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We present a general approach to a module frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We… (More)

- Michael Codish, Luís Cruz-Filipe, Michael Frank, Peter Schneider-Kamp
- 2014 IEEE 26th International Conference on Tools…
- 2014

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)

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded… (More)

- Michael Frank, Vern I Paulsen, Terry R Tiballi
- 1998

We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces. A crucial role is played by the Hilbert-Schmidt property of a certain operator related to the initial frame or basis.

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)

- Qiaoli Li, Michael Frank, +6 authors Jouni Uitto
- Disease models & mechanisms
- 2011

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)

- M. Frank, P. Găvruţa, M. S. Moslehian
- 2008

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)

- Michael Codish, Luís Cruz-Filipe, Michael Frank, Peter Schneider-Kamp
- J. Comput. Syst. Sci.
- 2016

- Michael Codish, Michael Frank, Avraham Itzhakov, Alice Miller
- Constraints
- 2016

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)

- MICHAEL FRANK
- 2006

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)