19,972 research outputs found
On Colorful Bin Packing Games
We consider colorful bin packing games in which selfish players control a set
of items which are to be packed into a minimum number of unit capacity bins.
Each item has one of colors and cannot be packed next to an item of
the same color. All bins have the same unitary cost which is shared among the
items it contains, so that players are interested in selecting a bin of minimum
shared cost. We adopt two standard cost sharing functions: the egalitarian cost
function which equally shares the cost of a bin among the items it contains,
and the proportional cost function which shares the cost of a bin among the
items it contains proportionally to their sizes. Although, under both cost
functions, colorful bin packing games do not converge in general to a (pure)
Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we
design an algorithm for computing a Nash equilibrium whose running time is
polynomial under the egalitarian cost function and pseudo-polynomial for a
constant number of colors under the proportional one. We also provide a
complete characterization of the efficiency of Nash equilibria under both cost
functions for general games, by showing that the prices of anarchy and
stability are unbounded when while they are equal to 3 for black and
white games, where . We finally focus on games with uniform sizes (i.e.,
all items have the same size) for which the two cost functions coincide. We
show again a tight characterization of the efficiency of Nash equilibria and
design an algorithm which returns Nash equilibria with best achievable
performance
The inevitability of unconditionally deleterious substitutions during adaptation
Studies on the genetics of adaptation typically neglect the possibility that
a deleterious mutation might fix. Nonetheless, here we show that, in many
regimes, the first substitution is most often deleterious, even when fitness is
expected to increase in the long term. In particular, we prove that this
phenomenon occurs under weak mutation for any house-of-cards model with an
equilibrium distribution. We find that the same qualitative results hold under
Fisher's geometric model. We also provide a simple intuition for the surprising
prevalence of unconditionally deleterious substitutions during early
adaptation. Importantly, the phenomenon we describe occurs on fitness
landscapes without any local maxima and is therefore distinct from
"valley-crossing". Our results imply that the common practice of ignoring
deleterious substitutions leads to qualitatively incorrect predictions in many
regimes. Our results also have implications for the substitution process at
equilibrium and for the response to a sudden decrease in population size.Comment: Corrected typos and minor errors in Supporting Informatio
A Robust AFPTAS for Online Bin Packing with Polynomial Migration
In this paper we develop general LP and ILP techniques to find an approximate
solution with improved objective value close to an existing solution. The task
of improving an approximate solution is closely related to a classical theorem
of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is
often applied in designing robust algorithms for online problems. We apply our
new techniques to the online bin packing problem, where it is allowed to
reassign a certain number of items, measured by the migration factor. The
migration factor is defined by the total size of reassigned items divided by
the size of the arriving item. We obtain a robust asymptotic fully polynomial
time approximation scheme (AFPTAS) for the online bin packing problem with
migration factor bounded by a polynomial in . This answers
an open question stated by Epstein and Levin in the affirmative. As a byproduct
we prove an approximate variant of the sensitivity theorem by Cook at el. for
linear programs
D/H of water released by stepped heating of Shergotty, Zagami, Chassigny, ALH 84001, and Nakhla
We report the yield and D/H of water released by stepped heating of bulk Shergotty, Zagami, Chassigny, and the newest martian meteorite, ALH 84001. For comparison, we also report data from Nakhla using the same procedure since the heating steps in this study are slightly different than our previously reported nakhlite analyses
A Superluminal Subway: The Krasnikov Tube
The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps
Online unit clustering in higher dimensions
We revisit the online Unit Clustering and Unit Covering problems in higher
dimensions: Given a set of points in a metric space, that arrive one by
one, Unit Clustering asks to partition the points into the minimum number of
clusters (subsets) of diameter at most one; while Unit Covering asks to cover
all points by the minimum number of balls of unit radius. In this paper, we
work in using the norm.
We show that the competitive ratio of any online algorithm (deterministic or
randomized) for Unit Clustering must depend on the dimension . We also give
a randomized online algorithm with competitive ratio for Unit
Clustering}of integer points (i.e., points in , , under norm). We show that the competitive ratio of
any deterministic online algorithm for Unit Covering is at least . This
ratio is the best possible, as it can be attained by a simple deterministic
algorithm that assigns points to a predefined set of unit cubes. We complement
these results with some additional lower bounds for related problems in higher
dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA
2017
Effect of prolonged space flight on cardiac function and dimensions
Echocardiographic studies were performed preflight 5 days before launch and on recovery day and 1, 2, 4, 11, 31 and 68 days postflight. From these echocardiograms measurements were made. From these primary measurements, left ventricular end-diastolic volume, end-systolic volume, stroke volume, and mass were derived using the accepted assumptions. Findings in the Scientist Pilot and Pilot resemble those seen in trained distance runners. Wall thickness measurements were normal in all three crewmembers preflight. Postflight basal studies were unchanged in the Commander on recovery day through 68 days postflight in both the Scientist Pilot and Pilot, however, the left ventricular end-diastolic volume, stroke volume, and mass were decreased slightly. Left ventricular function curves were constructed for the Commander and Pilot by plotting stroke volume versus end-diastolic volume. In both astronauts, preflight and postflight data fell on the same straight line demonstrating that no deterioration in cardiac function had occurred. These data indicate that the cardiovascular system adapts well to prolonged weightlessness and suggest that alterations in cardiac dimensions and function are unlikely to limit man's future in space
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