A geometric view of cryptographic equation solving

This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods

Anatomy of Ursa Majoris

A nearby friable cloud in Ursa Majoris contains 270 galaxies with radial velocities 500 < VLG < 1500 km s^-1 inside the area of RA= [11h; 13h] and DEC= [+40deg; +60deg]. At present, 97 galaxies of them have individual distance estimates. We use these data to clarify the structure and kinematics of the UMa complex. According to Makarov & Karachentsev (2011), most of the UMa galaxies belong to seven bound groups, which have the following median parameters: velocity dispersion of 58 km s^-1, harmonic projected radius of 300 kpc, virial mass of 2.10^12 Msol, and virial- mass-to-K-band-luminosity of 27Msol/Lsol. Almost a half of the UMa cloud population are gas-rich dwarfs (Ir, Im, BCD) with active star formation seen in the GALEX UV-survey. The UMa groups reside within 15-19 Mpc from us, being just at the same distance as Virgo cluster. The total virial mass of the UMa groups is 4.10^13 Msol, yielding the average density of dark matter in the UMa cloud to be Omega_m = 0.08, i.e. a factor three lower than the cosmic average. This is despite the fact that the UMa cloud resides in a region of the Universe that is an apparent overdensity. A possible explanation for this is that most mass in the Universe lies in the empty space between clusters. Herewith, the mean distances and velocities of the UMa groups follow nearly undisturbed Hubble flow without a sign of the 'Z-wave" effect caused by infall toward a massive attractor. This constrains the total amount of dark matter between the UMa groups within the cloud volume.Comment: correction of a typo in the abstract, 18 pages, 2 figures. accepted for MNRAS, nov 26, 201

What trends exist in regional housing market data?

While analysts have devoted much attention to housing market performance at the national, state, and even local level, far less attention has been paid to housing markets at the regional level. We investigate how regional vacancies, population, net migration, and other demographic variables have affected regional housing activity over several recent business cycles.Business cycles ; Housing

The Mid-Infrared Tully-Fisher Relation: Calibration of the SNIa Scale and Ho

This paper builds on a calibration of the SNIa absolute distance scale begun with a core of distances based on the correlation between galaxy rotation rates and optical Ic band photometry. This new work extends the calibration through the use of mid-infrared photometry acquired at 3.6 microns with Spitzer Space Telescope. The great virtue of the satellite observations is constancy of the photometry at a level better than 1% across the sky. The new calibration is based on 39 individual galaxies and 8 clusters that have been the sites of well observed SNIa. The new 3.6 micron calibration is not yet as extensively based as the Ic band calibration but is already sufficient to justify a preliminary report. Distances based on the mid-infrared photometry are 2% greater in the mean than reported at Ic band. This difference is only marginally significant. The Ic band result is confirmed with only a small adjustment. Incorporating a 1% decrease in the LMC distance, the present study indicates Ho = 75.2 +/- 3.0 km/s/Mpc.Comment: Accepted for publication in The Astrophysical Journal Letters, 6 pages, 2 figure

Giant disk galaxies : Where environment trumps mass in galaxy evolution

We identify some of the most HI massive and fastest rotating disk galaxies in the local universe with the aim of probing the processes that drive the formation of these extreme disk galaxies. By combining data from the Cosmic Flows project, which has consistently reanalyzed archival galaxy HI profiles, and 3.6$\mu$m photometry obtained with the Spitzer Space Telescope, with which we can measure stellar mass, we use the baryonic Tully-Fisher (BTF) relationship to explore whether these massive galaxies are distinct. We discuss several results, but the most striking is the systematic offset of the HI-massive sample above the BTF. These galaxies have both more gas and more stars in their disks than the typical disk galaxy of similar rotational velocity. The "condensed" baryon fraction, $f_C$, the fraction of the baryons in a dark matter halo that settle either as cold gas or stars into the disk, is twice as high in the HI-massive sample than typical, and almost reaches the universal baryon fraction in some cases, suggesting that the most extreme of these galaxies have little in the way of a hot baryonic component or cold baryons distributed well outside the disk. In contrast, the star formation efficiency, measured as the ratio of the mass in stars to that in both stars and gas, shows no difference between the HI-massive sample and the typical disk galaxies. We conclude that the star formation efficiency is driven by an internal, self-regulating process, while $f_C$ is affected by external factors. We also found that the most massive HI detected galaxies are located preferentially in filaments. We present the first evidence of an environmental effect on galaxy evolution using a dynamical definition of a filament.Comment: 14 pages, in press MNRA

Bimodality of Galaxy Disk Central Surface Brightness Distribution in the Spitzer 3.6 micron band

We report on measurements of the disk central surface brightnesses (mu0) at 3.6 microns for 438 galaxies selected by distance and absolute magnitude cutoffs from the 2350+ galaxies in the Spitzer Survey of Stellar Structure in Galaxies (S4G), one of the largest and deepest homogeneous mid-infrared datasets of nearby galaxies. Our sample contains nearly 3 times more galaxies than the most recent study of the mu0 distribution. We demonstrate that there is a bimodality in the distribution of mu0. Between the low and high surface brightness galaxy regimes there is a lack of intermediate surface brightness galaxies. Caveats invoked in the literature from small number statistics to the knowledge of the environmental influences, and possible biases from low signal to noise data or corrections for galaxy inclination are investigated. Analyses show that the bimodal distribution of mu0 cannot be due to any of these biases or statistical fluctuations. It is highly probable that galaxies settle in two stable modes: a dark matter dominated mode where the dark matter dominates at all radii - this gives birth to low surface brightness galaxies - and a baryonic matter dominated mode where the baryons dominate the dark matter in the central parts - this gives rise to the high surface brightness disks. The lack of intermediate surface brightness objects suggests that galaxies avoid (staying in) a mode where dark matter and baryons are co-dominant in the central parts of galaxies.Comment: Accepted for publication in MNRAS, 9 pages, 10 figures, 1 tabl

The mid-infrared Tully-Fisher relation: Spitzer Surface Photometry

The availability of photometric imaging of several thousand galaxies with the Spitzer Space Telescope enables a mid-infrared calibration of the correlation between luminosity and rotation in spiral galaxies. The most important advantage of the new calibration in the 3.6 micron band, IRAC ch.1, is photometric consistency across the entire sky. Additional advantages are minimal obscuration, observations of flux dominated by old stars, and sensitivity to low surface brightness levels due to favorable backgrounds. Through Spitzer cycle 7 roughly 3000 galaxies had been observed and images of these are available at the Spitzer archive. In cycle 8 a program called Cosmic Flows with Spitzer has been initiated that will increase by 1274 the available sample of spiral galaxies with inclinations greater than 45 degrees from face-on suitable for distance measurements. This paper describes procedures based on the photometry package Archangel that are being employed to analyze both the archival and the new data in a uniform way. We give results for 235 galaxies, our calibrator sample for the Tully-Fisher relation. Galaxy magnitudes are determined with uncertainties held below 0.05 mag for normal spiral systems. A subsequent paper will describe the calibration of the [3.6] luminosity-rotation relation.Comment: Accepted for publication in The Astronomical Journal, 12 pages, 9 figure

The Josephson critical current in a long mesoscopic S-N-S junction

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/\epsilon_{c}$ and $k_{B}T/\epsilon_{c}$ where $\epsilon_{c}$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.Comment: 5 pages, 4 figures, slighly modified version, publishe