565 research outputs found
Smoothed Complexity Theory
Smoothed analysis is a new way of analyzing algorithms introduced by Spielman
and Teng (J. ACM, 2004). Classical methods like worst-case or average-case
analysis have accompanying complexity classes, like P and AvgP, respectively.
While worst-case or average-case analysis give us a means to talk about the
running time of a particular algorithm, complexity classes allows us to talk
about the inherent difficulty of problems.
Smoothed analysis is a hybrid of worst-case and average-case analysis and
compensates some of their drawbacks. Despite its success for the analysis of
single algorithms and problems, there is no embedding of smoothed analysis into
computational complexity theory, which is necessary to classify problems
according to their intrinsic difficulty.
We propose a framework for smoothed complexity theory, define the relevant
classes, and prove some first hardness results (of bounded halting and tiling)
and tractability results (binary optimization problems, graph coloring,
satisfiability). Furthermore, we discuss extensions and shortcomings of our
model and relate it to semi-random models.Comment: to be presented at MFCS 201
Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
Quenched QCD simulations on three volumes, , and
and three couplings, , 5.85 and 6.0 using domain
wall fermions provide a consistent picture of quenched QCD. We demonstrate that
the small induced effects of chiral symmetry breaking inherent in this
formulation can be described by a residual mass (\mres) whose size decreases
as the separation between the domain walls () is increased. However, at
stronger couplings much larger values of are required to achieve a given
physical value of \mres. For and , we find
\mres/m_s=0.033(3), while for , and ,
\mres/m_s=0.074(5), where is the strange quark mass. These values are
significantly smaller than those obtained from a more naive determination in
our earlier studies. Important effects of topological near zero modes which
should afflict an accurate quenched calculation are easily visible in both the
chiral condensate and the pion propagator. These effects can be controlled by
working at an appropriately large volume. A non-linear behavior of in
the limit of small quark mass suggests the presence of additional infrared
subtlety in the quenched approximation. Good scaling is seen both in masses and
in over our entire range, with inverse lattice spacing varying between
1 and 2 GeV.Comment: 91 pages, 34 figure
Lack of effect of treating Helicobacter pylori infection in patients with nonulcer dyspepsia. Omeprazole plus Clarithromycin and Amoxicillin Effect One Year after Treatment (OCAY) Study Group.
It is uncertain whether treatment of Helicobacter pylori infection relieves symptoms in patients with nonulcer, or functional, dyspepsia. METHODS: We conducted a double-blind, multicenter trial of patients with H. pylori infection and dyspeptic symptoms (moderate-to-very-severe pain and discomfort centered in the upper abdomen). Patients were excluded if they had a history of peptic ulcer disease or gastroesophageal reflux disease and had abnormal findings on upper endoscopy. Patients were randomly assigned to seven days of treatment with 20 mg of omeprazole twice daily, 1000 mg of amoxicillin twice daily, and 500 mg of clarithromycin twice daily or with omeprazole alone and then followed up for one year. Treatment success was defined as the absence of dyspeptic symptoms or the presence of minimal symptoms on any of the 7 days preceding the 12-month visit. RESULTS: Twenty of the 348 patients were excluded after randomization because they were not infected with H. pylori, were not treated, or had no data available. For the remaining 328 patients (164 in each group), treatment was successful for 27.4 percent of those assigned to receive omeprazole and antibiotics and 20.7 percent of those assigned to receive omeprazole alone (P=0.17; absolute difference between groups, 6.7 percent; 95 percent confidence interval, -2.6 to 16.0). After 12 months, gastritis had healed in 75.0 percent of the patients in the group given omeprazole and antibiotics and in 3.0 percent of the patients in the omeprazole group (P<0.001); the respective rates of H. pylori eradication were 79 percent and 2 percent. In the group given omeprazole and antibiotics, the rate of treatment success among patients with persistent H. pylori infection was similar to that among patients in whom the infection was eradicated (26 percent vs. 31 percent). There were no significant differences between the groups in the quality of life after treatment. CONCLUSIONS: In patients with nonulcer dyspepsia, the eradication of H. pylori infection is not likely to relieve symptoms
Signatures of small-world and scale-free properties in large computer programs
A large computer program is typically divided into many hundreds or even
thousands of smaller units, whose logical connections define a network in a
natural way. This network reflects the internal structure of the program, and
defines the ``information flow'' within the program. We show that, (1) due to
its growth in time this network displays a scale-free feature in that the
probability of the number of links at a node obeys a power-law distribution,
and (2) as a result of performance optimization of the program the network has
a small-world structure. We believe that these features are generic for large
computer programs. Our work extends the previous studies on growing networks,
which have mostly been for physical networks, to the domain of computer
software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.
