that optimal VaR is within 1% of global minimum if found and as efficient as finding a solution to a convex conditional-VaR minimization problem.
Control theory: Real world application
Abstract: This presentation will discuss the application of control theory to various mechanical systems that Dr. Lew has developed/led under government and industry R&D programs. He intends to share his experience and view on how mathematics plays an important role in the area of control engineering. His topics and examples will include (1) Structural vibration control of the long-reach robotic arm for nuclear waste underground storage tanks; (2) Sea basing: Ship-to-ship cargo/vehicles transfer under relative motion; (3) Vehicle stability control - HUMVEE rollover mitigation; and (4) Electro-hydraulic actuator control system.
A compact high power singlemode microstructured fiber laser
Abstract: We will discuss the design and fabrication of a compact, high power, singlemode, microstructured (photonic crystal) fiber laser. A low index core (antiguiding) assisted by the geometry of the microstructure is used to maximize the core size while maintaining the number of propagating modes. Beam quality factor (M2) is studied for these fibers and is successfully used as a design tool. Some design concepts for scaling up the power using single-supermode multicore microstructure fibers will also be discussed.
Data fusion in a UAV surveillance system
Abstract: This talk will be about a recent Lockheed Martin project, the implementation of data fusion methods for Maritime Surveillance Applications. In this context data fusion is the problem of sequentially estimating the state of a dynamic system - ships at sea - given a sequence of noisy and incomplete measurements from the sensor suite on maritime surveillance applications: radar, an Electro-Optical/Infrared (EO/IR) camera, and an Automatic Identification System (AIS) receiver.
We will present the basic algorithms used in this project, and will then discuss their limitations and possible improvements.
Optical synthetic aperture imaging
Abstract: The spatial resolution of a conventional imaging ladar system is constrained by the diffraction limit of the telescope's aperture. At Lockheed Martin Coherent Technologies (LMCT) we are implementing techniques known as synthetic-aperture imaging laser radar (SAIL), which employs aperture synthesis with coherent laser radar to overcome the diffraction limit and achieve fine-resolution, long-range, two-dimensional imaging with modest aperture diameters. I will discuss the results of my experiments while at The Aerospace Corporation which represent the first optical synthetic aperture images of a fixed, diffusely scattering target with moving aperture, as well as the current research program being developed at LMCT.
Downhole analysis of hydrocarbons
Abstract: Quick and accurate estimation of the composition of the hydrocarbon fluid in the formation is essential in assessing an oil reservoir value and determining optimal production strategies. This task is complicated by contamination from oil- and synthetic-based drilling mud filtrates. In this talk we will describe the visible - near-infrared spectroscopy technique to estimate the composition of formation fluid and level of contamination from the downhole optical absorption spectroscopy measurements.
Tensor decompositions, the MATLAB tensor toolbox, and applications to data analysis Slides
Abstract: Tensors (also known as multidimensional arrays or N-way arrays) provide powerful tools for data representation and analysis. Consequently, they have been used in a variety of sciences ranging from chemometrics to psychometrics and most recently to data mining. In this talk, I'll provide a brief tutorial on tensors and their decompositions, assuming only a background in linear algebra. I will then describe the MATLAB Tensor Toolbox for working with dense, sparse, and structured tensors. I'll conclude with examples from several data mining contexts including web mining and cross-language information retrieval. This is joint work with Brett Bader, Sandia National Labs.
Pattern discovery in bioinformatics Slides
Abstract: In this talk we look at the combinatorics and statistics of patterns that computational biologists discover at different levels in biological data be it nucleic acid sequence, microarray data or other formal structures. Is there a commonality that runs across these various domains? Can we apply the lessons learned in one domain in another? In this talk we focus on an interesting class of patterns called permutation patterns. We apply these mathematical structures to some problems arising naturally in the area of computational biology such as the problem of common gene clusters across species, phylogeny within populations, and the task of modeling complex control of transcriptions via motifs. In each of these cases we identify the underlying mathematical problems and show some promising results of applying the proposed solutions to biological data. We also discuss the problem of formulating and computing the statistical significance of the permutations motifs in the different domains.