Hall conductivity as bulk signature of topological transitions in superconductors

Topological superconductors may undergo transitions between phases with different topological numbers which, like the case of topological insulators, are related to the presence of gapless (Majorana) edge states. In $\mathbb{Z}$ topological insulators the charge Hall conductivity is quantized, being proportional to the number of gapless states running at the edge. In a superconductor, however, charge is not conserved and, therefore, $\sigma_{xy}$ is not quantized, even in the case of a $\mathbb{Z}$ topological superconductor. Here it is shown that while the $\sigma_{xy}$ evolves continuously between different topological phases of a $\mathbb{Z}$ topological superconductor, its derivatives display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO) coupling and externally applied Zeeman spin splitting. Generalization to the cases where the pairing vector is not aligned with that of the SO coupling is given. We generalize also to the cases where the normal system is already topologically non-trivial.Comment: 10 pages, 10 figure

Embodied cognition with and without mental representations: The case of embodied choices in sports

© 2019 Raab and Araújo. In this conceptual analysis contribution to the special issue on radical embodied cognition, we discuss how embodied cognition can exist with and without representations. We explore this concept through the lens of judgment and decision-making in sports (JDMS). Embodied cognition has featured in many investigations of human behavior, but no single approach has emerged. Indeed, the very definitions of the concepts “embodiment” and “cognition” lack consensus, and consequently the degree of “radicalism” is not universally defined, either. In this paper, we address JDMS not from a rigid theoretical perspective but from two embodied cognition approaches: one that assumes there is mediation between the athlete and the environment through mental representation, and another that assumes direct contact between the athlete and the environment and thus no need for mental representation. Importantly, our aim was not to arrive at a theoretical consensus or set up a competition between approaches but rather to provide a legitimate scientific discussion about how to explain empirical results in JDMS from contrasting perspectives within embodied cognition. For this, we first outline the definitions and constructs of embodied cognition in JDMS. Second, we detail the theory underlying the mental representation and direct contact approaches. Third, we comment on two published research papers on JDMS, one selected by each of us: (1) Correia et al. (2012) and (2) Pizzera (2012). Fourth, following the interpretation of the empirical findings of these papers, we present a discussion on the commonalities and divergences of these two perspectives and the consequences of using one or the other approach in the study of JDMS

Hierarchical ResNeXt Models for Breast Cancer Histology Image Classification

Microscopic histology image analysis is a cornerstone in early detection of breast cancer. However these images are very large and manual analysis is error prone and very time consuming. Thus automating this process is in high demand. We proposed a hierarchical system of convolutional neural networks (CNN) that classifies automatically patches of these images into four pathologies: normal, benign, in situ carcinoma and invasive carcinoma. We evaluated our system on the BACH challenge dataset of image-wise classification and a small dataset that we used to extend it. Using a train/test split of 75%/25%, we achieved an accuracy rate of 0.99 on the test split for the BACH dataset and 0.96 on that of the extension. On the test of the BACH challenge, we've reached an accuracy of 0.81 which rank us to the 8th out of 51 teams

What could an ecological dynamics rationale offer Quiet Eye research? Comment on Vickers

In this commentary, we respond to suggestions in previous Quiet Eye (QE) research that future work is needed to understand how theories of ecological psychology and nonlinear dynamics might frame empirical and practical work. We raise questions on the assumptions behind an information processing explanation for programming of parameters such as duration, onsets and offsets of QE, and we concur with previous calls for more research considering how visual search behaviours, such as QE, emerge under interacting personal, task and environmental constraints. However, initial work needs to frame a more general ecological dynamics explanation for QE, capturing how a process-oriented approach is needed to address how perceived affordances and adaptive functional variability might shape emergent coordination tendencies, including QE, in individual performers

Gaussian model of explosive percolation in three and higher dimensions

The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple-cubic lattice, in the thermodynamic limit, we report a finite jump of the order parameter, $J=0.415 \pm 0.005$. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension $d_A = 2.5 \pm 0.2$. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with finite number of clusters at the threshold