2,748 research outputs found
Beating the Generator-Enumeration Bound for -Group Isomorphism
We consider the group isomorphism problem: given two finite groups G and H
specified by their multiplication tables, decide if G cong H. For several
decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the
smallest prime dividing the order of the group) has been the best worst-case
result for general groups. In this work, we show the first improvement over the
generator-enumeration bound for p-groups, which are believed to be the hard
case of the group isomorphism problem. We start by giving a Turing reduction
from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of p-group
composition-series isomorphism. By showing a Karp reduction from p-group
composition-series isomorphism to testing isomorphism of graphs of degree at
most p + O(1) and applying algorithms for testing isomorphism of graphs of
bounded degree, we obtain an n^(O(p)) time algorithm for p-group
composition-series isomorphism. Combining these two results yields an algorithm
for p-group isomorphism that takes at most n^((1 / 2) log_p n + O(p)) time.
This algorithm is faster than generator-enumeration when p is small and slower
when p is large. Choosing the faster algorithm based on p and n yields an upper
bound of n^((1 / 2 + o(1)) log n) for p-group isomorphism.Comment: 15 pages. This is an updated and improved version of the results for
p-groups in arXiv:1205.0642 and TR11-052 in ECC
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MPRAnalyze: statistical framework for massively parallel reporter assays.
Massively parallel reporter assays (MPRAs) can measure the regulatory function of thousands of DNA sequences in a single experiment. Despite growing popularity, MPRA studies are limited by a lack of a unified framework for analyzing the resulting data. Here we present MPRAnalyze: a statistical framework for analyzing MPRA count data. Our model leverages the unique structure of MPRA data to quantify the function of regulatory sequences, compare sequences' activity across different conditions, and provide necessary flexibility in an evolving field. We demonstrate the accuracy and applicability of MPRAnalyze on simulated and published data and compare it with existing methods
Analysis of the root system architecture of Arabidopsis provides a quantitative readout of crosstalk between nutritional signals
As plant roots forage the soil for food and water, they translate a multifactorial input of environmental stimuli into a multifactorial developmental output that manifests itself as root system architecture (RSA). Our current understanding of the underlying regulatory network is limited because root responses have traditionally been studied separately for individual nutrient deficiencies. In this study, we quantified 13 RSA parameters of Arabidopsis thaliana in 32 binary combinations of N, P, K, S, and light. Analysis of variance showed that each RSA parameter was determined by a typical pattern of environmental signals and their interactions. P caused the most important single-nutrient effects, while N-effects were strongly light dependent. Effects of K and S occurred mostly through nutrient interactions in paired or multiple combinations. Several RSA parameters were selected for further analysis through mutant phenotyping, which revealed combinations of transporters, receptors, and kinases acting as signaling modules in K–N interactions. Furthermore, nutrient response profiles of individual RSA features across NPK combinations could be assigned to transcriptionally coregulated clusters of nutrient-responsive genes in the roots and to ionome patterns in the shoots. The obtained data set provides a quantitative basis for understanding how plants integrate multiple nutritional stimuli into complex developmental programs
Low-Mass X-ray Binaries and Globular Clusters in Early-Type Galaxies. I. Chandra Observations
We present a Chandra survey of LMXBs in 24 early-type galaxies. Correcting
for detection incompleteness, the X-ray luminosity function (XLF) of each
galaxy is consistent with a powerlaw with negative logarithmic differential
slope, beta~2.0. However, beta strongly correlates with incompleteness,
