Heuristics for The Whitehead Minimization Problem

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead's minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-minimal elements in a free group can be reduced by a Nielsen automorphism which can be identified by inspecting the structure of the corresponding Whitehead Graph

The dominant X-ray wind in massive star binaries

We investigate which shocked wind is responsible for the majority of the X-ray emission in colliding wind binaries, an issue where there is some confusion in the literature, and which we show is more complicated than has been assumed. We find that where both winds rapidly cool (typically close binaries), the ratio of the wind speeds is often more important than the momentum ratio, because it controls the energy flux ratio, and the faster wind is generally the dominant emitter. When both winds are largely adiabatic (typically long-period binaries), the slower and denser wind will cool faster and the stronger wind generally dominates the X-ray luminosity.Comment: 4 pages, 1 figure, accepted by A&A Letter

A Practical Cryptanalysis of the Algebraic Eraser

Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.Comment: 15 pages. Updated references, with brief comments added. Minor typos corrected. Final version, accepted for CRYPTO 201

Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation

Density of states, dynamic (optical) conductivity and phase diagram of paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean-field theory (DMFT+Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular "bare" density of states (DOS). The DMFT effective single impurity problem is solved by numerical renormalization group (NRG). Phases of "correlated metal", Mott insulator and correlated Anderson insulator are identified from the evolution of density of states, optical conductivity and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of the finite size, allowing us to construct the complete zero-temperature phase diagram of paramagnetic Anderson-Hubbard model. Localization length in our approximation is practically independent of the strength of Hubbard correlations. However, the divergence of localization length in finite size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.Comment: 10 pages, 10 figures, improve phase diagra

Mass-Loss Rate Determination for the Massive Binary V444 Cyg using 3-D Monte-Carlo Simulations of Line and Polarization Variability

A newly developed 3-D Monte Carlo model is used, in conjunction with a multi-line non-LTE radiative transfer model, to determine the mass-loss rate of the Wolf-Rayet (W-R) star in the massive binary \object{V444 Cyg} (WN5+O6). This independent estimate of mass-loss rate is attained by fitting the observed \HeI (5876) \AA and \HeII (5412) \AA line profiles, and the continuum light curves of three Stokes parameters ((I, Q, U)) in the (V) band simultaneously. The high accuracy of our determination arises from the use of many observational constraints, and the sensitivity of the continuum polarization to the mass-loss rate. Our best fit model suggests that the mass-loss rate of the system is (\dot{M}_{\WR}=0.6(\pm 0.2) \times 10^{-5} M_{\sun} \mathrm{yr}^{-1} ), and is independent of the assumed distance to \object{V444 Cyg}. The fits did not allow a unique value for the radius of the W-R star to be derived. The range of the volume filling factor for the W-R star atmosphere is estimated to be in the range of 0.050 (for R_{\WR}=5.0 R_{\sun}) to 0.075 (for R_{\WR}=2.5 R_{\sun}). We also found that the blue-side of \HeI (5876 ) \AA and \HeII (5412) \AA lines at phase 0.8 is relatively unaffected by the emission from the wind-wind interaction zone and the absorption by the O-star atmosphere; hence, the profiles at this phase are suitable for spectral line fittings using a spherical radiative transfer model.Comment: 18 pages, 17 figures: Accepeted for publication in A&

Mott-Hubbard Transition and Anderson Localization: Generalized Dynamical Mean-Field Theory Approach

Density of states, dynamic (optical) conductivity and phase diagram of strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of self-consistent theory of localization. The DMFT effective single impurity problem is solved by numerical renormalization group (NRG) and we consider the three-dimensional system with semi-elliptic density of states. Correlated metal, Mott insulator and correlated Anderson insulator phases are identified via the evolution of density of states and dynamic conductivity, demonstrating both Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of complete zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the possibility of disorder induced Mott insulator to metal transition.Comment: 15 pages, 16 figure

Numerical heat conduction in hydrodynamical models of colliding hypersonic flows

Hydrodynamical models of colliding hypersonic flows are presented which explore the dependence of the resulting dynamics and the characteristics of the derived X-ray emission on numerical conduction and viscosity. For the purpose of our investigation we present models of colliding flow with plane-parallel and cylindrical divergence. Numerical conduction causes erroneous heating of gas across the contact discontinuity which has implications for the rate at which the gas cools. We find that the dynamics of the shocked gas and the resulting X-ray emission are strongly dependent on the contrast in the density and temperature either side of the contact discontinuity, these effects being strongest where the postshock gas of one flow behaves quasi-adiabatically while the postshock gas of the other flow is strongly radiative. Introducing additional numerical viscosity into the simulations has the effect of damping the growth of instabilities, which in some cases act to increase the volume of shocked gas and can re-heat gas via sub-shocks as it flows downstream. The resulting reduction in the surface area between adjacent flows, and therefore of the amount of numerical conduction, leads to a commensurate reduction in spurious X-ray emission, though the dynamics of the collision are compromised. The simulation resolution also affects the degree of numerical conduction. A finer resolution better resolves the interfaces of high density and temperature contrast and although numerical conduction still exists the volume of affected gas is considerably reduced. However, since it is not always practical to increase the resolution, it is imperative that the degree of numerical conduction is understood so that inaccurate interpretations can be avoided. This work has implications for the dynamics and emission from astrophysical phenomena which involve high Mach number shocks.Comment: 14 pages, 10 figures, accepted for publication in MNRA

Quasi-simultaneous XMM-Newton and VLA observation of the non-thermal radio emitter HD\168112 (O5.5III(f^+))

We report the results of a multiwavelength study of the non-thermal radio emitter HD168112 (O5.5III(f^+)). The detailed analysis of two quasi-simultaneous XMM-Newton and VLA observations reveals strong variability of this star both in the X-ray and radio ranges. The X-ray observations separated by five months reveal a decrease of the X-ray flux of ~30%. The radio emission on the other hand increases by a factor 5-7 between the two observations obtained roughly simultaneously with the XMM-Newton pointings. The X-ray data reveal a hard emission that is most likely produced by a thermal plasma at kT ~2-3 keV while the VLA data confirm the non-thermal status of this star in the radio waveband. Comparison with archive X-ray and radio data confirms the variability of this source in both wavelength ranges over a yet ill defined time scale. The properties of HD168112 in the X-ray and radio domain point towards a binary system with a significant eccentricity and an orbital period of a few years. However, our optical spectra reveal no significant changes of the star's radial velocity suggesting that if HD168112 is indeed a binary, it must be seen under a fairly low inclination.Comment: 17 pages, 11 figures (10 postscript + 1 gif

Discriminating Groups

A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups

EXTENDED COREY-CHAYKOVSKY REACTION AS A PATHWAY FOR THE SYNTHESIS OF SUBSTITUTED FURANS

This work was supported by RSF № 21-73-10063