Browsing by Subject "Frames"
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Item Causal equivalence of frames(Texas A&M University, 2006-10-30) Henderson, Troy Lee, IVFrames have recently become popular in the area of applied mathematics known as digital signal processing. Frames offer a level of redundancy that bases do not provide. In a sub-area of signal processing known as data recovery, redundancy has become increasingly useful; therefore, so have frames. Just as orthonormal bases are desirable for numerical computations, Parseval frames provide similar properties as orthonormal bases while maintaining a desired level of redundancy. This dissertation will begin with a basic background on frames and will proceed to encapsulate my research as partial fulfillment of the requirements for the Ph.D. degree in Mathematics at Texas A&M University. More specifically, in this dissertation we investigate an apparently new concept we term causal equivalence of frames and techniques for transforming frames into Parseval frames in a way that generalizes the Classical Gram- Schmidt process for bases. Finally, we will compare and contrast these techniques.Item Climate change framing in the New York Times : the media’s impact on a polarized public(2015-12) Goff, Paepin D.; Jensen, Robert, 1958-; Wilson, KristopherWhile the threat of climate change grows stronger along with the consensus of scientists about the certainty of anthropogenic causes, researchers observe an opposite effect in the public’s acceptance of climate science. While climate change is a salient topic in society, the media’s presentation of climate change has varied over time and the public remains politically divided on the issue. This content analysis of 134 New York Times’ climate change articles between 2001 and 2013 identified six different types of media frames associated with climate change coverage and investigated the presentation of scientific information within those frames. This study also investigated the congruence between scientific consensus regarding climate change, the public’s perception of current scientific knowledge and the way climate change is talked about in the media.Item Surgery on frames(2009-05-15) Nguyen, Nga QuynhIn this dissertation, we investigate methods of modifying a tight frame sequence on a finite subset of the frame so that the result is a tight frame with better properties. We call this a surgery on the frame. There are basically three types of surgeries: transplants, expansions, and contractions. In this dissertation, it will be necessary to consider surgeries on not-necessarily-tight frames because the subsets of frames that are excised and replaced are usually not themselves tight frames on their spans, even if the initial frame and the final frame are tight. This makes the theory necessarily complicated, and richer than one might expect. Chapter I is devoted to an introduction to frame theory. In Chapter II, we investigate conditions under which expansion, contraction, and transplant problems have a solution. In particular, we consider the equiangular replacement problem. We show that we can always replace a set of three unit vectors with a set of three complex unit equiangular vectors which has the same Bessel operator as the Bessel operator of the original set. We show that this can not always be done if we require the replacement vectors to be real, even if the original vectors are real. We also prove that the minimum angle between pairs of vectors in the replacement set becomes largest when the replacement set is equiangular. Iterating this procedure can yield a frame with smaller maximal frame correlation than the original. Frames with optimal maximal frame correlation are called Grassmannian frames and no general method is known at the present time for constructing them. Addressing this, in Chapter III we introduce a spreading algorithm for finite unit tight frames by replacing vectors three-at-a-time to produce a unit tight frame with better maximal frame correlation than the original frame. This algorithm also provides a ?good? orientation for the replacement sets. The orientation part ensures stability in the sense that if a selected set of three unit vectors happens to already be equiangular, then the algorithm gives back the same three vectors in the original order. In chapter IV and chapter V, we investigate two special classes of frames called push-out frames and group frames. Chapter VI is devoted to some mathematical problems related to the ?cocktail party problem ?.