Elementary models of 3D topological insulators with chiral symmetry

We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of $\mathbb{Z}$ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole). There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For $\mathbb{Z}$ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in $\mathbb{Z}$ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in $\mathbb{Z}_2$ topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected

Rivulet: 3D Neuron Morphology Tracing with Iterative Back-Tracking

The digital reconstruction of single neurons from 3D confocal microscopic images is an important tool for understanding the neuron morphology and function. However the accurate automatic neuron reconstruction remains a challenging task due to the varying image quality and the complexity in the neuronal arborisation. Targeting the common challenges of neuron tracing, we propose a novel automatic 3D neuron reconstruction algorithm, named Rivulet, which is based on the multi-stencils fast-marching and iterative backtracking. The proposed Rivulet algorithm is capable of tracing discontinuous areas without being interrupted by densely distributed noises. By evaluating the proposed pipeline with the data provided by the Diadem challenge and the recent BigNeuron project, Rivulet is shown to be robust to challenging microscopic imagestacks. We discussed the algorithm design in technical details regarding the relationships between the proposed algorithm and the other state-of-the-art neuron tracing algorithms

Reconstruction of 3D neuron morphology using Rivulet back-tracking

The 3D reconstruction of neuronal morphology is a powerful technique for investigating nervous systems. Due to the noises in optical microscopic images, the automated reconstruction of neuronal morphology has been a challenging problem. We propose a novel automatic neuron reconstruction algorithm, Rivulet, to target the challenges raised by the poor quality of the optical microscopic images. After the neuron images being de-noised with an anisotropic filter, the Rivulet algorithm combines multi-stencils fast-marching and iterative back-tracking from the geodesic farthest point on the segmented foreground. The neuron segments are dumped or merged according to a set of criteria at the end of each iteration. The proposed Rivulet tracing algorithm is evaluated with data provided from the BigNeuron Project. The experimental results demonstrate that Rivulet outperforms the compared state-of-the-art tracing methods when the images are of poor quality