Joel Friedman

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The combination of divide-and-conquer and random sampling has proven very effective in the design of fast geometric algorithms. A flurry of efficient probabilistic algorithms have been recently discovered, based on this happy marriage. We show that all those algorithms can be derandomized with only polynomial overhead. In the process we establish results of(More)
A 3.5 angstrom resolution electron density map of the HIV-1 reverse transcriptase heterodimer complexed with nevirapine, a drug with potential for treatment of AIDS, reveals an asymmetric dimer. The polymerase (pol) domain of the 66-kilodalton subunit has a large cleft analogous to that of the Klenow fragment of Escherichia coli DNA polymerase I. However,(More)
The following is an extended abstract for two papers, one written by Kahn and Szemeredi, the other written by Friedman, which have been combined at the request of the STOC committee. The introduction was written jointly, the second section by Kahn and Szemeredi, and the third by Friedman, Let G be a d-regular (i.e. each vertex has degree d) undirected graph(More)
Consider a coloring of the n-dimensional Boolean cube with c = 2 colors in such a way that every kdimensional subcube is equicolored, i.e. each color occurs the same number of times. We show that for such a coloring we necessarily have (k − 1)/n ≥ θc = (c/2 − 1)/(c − 1). This resolves the “bit extraction” or “t-resilient functions” problem (also a special(More)
Let G be a fixed graph with largest (adjacency matrix) eigenvalue λ0 and with its universal cover having spectral radius ρ. We show that a random cover of large degree over G has its “new” eigenvalues bounded in absolute value by roughly √ λ0ρ. This gives a positive result about finite quotients of certain trees having “small” eigenvalues, provided we(More)
We study three mathematical notions, that of nodal regions for eigenfunctions of the Laplacian, that of covering theory, and that of fiber products, in the context of graph theory and spectral theory for graphs. We formulate analogous notions and theorems for graphs and their eigenpairs. These techniques suggest new ways of studying problems related to(More)
A new method for constructing wide-sense nonblocking networks is presented. Application of this method yields (among other things) wide-sense nonblocking generalized connectors with n inputs and outputs and size O(n log n), and with depth k and size O(n+ /k(Iog n)/k). Key words, nonblocking network, connection network, concentrator, generalizer AMS(MOS)(More)
In the course of an ethnopharmacological survey carried out among the Bedouins of the Negev desert, it was noticed that in addition to the use of modern medical services, medicinal plants were also being employed. We deemed it worthwhile, therefore, to investigate the current status of herbal medicine among the Negev Bedouins and to evaluate the relative(More)
We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages over other methods, both in theory and in practice. It requires small storage space in many cases. It seems to run quickly in practice, but its running time depends on a ratio, ν , of eigenvalues which we have yet to understand fully. We(More)