For many elegant mathematical examples, one can 1) find theories
behind them, 2) understand why they exist in the first place, 3)
explore the consequences in math and physics. If one takes the
Euler number as...
Polycrystalline materials, such as metals, ceramics and
geological materials, are aggregates of single-crystal grains that
are held together by highly defective boundaries. The structure of
grain boundaries is...
We study the complexity of computing some basic arithmetic
operations over GF(2^n), namely computing q-th root and q-th
residuosity, by constant depth arithmetic circuits over GF(2) (also
known as AC^0(parity)). Our main result is that these...
