  We address the question of how a localized microscopic defect, especially if
it is small with respect to certain dynamic parameters, affects the macroscopic
behavior of a system. In particular we consider two classical exactly solvable
models: Ulam's problem of the maximal increasing sequence and the totally
asymmetric simple exclusion process. For the first model, using its
representation as a Poissonian version of directed last passage percolation on
$\mathbb R^2$, we introduce the defect by placing a positive density of extra
points along the diagonal line. For the latter, the defect is produced by
decreasing the jump rate of each particle when it crosses the origin.
  The powerful algebraic tools for studying these processes break down in the
perturbed versions of the models. Taking a more geometric approach we show that
in both cases the presence of an arbitrarily small defect affects the
macroscopic behavior of the system: in Ulam's problem the time constant
increases, and for the exclusion process the flux of particles decreases. This,
in particular, settles the longstanding Slow Bond Problem.
