Field-dependent quantum nucleation of antiferromagnetic bubbles

The phenomenon of quantum nucleation is studied in a nanometer-scale antiferromagnet with biaxial symmetry in the presence of a magnetic field at an arbitrary angle. Within the instanton approach, we calculate the dependence of the rate of quantum nucleation and the crossover temperature on the orientation and strength of the field for bulk solids and two-dimensional films of antiferromagnets, respectively. Our results show that the rate of quantum nucleation and the crossover temperature from thermal-to-quantum transitions depend on the orientation and strength of the field distinctly, which can be tested with the use of existing experimental techniques.Comment: 21 pages, 5 figures, Final version and accepted by Eur. Phys. J

Orderly Spanning Trees with Applications

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an {\em orderly pair} for any connected planar graph $G$, consisting of a plane graph $H$ of $G$, and an orderly spanning tree of $H$. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem, (2) the first area-optimal 2-visibility drawing of $G$, and (3) the best known encodings of $G$ with O(1)-time query support. All algorithms in this paper run in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington D.C., USA, January 7-9, 2001, pp. 506-51

In-Process Global Interpretation for Graph Learning via Distribution Matching

Graphs neural networks (GNNs) have emerged as a powerful graph learning model due to their superior capacity in capturing critical graph patterns. To gain insights about the model mechanism for interpretable graph learning, previous efforts focus on post-hoc local interpretation by extracting the data pattern that a pre-trained GNN model uses to make an individual prediction. However, recent works show that post-hoc methods are highly sensitive to model initialization and local interpretation can only explain the model prediction specific to a particular instance. In this work, we address these limitations by answering an important question that is not yet studied: how to provide global interpretation of the model training procedure? We formulate this problem as in-process global interpretation, which targets on distilling high-level and human-intelligible patterns that dominate the training procedure of GNNs. We further propose Graph Distribution Matching (GDM) to synthesize interpretive graphs by matching the distribution of the original and interpretive graphs in the feature space of the GNN as its training proceeds. These few interpretive graphs demonstrate the most informative patterns the model captures during training. Extensive experiments on graph classification datasets demonstrate multiple advantages of the proposed method, including high explanation accuracy, time efficiency and the ability to reveal class-relevant structure.Comment: Under Revie

Optical fiber multiplexing interferometer system with a single laser diode and its application to online displacement measurement

A multiplexed optical fiber Michelson interferometer system that is self-referenced with a stabilizing feedback loop is presented. This system employs fiber Bragg gratings and wavelength division multiplexing technique to combine two optical fiber interferometers that share the same optical path in the main part of the optical system. When one Michelson interferometer, which uses the fiber Bragg gratings as reflective mirrors and is used as reference interferometer, is stabilized by an electric feedback loop, the other interferometer, which is used for the measurement, is also stabilized. This system is therefore suitable for online precision measurement. An active phase-tracking technique is applied for signal processing to achieve high resolution