2,641 research outputs found
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 3.6m 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, , 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 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 and where
is the Thouless energy. Experimental and theoretical results are in excellent
quantitative agreement.Comment: 5 pages, 4 figures, slighly modified version, publishe
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