Living cells function according to complex mechanisms that operate in different ways depending on conditions. Evolutionary theory suggests that such mechanisms evolved as a result of a random search guided by selection and realized by genetic mutations. However, as some observers have noted, there has existed no theory that would ... more >>>

We describe a short and easy to analyze construction of
constant-degree expanders. The construction relies on the
replacement-product, which we analyze using an elementary
combinatorial argument. The construction applies the replacement
product (only twice!) to turn the Cayley expanders of \cite{AR},
whose degree is polylog n, into constant degree
expanders.

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Given two binary linear codes R and C, their tensor product R \otimes C consists of all matrices with rows in R and columns in C. We analyze the "robustness" of the following test for this code (suggested by Ben-Sasson and Sudan~\cite{BenSasson-Sudan04}): Pick a random row (or column) and check ... more >>>