3,669 research outputs found
Uniform infinite planar triangulation and related time-reversed critical branching process
We establish a connection between the uniform infinite planar triangulation
and some critical time-reversed branching process. This allows to find a
scaling limit for the principal boundary component of a ball of radius R for
large R (i.e. for a boundary component separating the ball from infinity). We
show also that outside of R-ball a contour exists that has length linear in R.Comment: 27 pages, 5 figures, LaTe
The Discovery of Cepheids and a New Distance to NGC 2841 Using the Hubble Space Telescope
We report on the discovery of Cepheids in the spiral galaxy NGC 2841, based
on observations made with the Wide Field and Planetary Camera 2 on board the
Hubble Space Telescope. NGC 2841 was observed over 12 epochs using the F555W
filter, and over 5 epochs using the F814W filter. Photometry was performed
using the DAOPHOT/ALLFRAME package.
We discovered a total of 29 variables, including 18 high-quality Cepheids
with periods ranging from 15 to 40 days. Period-luminosity relations in the V
and I bands, based on the high-quality Cepheids, yield an extinction-corrected
distance modulus of 30.74 +/- 0.23 mag, which corresponds to a distance of 14.1
+/- 1.5 Mpc. Our distance is based on an assumed LMC distance modulus of 18.50
+/- 0.10 mag (D = 50+/- 2.5 kpc) and a metallicity dependence of the Cepheid
P-L relation of gamma (VI) = -0.2 +/- 0.2 mag/dex.Comment: 31 preprint pages including 10 figures. Accepted for publication in
ApJ. High-resolution version available from
http://cfa-www.harvard.edu/~lmacri/n2841.p
Recent origin of low trabecular bone density in modern humans
Humans are unique, compared with our closest living relatives (chimpanzees) and early fossil hominins, in having an enlarged body size and lower limb joint surfaces in combination with a relatively gracile skeleton (i.e., lower bone mass for our body size). Some analyses have observed that in at least a few anatomical regions modern humans today appear to have relatively low trabecular density, but little is known about how that density varies throughout the human skeleton and across species or how and when the present trabecular patterns emerged over the course of human evolution. Here, we test the hypotheses that (i) recent modern humans have low trabecular density throughout the upper and lower limbs compared with other primate taxa and (ii) the reduction in trabecular density first occurred in early Homo erectus, consistent with the shift toward a modern human locomotor anatomy, or more recently in concert with diaphyseal gracilization in Holocene humans. We used peripheral quantitative CT and microtomography to measure trabecular bone of limb epiphyses (long bone articular ends) in modern humans and chimpanzees and in fossil hominins attributed to Australopithecus africanus, Paranthropus robustus/early Homo from Swartkrans, Homo neanderthalensis, and early Homo sapiens. Results show that only recent modern humans have low trabecular density throughout the limb joints. Extinct hominins, including pre-Holocene Homo sapiens, retain the high levels seen in nonhuman primates. Thus, the low trabecular density of the recent modern human skeleton evolved late in our evolutionary history, potentially resulting from increased sedentism and reliance on technological and cultural innovations
Distinguishing cancerous from non-cancerous cells through analysis of electrical noise
Since 1984, electric cell-substrate impedance sensing (ECIS) has been used to
monitor cell behavior in tissue culture and has proven sensitive to cell
morphological changes and cell motility. We have taken ECIS measurements on
several cultures of non-cancerous (HOSE) and cancerous (SKOV) human ovarian
surface epithelial cells. By analyzing the noise in real and imaginary
electrical impedance, we demonstrate that it is possible to distinguish the two
cell types purely from signatures of their electrical noise. Our measures
include power-spectral exponents, Hurst and detrended fluctuation analysis, and
estimates of correlation time; principal-component analysis combines all the
measures. The noise from both cancerous and non-cancerous cultures shows
correlations on many time scales, but these correlations are stronger for the
non-cancerous cells.Comment: 8 pages, 4 figures; submitted to PR
Scaling functions from q-deformed Virasoro characters
We propose a renormalization group scaling function which is constructed from
q-deformed fermionic versions of Virasoro characters. By comparison with
alternative methods, which take their starting point in the massive theories,
we demonstrate that these new functions contain qualitatively the same
information. We show that these functions allow for RG-flows not only amongst
members of a particular series of conformal field theories, but also between
different series such as N=0,1,2 supersymmetric conformal field theories. We
provide a detailed analysis of how Weyl characters may be utilized in order to
solve various recurrence relations emerging at the fixed points of these flows.
The q-deformed Virasoro characters allow furthermore for the construction of
particle spectra, which involve unstable pseudo-particles.Comment: 31 pages of Latex, 5 figure
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula
on an orbifolded 2-sphere is elaborated and extended to higher dimensions using
the known heat-kernel coefficients for manifolds with piecewise-linear
boundaries. Several results are obtained that relate the coefficients, ,
in the Shephard-Todd polynomial to the geometry of the fundamental domain. For
the 3-sphere we show that is given by the ratio of the volume of the
fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected
Fermi-Dirac statistics and the number theory
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap
to partitions of given integers into distinct parts, studied in number theory.
Using methods of quantum statistical physics we derive analytic expressions for
cumulants of the probability distribution of the number of different
partitions.Comment: 7pages, 2 figures, epl.cls, revised versio
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