3,632 research outputs found
Duality and sensitivity analysis for fractional programs
"3-97-76."--handwritten on t.p. Cover title.Bibliography: p. 38-42.Supported in part by the U.S. Army Research Office (Durham) under contract no. DAHC04-732-0032 Supported in part by a Grant-in-Aid from Coca-Cola, U.S.A, administered at M.I.T. as OSP 27857by Gabriel R. Bitran and Thomas L. Magnanti
On Planetary Companions to the MACHO-98-BLG-35 Microlens Star
We present observations of microlensing event MACHO-98-BLG-35 which reached a
peak magnification factor of almost 80. These observations by the Microlensing
Planet Search (MPS) and the MOA Collaborations place strong constraints on the
possible planetary system of the lens star and show intriguing evidence for a
low mass planet with a mass fraction . A giant planet with is excluded from 95%
of the region between 0.4 and 2.5 from the lens star, where is the
Einstein ring radius of the lens. This exclusion region is more extensive than
the generic "lensing zone" which is . For smaller mass planets,
we can exclude 57% of the "lensing zone" for and 14% of
the lensing zone for . The mass fraction corresponds to an Earth mass planet for a lensing star of mass \sim
0.3 \msun. A number of similar events will provide statistically significant
constraints on the prevalence of Earth mass planets. In order to put our limits
in more familiar terms, we have compared our results to those expected for a
Solar System clone averaging over possible lens system distances and
orientations. We find that such a system is ruled out at the 90% confidence
level. A copy of the Solar System with Jupiter replaced by a second Saturn mass
planet can be ruled out at 70% confidence. Our low mass planetary signal (few
Earth masses to Neptune mass) is significant at the confidence
level. If this planetary interpretation is correct, the MACHO-98-BLG-35 lens
system constitutes the first detection of a low mass planet orbiting an
ordinary star without gas giant planets.Comment: ApJ, April 1, 2000; 27 pages including 8 color postscript figure
Applications of quark-hadron duality in F2 structure function
Inclusive electron-proton and electron-deuteron inelastic cross sections have
been measured at Jefferson Lab (JLab) in the resonance region, at large Bjorken
x, up to 0.92, and four-momentum transfer squared Q2 up to 7.5 GeV2 in the
experiment E00-116. These measurements are used to extend to larger x and Q2
precision, quantitative, studies of the phenomenon of quark-hadron duality. Our
analysis confirms, both globally and locally, the apparent violation of
quark-hadron duality previously observed at a Q2 of 3.5 GeV2 when resonance
data are compared to structure function data created from CTEQ6M and MRST2004
parton distribution functions (PDFs). More importantly, our new data show that
this discrepancy saturates by Q2 ~ 4 Gev2, becoming Q2 independent. This
suggests only small violations of Q2 evolution by contributions from the
higher-twist terms in the resonance region which is confirmed by our
comparisons to ALEKHIN and ALLM97.We conclude that the unconstrained strength
of the CTEQ6M and MRST2004 PDFs at large x is the major source of the
disagreement between data and these parameterizations in the kinematic regime
we study and that, in view of quark-hadron duality, properly averaged resonance
region data could be used in global QCD fits to reduce PDF uncertainties at
large x.Comment: 35 page
Online Mixed Packing and Covering
In many problems, the inputs arrive over time, and must be dealt with
irrevocably when they arrive. Such problems are online problems. A common
method of solving online problems is to first solve the corresponding linear
program, and then round the fractional solution online to obtain an integral
solution.
We give algorithms for solving linear programs with mixed packing and
covering constraints online. We first consider mixed packing and covering
linear programs, where packing constraints are given offline and covering
constraints are received online. The objective is to minimize the maximum
multiplicative factor by which any packing constraint is violated, while
satisfying the covering constraints. No prior sublinear competitive algorithms
are known for this problem. We give the first such --- a
polylogarithmic-competitive algorithm for solving mixed packing and covering
linear programs online. We also show a nearly tight lower bound.
Our techniques for the upper bound use an exponential penalty function in
conjunction with multiplicative updates. While exponential penalty functions
are used previously to solve linear programs offline approximately, offline
algorithms know the constraints beforehand and can optimize greedily. In
contrast, when constraints arrive online, updates need to be more complex.
We apply our techniques to solve two online fixed-charge problems with
congestion. These problems are motivated by applications in machine scheduling
and facility location. The linear program for these problems is more
complicated than mixed packing and covering, and presents unique challenges. We
show that our techniques combined with a randomized rounding procedure give
polylogarithmic-competitive integral solutions. These problems generalize
online set-cover, for which there is a polylogarithmic lower bound. Hence, our
results are close to tight
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
Approximability and proof complexity
This work is concerned with the proof-complexity of certifying that
optimization problems do \emph{not} have good solutions. Specifically we
consider bounded-degree "Sum of Squares" (SOS) proofs, a powerful algebraic
proof system introduced in 1999 by Grigoriev and Vorobjov. Work of Shor,
Lasserre, and Parrilo shows that this proof system is automatizable using
semidefinite programming (SDP), meaning that any -variable degree- proof
can be found in time . Furthermore, the SDP is dual to the well-known
Lasserre SDP hierarchy, meaning that the "-round Lasserre value" of an
optimization problem is equal to the best bound provable using a degree- SOS
proof. These ideas were exploited in a recent paper by Barak et al.\ (STOC
2012) which shows that the known "hard instances" for the Unique-Games problem
are in fact solved close to optimally by a constant level of the Lasserre SDP
hierarchy.
We continue the study of the power of SOS proofs in the context of difficult
optimization problems. In particular, we show that the Balanced-Separator
integrality gap instances proposed by Devanur et al.\ can have their optimal
value certified by a degree-4 SOS proof. The key ingredient is an SOS proof of
the KKL Theorem. We also investigate the extent to which the Khot--Vishnoi
Max-Cut integrality gap instances can have their optimum value certified by an
SOS proof. We show they can be certified to within a factor .952 ()
using a constant-degree proof. These investigations also raise an interesting
mathematical question: is there a constant-degree SOS proof of the Central
Limit Theorem?Comment: 34 page
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