  A long line of work in the past two decades or so established close
connections between several different pseudorandom objects and applications.
These connections essentially show that an asymptotically optimal construction
of one central object will lead to asymptotically optimal solutions to all the
others. However, despite considerable effort, previous works can get close but
still lack one final step to achieve truly asymptotically optimal
constructions.
  In this paper we provide the last missing link, thus simultaneously achieving
explicit, asymptotically optimal constructions and solutions for various well
studied extractors and applications, that have been the subjects of long lines
of research. Our results include:
  Asymptotically optimal seeded non-malleable extractors, which in turn give
two source extractors for asymptotically optimal min-entropy of $O(\log n)$,
explicit constructions of $K$-Ramsey graphs on $N$ vertices with $K=\log^{O(1)}
N$, and truly optimal privacy amplification protocols with an active adversary.
  Two source non-malleable extractors and affine non-malleable extractors for
some linear min-entropy with exponentially small error, which in turn give the
first explicit construction of non-malleable codes against $2$-split state
tampering and affine tampering with constant rate and \emph{exponentially}
small error.
  Explicit extractors for affine sources, sumset sources, interleaved sources,
and small space sources that achieve asymptotically optimal min-entropy of
$O(\log n)$ or $2s+O(\log n)$ (for space $s$ sources).
  An explicit function that requires strongly linear read once branching
programs of size $2^{n-O(\log n)}$, which is optimal up to the constant in
$O(\cdot)$. Previously, even for standard read once branching programs, the
best known size lower bound for an explicit function is $2^{n-O(\log^2 n)}$.
