9,042 research outputs found
Pricing for Online Resource Allocation: Intervals and Paths
We present pricing mechanisms for several online resource allocation problems
which obtain tight or nearly tight approximations to social welfare. In our
settings, buyers arrive online and purchase bundles of items; buyers' values
for the bundles are drawn from known distributions. This problem is closely
related to the so-called prophet-inequality of Krengel and Sucheston and its
extensions in recent literature. Motivated by applications to cloud economics,
we consider two kinds of buyer preferences. In the first, items correspond to
different units of time at which a resource is available; the items are
arranged in a total order and buyers desire intervals of items. The second
corresponds to bandwidth allocation over a tree network; the items are edges in
the network and buyers desire paths.
Because buyers' preferences have complementarities in the settings we
consider, recent constant-factor approximations via item prices do not apply,
and indeed strong negative results are known. We develop static, anonymous
bundle pricing mechanisms.
For the interval preferences setting, we show that static, anonymous bundle
pricings achieve a sublogarithmic competitive ratio, which is optimal (within
constant factors) over the class of all online allocation algorithms, truthful
or not. For the path preferences setting, we obtain a nearly-tight logarithmic
competitive ratio. Both of these results exhibit an exponential improvement
over item pricings for these settings. Our results extend to settings where the
seller has multiple copies of each item, with the competitive ratio decreasing
linearly with supply. Such a gradual tradeoff between supply and the
competitive ratio for welfare was previously known only for the single item
prophet inequality
The emergence of 4-cycles in polynomial maps over the extended integers
Let ; for each integer it is interesting to
consider the number of iterates , if possible, needed to satisfy
. The sets generated by the iterates of are
called cycles. For it is known that cycles of length 1 and 2
occur, and no others. While much is known for extensions to number fields, we
concentrate on extending by adjoining reciprocals of primes. Let
denote extended by adding in
the reciprocals of the primes and all their products and
powers with each other and the elements of .
Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in
under the appropriate
conditions. The problem of finding criteria under which 4-cycles emerge is
equivalent to determining how often a sum of four terms is zero, where the
terms are times a product of elements from the list of primes. We
investigate conditions on sets of primes under which 4-cycles emerge. We
characterize when 4-cycles emerge if the set has one or two primes, and
(assuming a generalization of the ABC conjecture) find conditions on sets of
primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur
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Synthesis, structures and cytotoxicity studies of p-sulfonatocalix[4]arene lanthanide complexes
A number of p-sulfonatocalix[4]arene complexes of the lanthanides (Tb, Gd, and Eu) have been prepared, some in the presence of tetraazamacrocycle 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid (DO3A), and fully characterised. Crystal structure determinations reveal lanthanide coordination at the sulfonate group, bridging several calixarene units, giving coordination polymers. All complexes in this study have been determined to be relatively non-toxic using in vitro cell assays with CC₅₀ values in the range 30–170 μM
Acceleration of energetic particles by large-scale compressible magnetohydrodynamic turbulence
Fast particles diffusing along magnetic field lines in a turbulent plasma can
diffuse through and then return to the same eddy many times before the eddy is
randomized in the turbulent flow. This leads to an enhancement of particle
acceleration by large-scale compressible turbulence relative to previous
estimates in which isotropic particle diffusion is assumed.Comment: 13 pages, 3 figures, accepted for publication in Ap
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