We give a randomized polynomial-time identity test for
noncommutative circuits of polynomial degree based on the isolation
lemma. Using this result, we show that derandomizing the isolation
lemma implies noncommutative circuit size lower bounds. More
precisely, we consider two restricted versions of the isolation
lemma and show that derandomizing each ... more >>>

Functions in arithmetic NC1 are known to have equivalent constant
width polynomial degree circuits, but the converse containment is
unknown. In a partial answer to this question, we show that syntactic
multilinear circuits of constant width and polynomial degree can be
depth-reduced, though the resulting circuits need not be ... more >>>

Following up on the work of Megiddo and Vazirani \cite{MV.2007}, who
determined continuity properties of equilibrium prices and
allocations for perhaps the simplest market model, Fisher's linear
case, we do the same for:
\begin{itemize}
\item
Fisher's model with piecewise-linear, concave utilities
\item
Fisher's model with spending constraint utilities
\item
Arrow-Debreu's ... more >>>