On the geometry and environment of repeating FRBs

ABSTRACT We propose a geometrical explanation for periodically and non-periodically repeating fast radio bursts (FRBs) under neutron star (NS)–companion systems. We suggest a constant critical binary separation, rc, within which the interaction between the NS and companion can trigger FRBs. For an elliptic orbit with the minimum and maximum binary separations, rmin and rmax, a periodically repeating FRB with an active period could be reproduced if rmin < rc < rmax. However, if rmax < rc, the modulation of orbital motion will not work due to persistent interaction, and this kind of repeating FRBs should be non-periodic. We test relevant NS–companion binary scenarios on the basis of FRB 180916.J0158+65 and FRB 121102 under this geometrical frame. It is found that the pulsar–asteroid belt impact model is more suitable to explain these two FRBs since this model is compatible with different companions (e.g. massive stars and black holes). At last, we point out that FRB 121102-like samples are potential objects that can reveal the evolution of star-forming region.

Double Additive Margin Softmax Loss for Face Recognition

Learning large-margin face features whose intra-class variance is small and inter-class diversity is one of important challenges in feature learning applying Deep Convolutional Neural Networks (DCNNs) for face recognition. Recently, an appealing line of research is to incorporate an angular margin in the original softmax loss functions for obtaining discriminative deep features during the training of DCNNs. In this paper we propose a novel loss function, termed as double additive margin Softmax loss (DAM-Softmax). The presented loss has a clearer geometrical explanation and can obtain highly discriminative features for face recognition. Extensive experimental evaluation of several recent state-of-the-art softmax loss functions are conducted on the relevant face recognition benchmarks, CASIA-Webface, LFW, CALFW, CPLFW, and CFP-FP. We show that the proposed loss function consistently outperforms the state-of-the-art.

Underlying structure in the dynamics of chase and escape interactions

Chase and escape behaviors are important skills in many sports. Previous studies have described the behaviors of the attacker (escaper) and defender (chaser) by focusing on their positional relationship and have presented several key parameters that affect the outcome (successful attack or defense). However, it remains unclear how each individual agent moves, and how the outcome is determined in this type of interaction. To address these questions, we constructed a chase and escape task in a virtual space that allowed us to manipulate agents’ kinematic parameters. We identified the basic strategies of each agent and their robustness to changes in their parameters. Moreover, we identified the determinants of the outcome and a geometrical explanation of their importance. Our results revealed the underlying structure of a simplified human chase and escape interaction and provided the insight that, although each agent apparently moves freely, their strategies in two-agent interactions are in fact rather constrained.

Physical models from noncommutative causality

We introduced few years ago a new notion of causality for noncommutative spacetimes directly related to the Dirac operator and the concept of Lorentzian spectral triple. In this paper, we review in a non-technical way the noncommutative causal structure of many toy models as almost commutative spacetimes and the Moyal-Weyl spacetime. We show that those models present some unexpected physical interpretations as a geometrical explanation of the Zitterbewegung trembling motion of a fermion as well as some geometrical constraints on translations and energy jumps of wave packets on the Moyal spacetime.

Geometric principles in the assembly of α-helical bundles

α-Helical coiled coils are usually stabilized by hydrophobic interfaces between the two constituent α-helices, in the form of ‘knobs-into-holes’ packing of non-polar residues arranged in repeating heptad patterns. Here we examine the corresponding ‘hydrophobic cores’ that stabilize bundles of four α-helices. In particular, we study three different kinds of bundle, involving four α-helices of identical sequence: two pack in a parallel and one in an anti-parallel orientation. We point out that the simplest way of understanding the packing of these 4-helix bundles is to use Crick's original idea that the helices are held together by ‘hydrophobic stripes’, which are readily visualized on the cylindrical surface lattice of the α-helices; and that the ‘helix-crossing angle’—which determines, in particular, whether supercoiling is left- or right-handed—is fixed by the slope of the lattice lines that contain the hydrophobic residues. In our three examples the constituent α-helices have hydrophobic repeat patterns of 7, 11 and 4 residues, respectively; and we associate the different overall conformations with ‘knobs-into-holes’ packing along the 7-, 11- and 4-start lines, respectively, of the cylindrical surface lattices of the constituent α-helices. For the first two examples, all four interfaces between adjacent helices are geometrically equivalent; but in the third, one of the four interfaces differs significantly from the others. We provide a geometrical explanation for this non-equivalence in terms of two different but equivalent ways of assembling this bundle, which may possibly constitute a bistable molecular ‘switch’ with a coaxial throw of about 12 Å. The geometrical ideas that we deploy in this paper provide the simplest and clearest description of the structure of helical bundles. In an appendix, we describe briefly a computer program that we have devised in order to search for ‘knobs-into-holes’ packing between α-helices in proteins.