Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided the data satisfy a natural stability notion. For example, Bilu and Linial (2010) and Awasthi et al. (2012) presented algorithms that output near-optimal solu...

1 Administrivia You should probably know that • the first problem set (due October 15) is posted on the class website, and • its hints are also posted there. Also, today in class there was a majority vote for posting problem sets earlier. Professor Kelner will post the problem sets from two years ago, but he reserves the right to add new problems once a problem set has already been posted. Ques...

What is the largest number of edges in a graph of order n and girth g? For dregular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p.163, problem 10). What is the maximal number of edges in a graph with n vertices and girth g? Put differently, wha...

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Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a set of functions. These methods offer the currently best approach to several central problems such as learning half spaces and learning DNF’s. In addition they are widely used in numerous applicatio...

Meth A gpllO has been tentatively identified as a tumor rejection antigen. Following isolation of a class I major histocompatibility complex (MHC)-restricted, CD8+ anti-Meth A cytotoxic T-lymphocyte (CTL), we sought to determine whether the determinant recognized by this CTL was: (a) functional in tumor rejection of Meth A sarcoma; and Un derived from Meth A gpllO. Initially, we isolated an ant...

Dimethyl fumarate and dimethyl maléate are potent inducers of cytosolic NAD(P)H:(quinone acceptor) oxidoreductase (here designated uninone reducÃ-ase)activity in Hepa Iclc? murine hepatoma cells in culture, whereas fumarie and maleic acids are much less potent, in agreement with the much greater reactivity of the esters as Michael reaction acceptors (P. Talalay, M. J. De Long, and H. J. Procha...

Dimethyl fumarate and dimethyl maléate are potent inducers of cytosolic NAD(P)H:(quinone acceptor) oxidoreductase (here designated uninone reducÃ-ase)activity in Hepa Iclc? murine hepatoma cells in culture, whereas fumarie and maleic acids are much less potent, in agreement with the much greater reactivity of the esters as Michael reaction acceptors (P. Talalay, M. J. De Long, and H. J. Procha...

4Crawford, L. V., R. Dulbecco, M. Fried, L. Montagnier, and M. G. P. Stoker, these PNoCEEDINGS, 52, 148 (1964). Bourgaux, P., D. Bourgaux-Ramoisy, and M. G. P. Stoker, Virology, 25, 364 (1965). 6Black, P. H., and W. P. Rowe, these PROCEEDINGS, 50, 606 (1963). 7Diderholm, H., B. Stenkvist, J. Ponten, and T. Wesslen, Exptl. Cell Res., 37, 452 (1965). 8 Black, P. H., and W. P. Rowe, J. Nati. Cance...

An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (“mutant”) strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the question of what happens when the size of the game increases: does an ESS exist for “almost every large” game? Letting the entries in the n × n game matrix be indepe...