Yonatan Bilu

Lifts, Discrepancy and Nearly Optimal Spectral Gap

We present a new explicit construction for expander graphs with nearly optimal spectral gap. The construction is based on a series of 2-lift operations. Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map π :H →G. It is not hard to see that all eigenvalues of G are also eigenvalues of H. In addition, H has n “new” eigenvalues. We conjecture that every d-regular graph has a 2-lift such that all new eigenvalues are in the range

Conservation of Expression and Sequence of Metabolic Genes Is Reflected by Activity Across Metabolic States

{\left[ { - 2{\sqrt {d - 1} },2{\sqrt {d - 1} }} \right]}

The Advantage of Functional Prediction Based on Clustering of Yeast Genes and Its Correlation with Non-Sequence Based Classifications

(if true, this is tight, e.g. by the Alon–Boppana bound). Here we show that every graph of maximal degree d has a 2-lift such that all “new” eigenvalues are in the range

On the predictive power of sequence similarity in yeast

{\left[ { - c{\sqrt {d\log ^{3} d} },c{\sqrt {d\log ^{3} d} }} \right]}

Ramanujan Signing of Regular Graphs

for some constant c. This leads to a deterministic polynomial time algorithm for constructing arbitrarily large d-regular graphs, with second eigenvalue