39,908 research outputs found
Black hole state counting in loop quantum gravity
The two ways of counting microscopic states of black holes in the U(1)
formulation of loop quantum gravity, one counting all allowed spin network
labels j,m and the other only m labels, are discussed in some detail. The
constraints on m are clarified and the map between the flux quantum numbers and
m discussed. Configurations with |m|=j, which are sometimes sought after, are
shown to be important only when large areas are involved. The discussion is
extended to the SU(2) formulation.Comment: 5 page
Reply to comment by Zaslavskii on extremal black hole action
It is shown that Zaslavskii's misunderstanding of our published proof of the
irrelevance of all extremal black hole configurations (whether with equal
charge and mass or not) rests on his refusal to see the essential difference
between the correct inequality governing extremal and non-extremal actions and
his incorrect version.Comment: 1 page, REVTeX, adapted from reply in PRL 80, 3413 (1998
Evaluation of missing data mechanisms in two and three dimensional incomplete tables
The analysis of incomplete contingency tables is a practical and an
interesting problem. In this paper, we provide characterizations for the
various missing mechanisms of a variable in terms of response and non-response
odds for two and three dimensional incomplete tables. Log-linear
parametrization and some distinctive properties of the missing data models for
the above tables are discussed. All possible cases in which data on one, two or
all variables may be missing are considered. We study the missingness of each
variable in a model, which is more insightful for analyzing cross-classified
data than the missingness of the outcome vector. For sensitivity analysis of
the incomplete tables, we propose easily verifiable procedures to evaluate the
missing at random (MAR), missing completely at random (MCAR) and not missing at
random (NMAR) assumptions of the missing data models. These methods depend only
on joint and marginal odds computed from fully and partially observed counts in
the tables, respectively. Finally, some real-life datasets are analyzed to
illustrate our results, which are confirmed based on simulation studies
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