Single-domain versus two-domain configuration in thin ferromagnetic prisms

Thin ferromagnetic elements in the form of rectangular prisms are theoretically investigated in order to study the transition from single-domain to two-domain state, with changing the in-plane aspect ratio p. We address two main questions: first, how general is the transition; second, how the critical value p_c depends on the physical parameters. We use two complementary methods: discrete-lattice calculations and a micromagnetic continuum approach. Ultrathin films do not appear to split in two domains. Instead, thicker films may undergo the above transition. We have used the continuum approach to analyze recent Magnetic Force Microscopy observations in 30 nm-thick patterned Permalloy elements, finding a good agreement for p_c.Comment: 22 pages, 5 figure

Towards String-to-Tree Neural Machine Translation

We present a simple method to incorporate syntactic information about the target language in a neural machine translation system by translating into linearized, lexicalized constituency trees. An experiment on the WMT16 German-English news translation task resulted in an improved BLEU score when compared to a syntax-agnostic NMT baseline trained on the same dataset. An analysis of the translations from the syntax-aware system shows that it performs more reordering during translation in comparison to the baseline. A small-scale human evaluation also showed an advantage to the syntax-aware system.Comment: Accepted as a short paper in ACL 201

Rainbow sets in the intersection of two matroids

Given sets $F_1, \ldots ,F_n$, a {\em partial rainbow function} is a partial choice function of the sets $F_i$. A {\em partial rainbow set} is the range of a partial rainbow function. Aharoni and Berger \cite{AhBer} conjectured that if $M$ and $N$ are matroids on the same ground set, and $F_1, \ldots ,F_n$ are pairwise disjoint sets of size $n$ belonging to $M \cap N$, then there exists a rainbow set of size $n-1$ belonging to $M \cap N$. Following an idea of Woolbright and Brower-de Vries-Wieringa, we prove that there exists such a rainbow set of size at least $n-\sqrt{n}$