Beating the Generator-Enumeration Bound for pp-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

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