91 research outputs found
Properties and Applications of Programs with Monotone and Convex Constraints
We study properties of programs with monotone and convex constraints. We
extend to these formalisms concepts and results from normal logic programming.
They include the notions of strong and uniform equivalence with their
characterizations, tight programs and Fages Lemma, program completion and loop
formulas. Our results provide an abstract account of properties of some recent
extensions of logic programming with aggregates, especially the formalism of
lparse programs. They imply a method to compute stable models of lparse
programs by means of off-the-shelf solvers of pseudo-boolean constraints, which
is often much faster than the smodels system
Spectral norm of products of random and deterministic matrices
We study the spectral norm of matrices M that can be factored as M=BA, where
A is a random matrix with independent mean zero entries, and B is a fixed
matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show
that the spectral norm of such an m by n matrix M is bounded by \sqrt{m} +
\sqrt{n}, which is sharp. In other words, in regard to the spectral norm,
products of random and deterministic matrices behave similarly to random
matrices with independent entries. This result along with the previous work of
M. Rudelson and the author implies that the smallest singular value of a random
m times n matrix with i.i.d. mean zero entries and bounded (4+epsilon)-th
moment is bounded below by \sqrt{m} - \sqrt{n-1} with high probability.Comment: One uncited reference removed from the bibliography. Journal version
to appear in PTRF
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