Browsing Mathematics - Ph.D. / Sc.D. by Title
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Browsing Mathematics - Ph.D. / Sc.D. by Title
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(Massachusetts Institute of Technology, 2012)In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...
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(Massachusetts Institute of Technology, 2008)This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a ...
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(Massachusetts Institute of Technology, 2002)We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a ...
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(Massachusetts Institute of Technology, 1991)
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(Massachusetts Institute of Technology, 2002)Geometry is the synthetic tool we use to unify all existing analytical cone-beam reconstruction methods. These reconstructions are based on formulae derived by Tuy [Tuy, 1983], Smith [Smith, 1985] and Grangeat [Grangeat, ...
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(Massachusetts Institute of Technology, 2004)In this work, we study geometry of Ricci-flat Kähler manifolds, and also provide some counterexample constructions. We study asymptotic behavior of complete Ricci-flat metrics at infinity and consider a construction of ...
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(Massachusetts Institute of Technology, 2000)
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 2013)The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ...
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(Massachusetts Institute of Technology, 2009)A property tester is a fast, randomized algorithm that reads only a few entries of the input, and based on the values of these entries, it distinguishes whether the input has a certain property or is "different" from any ...
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(Massachusetts Institute of Technology, 2013)In this thesis, we present several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can ...
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(Massachusetts Institute of Technology, 2008)The Mayer-Vietoris sequence in cohomology has an obvious Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. ...
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(Massachusetts Institute of Technology, 1996)
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 1961)
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(Massachusetts Institute of Technology, 1993)
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(Massachusetts Institute of Technology, 2005)In this thesis, we derive the asymptotic expansion of the Kiihler-Einstein metrics on certain quasi-projective varieties, which can be compactified by adding a divisor with simple normal crossings. The weighted Cheng-Yau ...
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(Massachusetts Institute of Technology, 2011)We present two recent parallel programming languages, PetaBricks and Julia, and demonstrate how we can use these two languages to re-examine classic numerical algorithms in new approaches for high-performance computing. ...
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(Massachusetts Institute of Technology, 2008)Preprojective algebras [Pi]q of quivers Q were introduced by Gelfand and Ponomarev in 1979 in order to provide a model for quiver representations (in the special case of finite Dynkin quivers). They showed that in the ...
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(Massachusetts Institute of Technology, 1986)
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