Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of arbitrary skew-symmetric matrices that is well suited both for the numeric and symbolic evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90) implementing both methods are given. We also provide simple implementations in Python and Mathematica for purpose of testing, or for exploratory studies of methods that make use of pfaffians.Comment: 13 pages, Download links: http://gamma.ft.uam.es/robledo/Downloads.html and http://www.phys.washington.edu/users/bertsch/computer.htm

Superradiance mediated by Graphene Surface Plasmons

We demonstrate that the interaction between two emitters can be controlled by means of the efficient excitation of surface plasmon modes in graphene. We consider graphene surface plasmons supported by either two-dimensional graphene sheets or one-dimensional graphene ribbons, showing in both cases that the coupling between the emitters can be strongly enhanced or suppressed. The super- and subradiant regimes are investigated in the reflection and transmission configurations. Importantly, the length scale of the coupling between emitters, which in vacuum is fixed by the free space wavelength, is now determined by the wavelength of the graphene surface plasmons that can be extremely short and be tuned at will via a gate voltage

Familial component of early-onset colorectal cancer: opportunity for prevention

[Background]: Individuals with a non-syndromic family history of colorectal cancer are known to have an increased risk. There is an opportunity to prevent early-onset colorectal cancer (age less than 50 years) (EOCRC) in this population. The aim was to explore the proportion of EOCRC that is preventable due to family history of colorectal cancer. [Methods]: This was a retrospective multicentre European study of patients with non-hereditary EOCRC. The impact of the European Society of Gastrointestinal Endoscopy (ESGE), U.S. Multi-Society Task Force (USMSTF), and National Comprehensive Cancer Network (NCCN) guidelines on prevention and early diagnosis was compared. Colorectal cancer was defined as potentially preventable if surveillance colonoscopy would have been performed at least 5 years before the age of diagnosis of colorectal cancer, and diagnosed early if colonoscopy was undertaken between 1 and 4 years before the diagnosis. [Results]: Some 903 patients with EOCRC were included. Criteria for familial colorectal cancer risk in ESGE, USMSTF, and NCCN guidelines were met in 6.3, 9.4, and 30.4 per cent of patients respectively. Based on ESGE, USMSTF, and NCCN guidelines, colorectal cancer could potentially have been prevented in 41, 55, and 30.3 per cent of patients, and diagnosed earlier in 11, 14, and 21.1 per cent respectively. In ESGE guidelines, if surveillance had started 10 years before the youngest relative, there would be a significant increase in prevention (41 versus 55 per cent; P = 0.010). [Conclusion]: ESGE, USMSTF, and NCCN criteria for familial colorectal cancer were met in 6.3, 9.4, and 30.4 per cent of patients with EOCRC respectively. In these patients, early detection and/or prevention could be achieved in 52, 70, and 51.4 per cent respectively. Early and accurate identification of familial colorectal cancer risk and increase in the uptake of early colonoscopy are key to decreasing familial EOCRC.This study was funded by Instituto de Salud Carlos III through project PI20/0974 to J.P and PI19/01867 to F.B. (co-funded by European Regional Development Fund ‘A way to make Europe’); and Agència de Gestió d’Ajuts Universitaris i de Recerca (Generalitat de Catalunya, GRC 2017SGR653). Centro de Investigación Biomédica en Red de Enfermedades Hepáticas y Digestivas is funded by the Instituto de Salud Carlos III