Learn More
This paper describes a computer-assisted non-existence proof of 9-input sorting networks consisting of 24 comparators, hence showing that the 25-comparator sorting network found by Floyd in 1964 is optimal. As a corollary, we obtain that the 29-comparator network found by Waksman in 1969 is optimal when sorting 10 inputs. This closes the two smallest open(More)
Fortune favors those who are able to align their plans and goals to accord with the constraints imposed on them by an intricate and dynamic world. However, this presents an exceedingly difficult assignment, since the constraints pressed on an organism are typically complex, uncertain, and even paradoxical. When foodstuffs run low in the fall, should a(More)
Zebrafish (Danio rerio) can serve as a model system to study heritable skin diseases. The skin is rapidly developed during the first 5-6 days of embryonic growth, accompanied by expression of skin-specific genes. Transmission electron microscopy (TEM) of wild-type zebrafish at day 5 reveals a two-cell-layer epidermis separated from the underlying(More)
Let X and Y be Hilbert C *-modules over a C *-algebra, and ϕ : X × Y → [0, ∞) be a function. A (not necessarily linear) mapping f : X → Y is called a ϕ-perturbation of an adjointable mapping if there exists a (not necessarily linear) corresponding mapping g : Y → X such that f (x), y − x, g(y) ≤ ϕ(x, y) x ∈ D(f) ⊆ X , y ∈ D(g) ⊆ Y. We prove that any(More)
The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is(More)
B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal sum-mand. We find out further generic properties of the(More)