arXiv subjects

Daowei Wang

Publications and source records attributed to Daowei Wang.

3 recordsLinked to original sources

arXiv2022

The Equivariance Criterion in a Linear Model for Fixed-X Cases

The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this article, we explored the usage of equivariance criterion in a normal linear model with fixed-$X$ and extended the model to allow multiple populations, which, in turn, leads to a multivariate invariant location-scale transformation group, compared than the commonly used univariate one. The minimum risk equivariant estimators of the coefficient vector and the diagonal covariance matrix were derived, which were consistent with literature works. This work serves as an early exploration of the usage of equivariance criterion in machine learning, where we confirmed that the least square approach widely used in machine learning indeed carries optimality in some sense at least in the framework of estimation. Meanwhile, the problems can be shown to be equivalent to a mixture from $p$ independent normal samples and via the principle of functional equivariance, an alternative proof can be derived. However, such an approach carries its own limitation with a strong tie to equivariance criterion.

math.ST↗

arXiv2016

Control and manipulation of a magnetic skyrmionium in nanostructures

A magnetic skyrmionium is a nontopological soliton, which has a doughnut-like out-of-plane spin texture in thin films, and can be phenomenologically viewed as a coalition of two topological magnetic skyrmions with opposite topological numbers. Due to its zero topological number ($Q=0$) and doughnut-like structure, the skyrmionium has its distinctive characteristics as compared to the skyrmion with $Q=\pm 1$. Here we systematically study the generation, manipulation and motion of a skyrmionium in ultrathin magnetic nanostructures by applying a magnetic field or a spin-polarized current. It is found that the skyrmionium moves faster than the skyrmion when they are driven by the out-of-plane current, and their velocity difference is proportional to the driving force. However, the skyrmionium and skyrmion exhibit an identical current-velocity relation when they are driven by the in-plane current. It is also found that a moving skyrmionium is less deformed in the current-in-plane geometry compared with the skyrmionum in the current-perpendicular-to-plane geometry. Furthermore we demonstrate the transformation of a skyrmionium with $Q=0$ into two skyrmions with $Q=+1$ in a nanotrack driven by a spin-polarized current, which can be seen as the unzipping process of a skyrmionium. We illustrate the energy and spin structure variations during the skyrmionium unzipping process, where linear relations between the spin structure and energies are found. These results could have technological implications in the emerging field of skyrmionics.

cond-mat.mes-hall↗

arXiv2015

Strain induced topological phase transitions in monolayer honeycomb structures of group-V binary compounds

We present first-principles calculations of electronic structures of a class of two-dimensional (2D) honeycomb structures of group-V binary compounds. Our results show these new 2D materials are stable semiconductors with direct or indirect band gaps. The band gap can be tuned by applying lattice strain. During their stretchable regime, they all exhibit metal-indirect gap semiconductor-direct gap semiconductor-topological insulator (TI) transitions with increasing strain from negative (compressive) to positive (tensile) values. The topological phase transition results from the band inversion at $Γ$ point due to lattice strain and is irrelevant to spin-orbit coupling (SOC).

cond-mat.mtrl-sci↗