Sensitive Dependence on Parameters of Continuous-time Nonlinear Dynamical Systems

We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Peer reviewedPostprin

A robust classifier of high predictive value to identify good prognosis patients in ER-negative breast cancer.

INTRODUCTION: Patients with primary operable oestrogen receptor (ER) negative (-) breast cancer account for about 30% of all cases and generally have a worse prognosis than ER-positive (+) patients. Nevertheless, a significant proportion of ER- cases have favourable outcomes and could potentially benefit from a less aggressive course of therapy. However, identification of such patients with a good prognosis remains difficult and at present is only possible through examining histopathological factors. METHODS: Building on a previously identified seven-gene prognostic immune response module for ER- breast cancer, we developed a novel statistical tool based on Mixture Discriminant Analysis in order to build a classifier that could accurately identify ER- patients with a good prognosis. RESULTS: We report the construction of a seven-gene expression classifier that accurately predicts, across a training cohort of 183 ER- tumours and six independent test cohorts (a total of 469 ER- tumours), ER- patients of good prognosis (in test sets, average predictive value = 94% [range 85 to 100%], average hazard ratio = 0.15 [range 0.07 to 0.36] p < 0.000001) independently of lymph node status and treatment. CONCLUSIONS: This seven-gene classifier could be used in a polymerase chain reaction-based clinical assay to identify ER- patients with a good prognosis, who may therefore benefit from less aggressive treatment regimens.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Torsion-Adding and Asymptotic Winding Number for Periodic Window Sequences

In parameter space of nonlinear dynamical systems, windows of periodic states are aligned following routes of period-adding configuring periodic window sequences. In state space of driven nonlinear oscillators, we determine the torsion associated with the periodic states and identify regions of uniform torsion in the window sequences. Moreover, we find that the measured of torsion differs by a constant between successive windows in periodic window sequences. We call this phenomenon as torsion-adding. Finally, combining the torsion and the period adding rules, we deduce a general rule to obtain the asymptotic winding number in the accumulation limit of such periodic window sequences

Phase Transition in Asymmetrical Superfluids I: Equal Fermi Surfaces

In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces $m_a\mu_a = m_b\mu_b$ is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added, accepted for publication in Phys. Rev.

First principle theory of correlated transport through nano-junctions

We report the inclusion of electron-electron correlation in the calculation of transport properties within an ab initio scheme. A key step is the reformulation of Landauer's approach in terms of an effective transmittance for the interacting electron system. We apply this framework to analyze the effect of short range interactions on Pt atomic wires and discuss the coherent and incoherent correction to the mean-field approach.Comment: 5 pages, 3 figure