Computing normalisers of intransitive groups

Funding: The first and third authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Groups, Representations and Applications: New perspectives”, where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. This work was also partially supported by a grant from the Simons Foundation. The first and second authors are supported by the Royal Society (RGF\EA\181005 and URF\R\180015).The normaliser problem takes as input subgroups G and H of the symmetric group Sn, and asks one to compute NG(H). The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for restricted classes of groups. In this paper, we will focus on groups with many orbits. We give a new algorithm for the normaliser problem for these groups that performs many orders of magnitude faster than previous implementations in GAP. We also prove that the normaliser problem for the special case G=Sn  is at least as hard as computing the group of monomial automorphisms of a linear code over any field of fixed prime order.Publisher PDFPeer reviewe

Effect of genital herpes on cervicovaginal HIV shedding in women co-infected with HIV AND HSV-2 in Tanzania.

To compare the presence and quantity of cervicovaginal HIV among HIV seropositive women with clinical herpes, subclinical HSV-2 infection and without HSV-2 infection respectively; to evaluate the association between cervicovaginal HIV and HSV shedding; and identify factors associated with quantity of cervicovaginal HIV. Four groups of HIV seropositive adult female barworkers were identified and examined at three-monthly intervals between October 2000 and March 2003 in Mbeya, Tanzania: (1) 57 women at 70 clinic visits with clinical genital herpes; (2) 39 of the same women at 46 clinic visits when asymptomatic; (3) 55 HSV-2 seropositive women at 60 clinic visits who were never observed with herpetic lesions; (4) 18 HSV-2 seronegative women at 45 clinic visits. Associations of genital HIV shedding with HIV plasma viral load (PVL), herpetic lesions, HSV shedding and other factors were examined. Prevalence of detectable genital HIV RNA varied from 73% in HSV-2 seronegative women to 94% in women with herpetic lesions (geometric means 1634 vs 3339 copies/ml, p = 0.03). In paired specimens from HSV-2 positive women, genital HIV viral shedding was similar during symptomatic and asymptomatic visits. On multivariate regression, genital HIV RNA (log10 copies/mL) was closely associated with HIV PVL (β = 0.51 per log10 copies/ml increase, 95%CI:0.41-0.60, p<0.001) and HSV shedding (β = 0.24 per log10 copies/ml increase, 95% CI:0.16-0.32, p<0.001) but not the presence of herpetic lesions (β = -0.10, 95%CI:-0.28-0.08, p = 0.27). HIV PVL and HSV shedding were more important determinants of genital HIV than the presence of herpetic lesions. These data support a role of HSV-2 infection in enhancing HIV transmissibility

Wrong Turn in Cyberspace: Using ICANN to Route Around the APA and the Constitution

The Internet relies on an underlying centralized hierarchy built into the domain name system (DNS) to control the routing for the vast majority of Internet traffic. At its heart is a single data file, known as the root. Control of the root provides singular power in cyberspace. This Article first describes how the United States government found itself in control of the root. It then describes how, in an attempt to meet concerns that the United States could so dominate an Internet chokepoint, the U. S. Department of Commerce (DoC) summoned into being the Internet Corporation for Assigned Names and Numbers (ICANN), a formally private nonprofit California corporation. DoC then signed contracts with ICANN in order to clothe it with most of the U. S. government\u27s power over the DNS, and convinced other parties to recognize ICANN\u27s authority. ICANN then took regulatory actions that the U. S. Department of Commerce was unable or unwilling to make itself, including the imposition on all registrants of Internet addresses of an idiosyncratic set of arbitration rules and procedures that benefit third-party trademark holders. Professor Froomkin then argues that the use of ICANN to regulate in the stead of an executive agency violates fundamental values and policies designed to ensure democratic control over the use of government power, and sets a precedent that risks being expanded into other regulatory activities. He argues that DoC\u27s use of ICANN to make rules either violates the APA\u27s requirement for notice and comment in rulemaking and judicial review, or it violates the Constitution\u27s nondelegation doctrine. Professor Froomkin reviews possible alternatives to ICANN, and ultimately proposes a decentralized structure in which the namespace of the DNS is spread out over a transnational group of policy partners with DoC

Prominence formation and ejection in cool stars

We acknowledge STFC (ST/M001296/1) and H2020 (682393).The observational signatures of prominences have been detected in single and binary G and K type stars for many years now, but recently this has been extended to the M dwarf regime. Prominences carry away both mass and angular momentum when they are ejected and the impact of this mass on any orbiting planets may be important for the evolution of exoplanetary atmospheres. By means of the classification used in the massive star community, that involves knowledge of two parameters (the co-rotation and Alfvén radii, rK and rA), we have determined which cool stars could support prominences. From a model of mechanical support, we have determined that the prominence mass mp/M*=(EM/EG)(r*/rK)2F where EMB2⋆r3⋆ and EG=GM2⋆/r⋆ are magnetic and gravitational energies and F is a geometric factor. Our calculated masses and ejection frequencies (typically 1016−1017g and 0.4 d, respectively) are consistent with observations and are sufficient to ensure that an exoplanet orbiting in the habitable zone of an M dwarf could suffer frequent impacts.PostprintPeer reviewe

Charge distribution and electroluminescence in cross-linked polyethylene under dc field

The intent of this paper is to cross-correlate the information obtained by space charge distribution analysis and electroluminescence (EL) detection in cross-linked polyethylene samples submitted to dc fields, with the objective to make a link between space charge phenomena and energy release as revealed by the detection of visible photons. Space charge measurements carried out at different field levels by the pulsed electro-acoustic method show the presence of a low-field threshold, close to 15-20 kV mm-1, above which considerable space charge begins to accumulate in the insulation. Charges are seen to cross the insulation thickness through a packet-like behaviour at higher fields, starting at about 60-70 kV mm-1. EL measurements show the existence of two distinct thresholds, one related to the continuous excitation of EL under voltage, the other being transient EL detected upon specimen short circuit. The former occurs at values of field corresponding to charge packet formation and the latter to the onset of space charge accumulation. The correspondence between pertinent values of the electric field obtained through space charge and EL analyses provides support for the existence of degradation thresholds in insulating materials. Special emphasis is given to the relationship between charge packet formation and propagation, and EL. Although the two phenomena are observed in the same field range, it is found that the onset of continuous EL follows the formation at the electrodes of positive and negative space charge regions that extend into the bulk prior to the propagation of charge packets. Charge recombination appears to be the excitation process of EL since oppositely charged domains meet in the material bulk. To gain an insight into specific light-excitation processes associated with charge packet propagation, EL has been recorded for several hours under fields at which charge packet dynamics were evidenced. It is shown that current and luminescence oscillations are detected during charge packet propagation, and that they are in phase. The mechanisms underlying EL and charge packets are further considered on the basis of these results