5,295 research outputs found
On Almost Paracontact Almost Paracomplex Riemannian Manifolds
Almost paracontact manifolds of an odd dimension having an almost paracomplex
structure on the paracontact distribution are studied. The components of the
fundamental (0,3)-tensor, derived by the covariant derivative of the structure
endomorphism and the metric on the considered manifolds in each of the basic
classes, are obtained. Then, the case of the lowest dimension 3 of these
manifolds is considered. An associated tensor of the Nijenhuis tensor is
introduced and the studied manifolds are characterized with respect to this
pair of tensors. Moreover, cases of paracontact and para-Sasakian types are
commented. A family of examples is given.Comment: 18 pages, 2 table
Redrawing the Boundaries on Purchasing Data from Privacy-Sensitive Individuals
We prove new positive and negative results concerning the existence of
truthful and individually rational mechanisms for purchasing private data from
individuals with unbounded and sensitive privacy preferences. We strengthen the
impossibility results of Ghosh and Roth (EC 2011) by extending it to a much
wider class of privacy valuations. In particular, these include privacy
valuations that are based on ({\epsilon}, {\delta})-differentially private
mechanisms for non-zero {\delta}, ones where the privacy costs are measured in
a per-database manner (rather than taking the worst case), and ones that do not
depend on the payments made to players (which might not be observable to an
adversary). To bypass this impossibility result, we study a natural special
setting where individuals have mono- tonic privacy valuations, which captures
common contexts where certain values for private data are expected to lead to
higher valuations for privacy (e.g. having a particular disease). We give new
mech- anisms that are individually rational for all players with monotonic
privacy valuations, truthful for all players whose privacy valuations are not
too large, and accurate if there are not too many players with too-large
privacy valuations. We also prove matching lower bounds showing that in some
respects our mechanism cannot be improved significantly
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