98 research outputs found
Prime tight frames
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use this characterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two
On R-duals and the duality principle in Gabor analysis
The concept of R-duals of a frame was introduced by Casazza, Kutyniok and
Lammers in 2004, with the motivation to obtain a general version of the duality
principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the
three authors were actually able to show that the duality principle is a
special case of general results for R-duals. In this paper we introduce various
alternative R-duals, with focus on what we call R-duals of type II and III. We
show how they are related and provide characterizations of the R-duals of type
II and III. In particular, we prove that for tight frames these classes
coincide with the R-duals by Casazza et el., which is desirable in the sense
that the motivating case of tight Gabor frames already is well covered by these
R-duals. On the other hand, all the introduced types of R-duals generalize the
duality principle for larger classes of Gabor frames than just the tight frames
and the Riesz bases; in particular, the R-duals of type III cover the duality
principle for all Gabor frames
Ethanol Oxidation and Toxicity: Role of Alcohol P-450 Oxygenase
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66172/1/j.1530-0277.1986.tb05179.x.pd
Highly symmetric POVMs and their informational power
We discuss the dependence of the Shannon entropy of normalized finite rank-1
POVMs on the choice of the input state, looking for the states that minimize
this quantity. To distinguish the class of measurements where the problem can
be solved analytically, we introduce the notion of highly symmetric POVMs and
classify them in dimension two (for qubits). In this case we prove that the
entropy is minimal, and hence the relative entropy (informational power) is
maximal, if and only if the input state is orthogonal to one of the states
constituting a POVM. The method used in the proof, employing the Michel theory
of critical points for group action, the Hermite interpolation and the
structure of invariant polynomials for unitary-antiunitary groups, can also be
applied in higher dimensions and for other entropy-like functions. The links
between entropy minimization and entropic uncertainty relations, the Wehrl
entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure
International AIDS Society global scientific strategy: towards an HIV cure 2016
Antiretroviral therapy is not curative. Given the challenges in providing lifelong therapy to a global population of more than 35 million people living with HIV, there is intense interest in developing a cure for HIV infection. The International AIDS Society convened a group of international experts to develop a scientific strategy for research towards an HIV cure. This Perspective summarizes the group's strategy
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