A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Assessment of patient-derived tumour xenografts (PDXs) as a discovery tool for cancer epigenomics

Background: The use of tumour xenografts is a well-established research tool in cancer genomics but has not yet been comprehensively evaluated for cancer epigenomics. Methods: In this study, we assessed the suitability of patient-derived tumour xenografts (PDXs) for methylome analysis using Infinium 450 K Beadchips and MeDIP-seq. Results: Controlled for confounding host (mouse) sequences, comparison of primary PDXs and matching patient tumours in a rare (osteosarcoma) and common (colon) cancer revealed that an average 2.7% of the assayed CpG sites undergo major (Δβ ≥ 0.51) methylation changes in a cancer-specific manner as a result of the xenografting procedure. No significant subsequent methylation changes were observed after a second round of xenografting between primary and secondary PDXs. Based on computational simulation using publically available methylation data, we additionally show that future studies comparing two groups of PDXs should use 15 or more samples in each group to minimise the impact of xenografting-associated changes in methylation on comparison results. Conclusions: Our results from rare and common cancers indicate that PDXs are a suitable discovery tool for cancer epigenomics and we provide guidance on how to overcome the observed limitations

Entropic Interactions in Suspensions of Semi-Flexible Rods: Short-Range Effects of Flexibility

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semi-flexible rods. Our model treats the semi-flexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of fd-virus is about two to three times smaller than the commonly used value of $2.2 \mu {m}$.Comment: 4 pages, 5 figures, submitted to PRE rapid communication

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

Dark matter halos and the anisotropy of ultra-high energy cosmic rays

Several explanations for the existence of Ultra High Energy Cosmic Rays invoke the idea that they originate from the decay of massive particles created in the reheating following inflation. It has been suggested that the decay products can explain the observed isotropic flux of cosmic rays. We have calculated the anisotropy expected for various models of the dark matter distribution and find that at present data are too sparse above $4 \times 10^{19}$ eV to discriminate between different models. However we show that with data from three years of operation of the southern section of the Pierre Auger Observatory significant progress in testing the proposals will be made.Comment: 21 pages, 6 figures (ps), Astroparticle Physics (accepted for publication

Gauge fixing and the Hamiltonian for cylindrical spacetimes

We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one of them rotational and the other one translational. The result of our gauge fixing is a constraint-free model whose phase space has four field-like degrees of freedom and that depends on three constant parameters. Two of these constants determine the global angular momentum and the linear momentum in the axis direction, while the third parameter is related with the behavior of the metric around the axis. We derive the explicit expression of the metric in terms of the physical degrees of freedom, calculate the reduced equations of motion and obtain the Hamiltonian that generates the reduced dynamics. We also find upper and lower bounds for this reduced Hamiltonian that provides the energy per unit length contained in the system. In addition, we show that the reduced formalism constructed is well defined and consistent at least when the linear momentum in the axis direction vanishes. Furthermore, in that case we prove that there exists an infinite number of solutions in which all physical fields are constant both in the surroundings of the axis and at sufficiently large distances from it. If the global angular momentum is different from zero, the isometry group of these solutions is generally not orthogonally transitive. Such solutions generalize the metric of a spinning cosmic string in the region where no closed timelike curves are present.Comment: 12 pages, accepted for publication in Physical Review

The clustering of ultra-high energy cosmic rays and their sources

The sky distribution of cosmic rays with energies above the 'GZK cutoff' holds important clues to their origin. The AGASA data, although consistent with isotropy, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as sources. It has also been suggested that clusters can arise if the cosmic rays come from the decays of very massive relic particles in the Galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are in fact not justified.Comment: 13 pages, 8 figures, version in press at Phys. Rev.

Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the following expression for the entropy: S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv -k\sum_{i=1}^W p_i \ln p_i) . The author of [1] already presented orally the essence of his arguments in 1993 during a scientific meeting in Buenos Aires. I am replying now simultaneously to the just cited paper, as well as to the 1993 objections (essentially, the violation of "fundamental thermodynamic concepts", as stated in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys. Rev. E 67, 036114 (2003

Charge-Symmetry Violation in Pion Scattering from Three-Body Nuclei

We discuss the experimental and theoretical status of charge-symmetry violation (CSV) in the elastic scattering of pi+ and pi- on 3H and 3He. Analysis of the experimental data for the ratios r1, r2, and R at Tpi = 142, 180, 220, and 256 MeV provides evidence for the presence of CSV. We describe pion scattering from the three-nucleon system in terms of single- and double-scattering amplitudes. External and internal Coulomb interactions as well as the Delta-mass splitting are taken into account as sources of CSV. Reasonable agreement between our theoretical calculations and the experimental data is obtained for Tpi = 180, 220, and 256 MeV. For these energies, it is found that the Delta-mass splitting and the internal Coulomb interaction are the most important contributions for CSV in the three-nucleon system. The CSV effects are rather sensitive to the choice of pion-nuclear scattering mechanisms, but at the same time, our theoretical predictions are much less sensitive to the choice of the nuclear wave function. It is found, however, that data for r2 and R at Tpi = 142 MeV do not agree with the predictions of our model, which may indicate that there are additional mechanisms for CSV which are important only at lower energies.Comment: 26 pages of RevTeX, 16 postscript figure

Nonextensivity of the cyclic Lattice Lotka Volterra model

We numerically show that the Lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a {\it finite} production, per unit time, of the nonextensive entropy $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i \ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode (growing droplet), and for $q=0$ for the $d=1$ one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is for the first time exhibited for a many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure