Identifying Transiting Circumbinary Planets

Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit, making BLS [Kovacs et al. 2002] almost ineffective. Therefore, a modified version for the identification of CB planets was developed - CB-BLS. We show that using CB-BLS it is possible to find CB planets in the residuals of light curves of eclipsing binaries (EBs) that have noise levels of 1% or more. Using CB-BLS will allow to easily harness the massive ground- and space- based photometric surveys to look for these objects. Detecting transiting CB planets is expected to have a wide range of implications, for e.g.: The frequency of CB planets depend on the planetary formation mechanism - and planets in close pairs of stars provides a most restrictive constraint on planet formation models. Furthermore, understanding very high precision light curves is limited by stellar parameters - and since for EBs the stellar parameters are much better determined, the resultant planetary structure models will have significantly smaller error bars, maybe even small enough to challenge theory.Comment: To appear on the IAU Symposium 253 proceedings. 4 pages, 4 figure

Small derived quotients in finite p-groups

More than 70 years ago, P. Hall showed that if $G$ is a finite $p$-group such that a term \der G{d+1} of the derived series is non-trivial, then the order of the quotient \der Gd/\der G{d+1} is at least $p^{2^d+1}$. Recently Mann proved that, in a finite $p$-group, Hall's lower bound can be taken for at most two distinct $d$. We improve this result and show that if $p$ is odd, then it can only be taken for two distinct $d$ in a group with order $p^6$.Comment: Two related papers have been submitted. The material have been reorganised for Versions 2 and results migrated between paper

Heartbreak hotel: a convergence in cardiac regeneration

In February 2016, the Company of Biologists hosted an intimate gathering of leading international researchers at the forefront of experimental cardiovascular regeneration, with its emphasis on ‘Transdifferentiation and Tissue Plasticity in Cardiovascular Rejuvenation’. As I review here, participants at the workshop revealed how understanding cardiac growth and lineage decisions at their most fundamental level has transformed the strategies in hand that presently energize the prospects for human heart repair

Polynomial sequences of binomial-type arising in graph theory

In this paper, we show that the solution to a large class of "tiling" problems is given by a polynomial sequence of binomial type. More specifically, we show that the number of ways to place a fixed set of polyominos on an $n\times n$ toroidal chessboard such that no two polyominos overlap is eventually a polynomial in $n$, and that certain sets of these polynomials satisfy binomial-type recurrences. We exhibit generalizations of this theorem to higher dimensions and other lattices. Finally, we apply the techniques developed in this paper to resolve an open question about the structure of coefficients of chromatic polynomials of certain grid graphs (namely that they also satisfy a binomial-type recurrence).Comment: 15 page

Magnetic Field induced Dimensional Crossover Phenomena in Cuprate Superconductors and their Implications

We discuss the occurrence of crossing points in the magnetization - temperature $(m,T$) plane within the framework of critical phenomena. It is shown that in a two-dimensional superconducting slab of thickness $d_{s}$ $m_{z}(\delta)$ versus temperature $T$ curves measured in different fields $\mathbf{H} = H(0,\sin (\delta) ,\cos (\delta))$ will cross at the critical temperature T_c of the slab. In contrast, in a 3D anisotropic bulk superconductor the crossing point occurs in the plot $m_{z}(\delta) /H_{z}^{1/2}$ versus $T$. The experimental facts that 2D crossing point features have been observed in ceramics and in single crystals for $\mathbf{H}$ close to $\mathbf{H} = H(0,0,1)$, but not for $\mathbf{H} = H(0,1,0)$, is explained in terms of an angle-dependent crossover field separating the regions where 2D or 3D thermal fluctuations dominate. The measured 2D-crossing point data are used to estimate one of the fundamental parameters of cuprate superconductors, the minimum thickness of the slab $(d_{s})$, which remains superconducting. Our estimates, based on experimental 2D-crossing point data for single crystals, reveal that this length adopts material dependent values. Therefore, experimental data for T_c and $\lambda_{\Vert}^{2}(T=0)$, plotted in terms of T_c versus $1/\lambda_{\Vert}^{2}(T=0)$ will not tend to a straight line with universal slope as the underdoped limit is approached. Implications for magnetic torque measurements are also worked out