indicating the XLF flattens at low-Lx. The composite XLF is well-fitted by a
powerlaw with a break at 2.21(+0.65,-0.56)E38 erg/s and beta=1.40(+0.10,-0.13)
and 2.84(+0.39,-0.30) below and above it, respectively. The break is close to
the Eddington limit for a 1.4Msun neutron-star, but the XLF shape rules out its
representing the division between neutron-star and black-hole systems. Although
the XLFs are similar, we find evidence of some variation between galaxies. The
high-Lx XLF slope does not correlate with age, but may correlate with
[alpha/Fe]. Considering only LMXBs with Lx>1E37 erg/s, matching the LMXBs with
globular clusters (GCs) identified in HST observations of 19 of the galaxies,
we find the probability a GC hosts an LMXB is proportional to LGC^alpha
ZFe^gamma} where alpha=1.01+/-0.19 and gamma=0.33+/-0.11. Correcting for GC
luminosity and colour effects, and detection incompleteness, we find no
evidence that the fraction of LMXBs with Lx>1e37 erg/s in GCs (40%), or the
fraction of GCs hosting LMXBs (~6.5%) varies between galaxies. The spatial
distribution of LMXBs resembles that of GCs, and the specific frequency of
LMXBs is proportional to the GC specific luminosity, consistent with the
hypothesis that all LMXBs form in GCs. If the LMXB lifetime is tau and the duty
cycle is Fd, our results imply ~1.5 (tau/1E8 yr)^-1 /Fd LMXBs are formed per
Gyr per GC and we place an upper limit of 1 active LMXB in the field per
3.4E9Lsun of V-band luminosity.Comment: 24 pages, 17 figures and 6 tables. Accepted for publication in the
Astrophysical Journal. Expanded discussion and various minor revisions to
improve robustness of results. Conclusions unchange
Kondo effect in spin-orbit mesoscopic interferometers
We consider a flux-threaded Aharonov-Bohm ring with an embedded quantum dot
coupled to two normal leads. The local Rashba spin-orbit interaction acting on
the dot electrons leads to a spin-dependent phase factor in addition to the
Aharonov-Bohm phase caused by the external flux. Using the numerical
renormalization group method, we find a splitting of the Kondo resonance at the
Fermi level which can be compensated by an external magnetic field. To fully
understand the nature of this compensation effect, we perform a scaling
analysis and derive an expression for the effective magnetic field. The
analysis is based on a tight-binding model which leads to an effective Anderson
model with a spin-dependent density of states for the transformed lead states.
We find that the effective field originates from the combined effect of Rashba
interaction and magnetic flux and that it contains important corrections due to
electron-electron interactions. We show that the compensating field is an
oscillatory function of both the spin-orbit and the Aharonov-Bohm phases.
Moreover, the effective field never vanishes due to the particle-hole symmetry
breaking independently of the gate voltage.Comment: 9 pages, 5 figure
Suppression of 2\pi\ phase-slip due to hidden zero modes in one dimensional topological superconductors
We study phase slips in one-dimensional topological superconducting wires.
These wires have been proposed as building blocks for topologically protected
qubits in which the quantum information is distributed over the length of the
device and thus is immune to local sources of decoherence. However, phase-slips
are non-local events that can result in decoherence. Phase slips in topological
superconductors are peculiar for the reason that they occur in multiples of
4\pi\ (instead of 2\pi\ in conventional superconductors). We re-establish this
fact via a beautiful analogy to the particle physics concept of dynamic
symmetry breaking by explicitly finding a "hidden" zero mode in the fermion
spectrum computed in the background of a 2\pi\ phase-slip. Armed with the
understanding of phase-slips in topological superconductors, we propose a
simple experimental setup with which the predictions can be tested by
monitoring tunneling rate of a superconducting flux quantum through a
topological superconducting wire.Comment: 18 pages,14 figures, Updated referenc
Erupting Cataclysmic Variable Stars in the Nearest Globular Cluster, NGC 6397: Intermediate Polars?
