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

A non-constructive proof of the Four Colour Theorem

The approach is through a singularity analysis of generating functions for 3- and 4-connected triangulations, asymptotic analysis, properties of the ${{}_3F_2}$ hypergeometric series, and Tutte's enumerative work on planar maps and chromatic polynomials

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, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ 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