  We give several new lower bounds on size of homogeneous non-commutative
circuits. We present an explicit homogeneous bivariate polynomial of degree $d$
which requires homogeneous non-commutative circuit of size $\Omega(d/\log d)$.
For an $n$-variate polynomial with $n>1$, the result can be improved to
$\Omega(nd)$, if $d\leq n$, or $\Omega(nd \frac{\log n}{\log d})$, if $d\geq
n$.
  Under the same assumptions, we also give a quadratic lower bound for the
ordered version of the central symmetric polynomial.
