2,994 research outputs found
The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics
By combining the join construction from Sasakian geometry with the
Hamiltonian 2-form construction from K\"ahler geometry, we recover
Sasaki-Einstein metrics discovered by physicists. Our geometrical approach
allows us to give an algorithm for computing the topology of these
Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology
rings for several cases of interest and give a formula for homotopy equivalence
in one particular 7-dimensional case. We also show that our construction gives
at least a two dimensional cone of both Sasaki-Ricci solitons and extremal
Sasaki metrics.Comment: 38 pages, paragraph added to introduction and Proposition 4.1 added,
Proposition 4.15 corrected, Remark 5.5 added, and explanation for irregular
Sasaki-Einstein structures expanded. Reference adde
The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature
We describe a general procedure for constructing new Sasaki metrics of
constant scalar curvature from old ones. Explicitly, we begin with a regular
Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact
manifold M and construct a sequence, depending on four integer parameters, of
rays of constant scalar curvature (CSC) Sasaki metrics on a compact Sasaki
manifold of dimension . We also give examples which show that the CSC
rays are often not unique on a fixed strictly pseudoconvex CR manifold or a
fixed contact manifold. Moreover, it is shown that when the first Chern class
of the contact bundle vanishes, there is a two dimensional subcone of Sasaki
Ricci solitons in the Sasaki cone, and a unique Sasaki-Einstein metric in each
of the two dimensional sub cones.Comment: 32 pages. A gap in the argument of applying the admissibility
conditions to irregular Sasakian structures is filled. Some minor corrections
and additions are also made. This is the final version which will appear in
the Journal of Geometric Analysis. It also encorporates much from our paper
arXiv:1309.706
The Frequency Interpretation in Probability
AbstractWe formulate and discuss the notion of generic sequence (and random sequence) associated with a sequence of random variables. These are substantial generalizations of the notion of “collective” introduced by R. von Mises as an attempt to give an operational meaning to various probabilistic ideas. The definition of collectives lacked a precise formulation, and A. Church and others attempted to give a rigorous meaning to the theory by utilizing ideas from the theory of computability. Nevertheless, the theory had major flaws. Even though some important contributions to special cases were made by P. Martin-Löf, the whole circle of ideas has languished due to lack of generality. The theory presented in the present article resolves many of these problems, and provides a coherent framework for the relevant ideas
Educating Health Professionals in the Era of Ubiquitous Information
Dr. Charles Chuck Friedman, an internationally known biomedical informatics scholar and health IT expert, will give a talk as part of the Chancellor\u27s Leadership Forum on Monday, December 17. This is a reprise of a highly acclaimed talk he gave at a recent national meeting of the Association of American Medical Colleges (AAMC). Dr. Friedman will discuss the following: • How the ubiquity of information available from the Internet will impact medical student learning • The implications of medical education we can reasonably expect by 2020\u2
Computable knowledge: An imperative for Learning Health Systems
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151989/1/lrh210203.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151989/2/lrh210203_am.pd
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