Laplacian Spectra of Persistent Structures in Taiwan, Singapore, and US Stock Markets.

An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic.

Optical determination of layered-materials InSe thickness via RGB contrast method and regression analysis.

Indium selenide (InSe) features intriguing thickness-dependent optoelectronic properties, and a simple, and precise way to identify the thickness is essential for the rapid development of InSe research. Here, a red, green, and blue (RGB) color contrast method with regression analysis for quantitative correlation of three optical contrasts from RGB channels with the InSe thickness (1-35 nm), is demonstrated. The lower accuracy of the thickness identification obtained from the individual channels was discussed.

First-principles study of the crystal and magnetic structures of multiferroic CuOCl.

Recently, the discovery of multiferroicity in pyrochlore-like compound CuOClhas generated significant interest, and several studies have been performed in this area. This transition metal oxychloride is unique because the divalent copper atoms create anS=1/2correlated insulator and the pyrochlore lattice tends to frustrate spins. From neutron powder diffraction measurements, an incommensurate magnetic order of the ordering vectorq=(0.

Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash.

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions.