9,942 research outputs found
Preservation and decomposition theorems for bounded degree structures
We provide elementary algorithms for two preservation theorems for
first-order sentences (FO) on the class \^ad of all finite structures of degree
at most d: For each FO-sentence that is preserved under extensions
(homomorphisms) on \^ad, a \^ad-equivalent existential (existential-positive)
FO-sentence can be constructed in 5-fold (4-fold) exponential time. This is
complemented by lower bounds showing that a 3-fold exponential blow-up of the
computed existential (existential-positive) sentence is unavoidable. Both
algorithms can be extended (while maintaining the upper and lower bounds on
their time complexity) to input first-order sentences with modulo m counting
quantifiers (FO+MODm). Furthermore, we show that for an input FO-formula, a
\^ad-equivalent Feferman-Vaught decomposition can be computed in 3-fold
exponential time. We also provide a matching lower bound.Comment: 42 pages and 3 figures. This is the full version of: Frederik
Harwath, Lucas Heimberg, and Nicole Schweikardt. Preservation and
decomposition theorems for bounded degree structures. In Joint Meeting of the
23rd EACSL Annual Conference on Computer Science Logic (CSL) and the 29th
Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS'14,
pages 49:1-49:10. ACM, 201
Unions of 3-punctured spheres in hyperbolic 3-manifolds
We classify the topological types for the unions of the totally geodesic
3-punctured spheres in orientable hyperbolic 3-manifolds. General types of the
unions appear in various hyperbolic 3-manifolds. Each of the special types of
the unions appears only in a single hyperbolic 3-manifold or Dehn fillings of a
single hyperbolic 3-manifold. Furthermore, we investigate bounds of the moduli
of adjacent cusps for the union of linearly placed 3-punctured spheres.Comment: 40 pages, 32 figures. v2: Section 5 extended, references added, v3:
Theorem 1.3 added, which concerns infinitely many 3-punctured spheres, v4:
reference added; to appear in Communications in Analysis and Geometr
On the pointwise domination of a function by its maximal function
We show that under rather general circumstances, the almost everywhere
pointwise inequality is equivalent to a weak form of the
Lebesgue density theorem, for totally bounded closed sets. We derive both
positive and negative results from this characterization.Comment: 13 pages, incorporates suggestions by a refere
Symmetric ribbon disks
We study the ribbon discs that arise from a symmetric union presentation of a
ribbon knot. A natural notion of symmetric ribbon number is introduced and
compared with the classical ribbon number. We show that the gap between these
numbers can be arbitrarily large by constructing an infinite family of ribbon
knots with ribbon number 2 and arbitrarily large symmetric ribbon number. The
proof is based on a particularly simple description of symmetric unions in
terms of certain band diagrams which leads to an upper bound for the Heegaard
genus of their branched double covers.Comment: 9 pages, 10 figures. Few typos corrected. Final version published in
JKT
Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets
This paper investigates the problem of recovering the support of structured
signals via adaptive compressive sensing. We examine several classes of
structured support sets, and characterize the fundamental limits of accurately
recovering such sets through compressive measurements, while simultaneously
providing adaptive support recovery protocols that perform near optimally for
these classes. We show that by adaptively designing the sensing matrix we can
attain significant performance gains over non-adaptive protocols. These gains
arise from the fact that adaptive sensing can: (i) better mitigate the effects
of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor
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