Ram Sriharsha

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This paper shows that one can be competitive with the kmeans objective while operating online. In this model, the algorithm receives vectors v1, . . . , vn one by one in an arbitrary order. For each vector vt the algorithm outputs a cluster identifier before receiving vt+1. Our online algorithm generates Õ(k) clusters whose k-means cost is Õ(W ∗) where W ∗(More)
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s(More)
We study a new type of warped compactifications of M-theory on eight manifolds for which nowhere vanishing covariantly constant spinors of indefinite chirality on the internal manifold can be found. We derive the constraints on the fluxes and the warp factor following from supersymmetry and the equations of motion. We show, that the lift of Type IIB(More)
Title of dissertation: ON STRING COMPACTIFICATIONS TO TWO (AND THREE) DIMENSIONS: CRITICAL AND NONCRITICAL Ram Sriharsha Doctor of Philosophy, 2007 Dissertation directed by: Professor Sylvester James Gates Jr. Department of Physics This thesis is devoted to certain aspects of string compactifications to two and three dimensions. We construct vacua that(More)
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