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This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v 1 ,. .. , v n one by one in an arbitrary order. For each vector v t the algorithm outputs a cluster identifier before receiving v t+1. Our online algorithm generates˜O(k) clusters whose k-means cost is˜O(W *) where(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)
This thesis is devoted to certain aspects of string compactifications to two and three dimensions. We construct vacua that describe the propagation of non-critical strings on a singular Spin(7) space. We also examine compactifications which preserve six supercharges, and obtain the classical and quantum moduli space of such theories. We also consider(More)
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