Fundamental Reflection Domains for Hyperbolic Tesselations

This paper summarizes Vinberg\u27s algorithm for finding the subgroup generated by reflections of the group of integral matrices that preserve particular quadratic forms of signature (n,1). Also, many fundamental reflection domains of different hyperboloids, found by the author using Vinberg\u27s algorithm, are listed in this paper. Plus, Matlab code, written by the author, is included, which serves to help one discover potential perpendicular vectors to the hyperplanes (mirrors) that enclose the fundamental domain.

Selecting a Small Set of Optimal Gestures from an Extensive Lexicon

Finding the best set of gestures to use for a given computer recognition problem is an essential part of optimizing the recognition performance while being mindful to those who may articulate the gestures. An objective function, called the ellipsoidal distance ratio metric (EDRM), for determining the best gestures from a larger lexicon library is presented, along with a numerical method for incorporating subjective preferences. In particular, we demonstrate an efficient algorithm that chooses the best $n$ gestures from a lexicon of $m$ gestures where typically $n \ll m$ using a weighting of both subjective and objective measures.Comment: 27 pages, 7 figure

Simulation of Optical Fiber Amplifier Gain Using Equivalent Short Fibers

Electromagnetic wave propagation in optical fiber amplifiers obeys Maxwell equations. Using coupled mode theory, the full Maxwell system within an optical fiber amplifier is reduced to a simpler model. The simpler model is made more efficient through a new scale model, referred to as an equivalent short fiber, which captures some of the essential characteristics of a longer fiber. The equivalent short fiber can be viewed as a fiber made using artificial (unphysical) material properties that in some sense compensates for its reduced length. The computations can be accelerated by a factor approximately equal to the ratio of the original length to the reduced length of the equivalent fiber. Computations using models of two commercially available fibers -- one doped with ytterbium, and the other with thulium -- show the practical utility of the concept. Extensive numerical studies are conducted to assess when the equivalent short fiber model is useful and when it is not

Sensitivity of Confinement Losses in Optical Fibers to Modeling Approach

A prime objective of modeling optical fibers is capturing mode confinement losses correctly. This paper demonstrates that specific modeling choices, especially regarding the outer fiber cladding regions and the placement of the computational boundary, have significant impacts on the calculated mode losses. Our results illustrate that one can obtain disparate mode confinement loss profiles for the same optical fiber design simply by moving the boundary to a new material region. We conclude with new recommendations for how to better model these losses

Robust Real-Time Image Processing Through Dynamic Mode Decomposition

Thesis (Ph.D.)--University of Washington, 2013In many areas of research, robust and efficient data-mining, and data-driven modeling, have become essential to progressing our understanding of increasingly complex and nonlinear relations often embedded in cluttered and/or corrupted data. Applications in the industry and technology sectors are demanding high-performance algorithms that can tease out important information in real-time, and help humans interact better with computers. Researchers are starting to explore sparse modeling techniques that can sample sparsely and project onto a low-dimensional bases, where the essential information that drives the system can be extracted without having to build and run costly models of the full dynamics of the entire system. The focus of this work will be on the development of data analysis techniques that can be applied to solving the gesture recognition problem, with the goal of improving performance. One of the most exciting results of the research presented here is found in the use of dynamic mode decomposition (DMD) as a viable and effective method for subtracting out the backgrounds for moving objects in videos. The method will be introduced and compared against the current standard method in the background subtraction field, namely robust principal component analysis (RPCA). The computational speed and accuracy of the DMD separation method offers a comfortable margin for real-time, online data processing. The fact that DMD approximates RPCA's low-rank/sparse separation of data matrices opens the possibilities of various applications in the time-scale separation of dynamics arena, and even in the data compression and sparse sensing fields. It will be shown that through enhanced pre-processing techniques, robust, accurate, and real-time gesture recognition can be achieved, even on heavily down-sampled images where gestures are nearly indistinguishable to the human eye. This is compared to the current trend in the computer vision field that advocates more complicated and computationally expensive feature selection and statistical learning routines that become problem specific and often still suffer from gesture irregularity in the data. Gesture recognition can be further improved by selecting the most appropriate gestures for the given task, accounting for ergonomic, vernacular, and algorithmic considerations. A new method, which combines these subjective and objective constraints into a single measure that indicates which gestures are best for the given application, is developed and tested on a real hand gesture recognition problem. Insights from the way that gestures render themselves in feature space help guarantee that this best lexicon methodology will be useful and reliable for realistic recognition problems. In the appendix of this work, the theoretical background and practical implementation techniques needed in order to model a high-power Raman fiber laser/amplifier system that includes stimulated Brillouin scattering (SBS) and four-wave mixing (FWM) effects will be delineated, and the strengths and weaknesses of the computer model will be discussed