Spin dynamics of Mn12-acetate in the thermally-activated tunneling regime: ac-susceptibility and magnetization relaxation
In this work, we study the spin dynamics of Mn12-acetate molecules in the
regime of thermally assisted tunneling. In particular, we describe the system
in the presence of a strong transverse magnetic field. Similar to recent
experiments, the relaxation time/rate is found to display a series of
resonances; their Lorentzian shape is found to stem from the tunneling. The
dynamic susceptibility is calculated starting from the microscopic
Hamiltonian and the resonant structure manifests itself also in .
Similar to recent results reported on another molecular magnet, Fe8, we find
oscillations of the relaxation rate as a function of the transverse magnetic
field when the field is directed along a hard axis of the molecules. This
phenomenon is attributed to the interference of the geometrical or Berry phase.
We propose susceptibility experiments to be carried out for strong transverse
magnetic fields to study of these oscillations and for a better resolution of
the sharp satellite peaks in the relaxation rates.Comment: 22 pages, 23 figures; submitted to Phys. Rev. B; citations/references
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Measuring Black Hole Spin using X-ray Reflection Spectroscopy
I review the current status of X-ray reflection (a.k.a. broad iron line)
based black hole spin measurements. This is a powerful technique that allows us
to measure robust black hole spins across the mass range, from the stellar-mass
black holes in X-ray binaries to the supermassive black holes in active
galactic nuclei. After describing the basic assumptions of this approach, I lay
out the detailed methodology focusing on "best practices" that have been found
necessary to obtain robust results. Reflecting my own biases, this review is
slanted towards a discussion of supermassive black hole (SMBH) spin in active
galactic nuclei (AGN). Pulling together all of the available XMM-Newton and
Suzaku results from the literature that satisfy objective quality control
criteria, it is clear that a large fraction of SMBHs are rapidly-spinning,
although there are tentative hints of a more slowly spinning population at high
(M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of
the spins of stellar-mass black holes in X-ray binaries. In general,
reflection-based and continuum-fitting based spin measures are in agreement,
although there remain two objects (GROJ1655-40 and 4U1543-475) for which that
is not true. I end this review by discussing the exciting frontier of
relativistic reverberation, particularly the discovery of broad iron line
reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and
MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk
reflection, this detection of reverberation demonstrates that future large-area
X-ray observatories such as LOFT will make tremendous progress in studies of
strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The
Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds
a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the
referencing of the discovery of soft lags in 1H0707-495 (which were in fact
first reported in Fabian et al. 2009
Stellar structure and compact objects before 1940: Towards relativistic astrophysics
Since the mid-1920s, different strands of research used stars as "physics
laboratories" for investigating the nature of matter under extreme densities
and pressures, impossible to realize on Earth. To trace this process this paper
is following the evolution of the concept of a dense core in stars, which was
important both for an understanding of stellar evolution and as a testing
ground for the fast-evolving field of nuclear physics. In spite of the divide
between physicists and astrophysicists, some key actors working in the
cross-fertilized soil of overlapping but different scientific cultures
formulated models and tentative theories that gradually evolved into more
realistic and structured astrophysical objects. These investigations culminated
in the first contact with general relativity in 1939, when J. Robert
Oppenheimer and his students George Volkoff and Hartland Snyder systematically
applied the theory to the dense core of a collapsing neutron star. This
pioneering application of Einstein's theory to an astrophysical compact object
can be regarded as a milestone in the path eventually leading to the emergence
of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal
Star Formation and Dynamics in the Galactic Centre
The centre of our Galaxy is one of the most studied and yet enigmatic places
in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre
(GC) is the ideal environment to study the extreme processes that take place in
the vicinity of a supermassive black hole (SMBH). Despite the hostile
environment, several tens of early-type stars populate the central parsec of
our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and
inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the
SMBH (<0.04 pc), have randomly oriented and highly eccentric orbits. The
formation of such early-type stars has been a puzzle for a long time: molecular
clouds should be tidally disrupted by the SMBH before they can fragment into
stars. We review the main scenarios proposed to explain the formation and the
dynamical evolution of the early-type stars in the GC. In particular, we
discuss the most popular in situ scenarios (accretion disc fragmentation and
molecular cloud disruption) and migration scenarios (star cluster inspiral and
Hills mechanism). We focus on the most pressing challenges that must be faced
to shed light on the process of star formation in the vicinity of a SMBH.Comment: 68 pages, 35 figures; invited review chapter, to be published in
expanded form in Haardt, F., Gorini, V., Moschella, U. and Treves, A.,
'Astrophysical Black Holes'. Lecture Notes in Physics. Springer 201
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