NGC 6397 is the closest globular cluster, and hence the ideal place to search
for faint stellar populations such as cataclysmic variables (CVs). HST and
Chandra observers have identified nine certain and likely CVs in this nearby
cluster, including several magnetic CV candidates. We have combined our recent
UV imagery with archival HST images of NGC 6397 to search for new CV candidates
and especially to look for dwarf nova-like eruptive events. We find remarkable
and somewhat unexpected dwarf nova-like eruptions of the two well-known
cataclysmic systems CV2 and CV3. These two objects have been claimed to be {\it
magnetic} CVs, as indicated by their helium emission-line spectra. Magnetic
fields in CVs are usually expected to prevent the disk instability that leads
to dwarf nova eruptions. In fact, most field magnetic CVs are observed to not
undergo eruptions. Our observations of the dwarf nova eruptions of CV2 and CV3
can be reconciled with these objects' HeII emission lines if both objects are
infrequently-erupting intermediate polars, similar to EX Hya. If this is the
case for most globular cluster CVs then we can reconcile the many X-ray and UV
bright CV candidates seen by Chandra and HST with the very small numbers of
erupting dwarf novae observed in cluster cores.Comment: 12 pages, 3 figures. Accepted for publication in The Astronomical
Journal. Two additional authors adde
History of the Innovation of Damage Control for Management of Trauma Patients: 1902-2016
Objective: To review the history of the innovation of damage control (DC) for management of trauma patients. Background: DC is an important development in trauma care that provides a valuable case study in surgical innovation. Methods: We searched bibliographic databases (1950-2015), conference abstracts (2009-2013), Web sites, textbooks, and bibliographies for articles relating to trauma DC. The innovation of DC was then classified according to the Innovation, Development, Exploration, Assessment, and Long-term study model of surgical innovation. Results: The innovation\u27\u27 of DC originated from the use of therapeutic liver packing, a practice that had previously been abandoned after World War II because of adverse events. It then developed\u27\u27 into abbreviated laparotomy using rapid conservative operative techniques.\u27\u27 Subsequent exploration\u27\u27 resulted in the application of DC to increasingly complex abdominal injuries and thoracic, peripheral vascular, and orthopedic injuries. Increasing use of DC laparotomy was followed by growing reports of postinjury abdominal compartment syndrome and prophylactic use of the open abdomen to prevent intra-abdominal hypertension after DC laparotomy. By the year 2000, DC surgery had been widely adopted and was recommended for use in surgical journals, textbooks, and teaching courses ( assessment\u27\u27 stage of innovation). Long-term study\u27\u27 of DC is raising questions about whether the procedure should be used more selectively in the context of improving resuscitation practices. Conclusions: The history of the innovation of DC illustrates how a previously abandoned surgical technique was adapted and readopted in response to an increased understanding of trauma patient physiology and changing injury patterns and trauma resuscitation practices
Mass-loaded spherical accretion flows
We have calculated the evolution of spherical accretion flows undergoing mass-loading from embedded clouds through either conduction or hydrodynamical ablation. We have observed the effect of varying the ratios of the mass-loading timescale and the cooling timescale to the ballistic crossing timescale through the mass-loading region.
We have also varied the ratio of the potential energy of a particle injected into the flow near the outer region of mass-loading to the temperature at which a minimum occurs in the cooling curve. The two types of mass-loading produce qualitatively different types of behaviour in the accretion flow, since mass-loading through conduction requires the ambient gas to be hot, whereas mass ablation from clumps occurs throughout the flow. Higher ratios of injected to accreted mass typically occur with hydrodynamical ablation, in agreement with previous work on wind-blown bubbles and supernova remnants. We find that mass-loading damps the radiative overstability of such flows, in agreement with our earlier work. If the mass-loading is high enough it can stabilize the accretion shock at a constant radius, yielding an almost isothermal subsonic post-shock flow. Such solutions may be relevant to cooling flows onto massive galaxies. Mass-loading can also lead to the formation of isolated shells of high temperature material, separated by gas at cooler temperatures
High resolution soft X-ray spectroscopy of the elliptical galaxy NGC 5044. Results from the reflection grating spectrometer on-board XMM-Newton
The results from an X-ray spectroscopic study of the giant elliptical galaxy
NGC5044 in the center of a galaxy group are presented. The line dominated soft
X-ray spectra (mainly Fe-L and O VIII Ly_a) from the diffuse gas are resolved
for the first time in this system with the Reflection Grating Spectrometers
on-board XMM-Newton and provide a strong constraint on the temperature
structure. The spectra integrated over 2' (\sim 20kpc) in full-width can be
described by a two temperature plasma model of 0.7keV and 1.1keV. Most of the
latter component is consistent with originating from off-center regions.
Compared to the isobaric cooling flow prediction, the observation shows a clear
cut-off below a temperature of 0.6 +-0.1keV. Furthermore, the Fe and O
abundances within the central 10--20kpc in radius are accurately measured to be
0.55+-0.05 and 0.25+-0.1 times the solar ratios, respectively. The observed
cut-off temperature of this galaxy and other central galaxies in galaxy groups
and clusters are compared with the scale of the galaxy and properties of the
surrounding intra-cluster medium. Based on this comparison, the origin of the
lack of predicted cool emission is discussed.Comment: Accepted for publication in Astronomy & Astrophysic
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