  We study almost symmetric numerical semigroups and semigroup rings. We
describe a characteristic property of the minimal free resolution of the
semigroup ring of an almost symmetric numerical semigroup.
  For almost symmetric semigroups generated by $4$ elements we will give a
structure theorem by using the \lq\lq row-factorization matrices", introduced
by Moscariello. As a result, we give a simpler proof of Komeda's structure
theorem of pseudo-symmetric numerical semigroups generated by $4$ elements.
Row-factorization matrices are also used to study shifted families of numerical
semigroups.
