Dependence of the Spin Transfer Torque Switching Current Density on the Exchange Stiffness Constant

We investigate the dependence of the switching current density on the exchange stiffness constant in the spin transfer torque magnetic tunneling junction structure with micromagnetic simulations. Since the widely accepted analytic expression of the switching current density is based on the macro-spin model, there is no dependence of the exchange stiffness constant. When the switching is occurred, however, the spin configuration forms C-, S-type, or complicated domain structures. Since the spin configuration is determined by the shape anisotropy and the exchange stiffness constant, the switching current density is very sensitive on their variations. It implies that there are more rooms for the optimization of the switching current density with by controlling the exchange stiffness constant, which is determined by composition and the detail fabrication processes

Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.Comment: 15 pages, 6 figures, accepted to CVPR 2016 for oral presentatio