Binomial Difference Ideal and Toric Difference Variety

In this paper, the concepts of binomial difference ideals and toric difference varieties are defined and their properties are proved. Two canonical representations for Laurent binomial difference ideals are given using the reduced Groebner basis of Z[x]-lattices and regular and coherent difference ascending chains, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, perfect, and toric are given in terms of their support lattices which are Z[x]-lattices. The reflexive, well-mixed, and perfect closures of a Laurent binomial difference ideal are shown to be binomial. Four equivalent definitions for toric difference varieties are presented. Finally, algorithms are given to check whether a given Laurent binomial difference ideal I is reflexive, prime, well-mixed, perfect, or toric, and in the negative case, to compute the reflexive, well-mixed, and perfect closures of I. An algorithm is given to decompose a finitely generated perfect binomial difference ideal as the intersection of reflexive prime binomial difference ideals.Comment: 72 page

Dynamics of Topological Excitations in a Model Quantum Spin Ice

We study the quantum spin dynamics of a frustrated XXZ model on a pyrochlore lattice by using large-scale quantum Monte Carlo simulation and stochastic analytic continuation. In the low-temperature quantum spin ice regime, we observe signatures of coherent photon and spinon excitations in the dynamic spin structure factor. As the temperature rises to the classical spin ice regime, the photon disappears from the dynamic spin structure factor, whereas the dynamics of the spinon remain coherent in a broad temperature window. Our results provide experimentally relevant, quantitative information for the ongoing pursuit of quantum spin ice materials.Comment: 10 pages, 5 figure

Predicting RNA-binding residues from evolutionary information and sequence conservation

Abstract Background RNA-binding proteins (RBPs) play crucial roles in post-transcriptional control of RNA. RBPs are designed to efficiently recognize specific RNA sequences after it is derived from the DNA sequence. To satisfy diverse functional requirements, RNA binding proteins are composed of multiple blocks of RNA-binding domains (RBDs) presented in various structural arrangements to provide versatile functions. The ability to computationally predict RNA-binding residues in a RNA-binding protein can help biologists reveal important site-directed mutagenesis in wet-lab experiments. Results The proposed prediction framework named “ProteRNA” combines a SVM-based classifier with conserved residue discovery by WildSpan to identify the residues that interact with RNA in a RNA-binding protein. Although these conserved residues can be either functionally conserved residues or structurally conserved residues, they provide clues on the important residues in a protein sequence. In the independent testing dataset, ProteRNA has been able to deliver overall accuracy of 89.78%, MCC of 0.2628, F-score of 0.3075, and F0.5-score of 0.3546. Conclusions This article presents the design of a sequence-based predictor aiming to identify the RNA-binding residues in a RNA-binding protein by combining machine learning and pattern mining approaches. RNA-binding proteins have diverse functions while interacting with different categories of RNAs because these proteins are composed of multiple copies of RNA-binding domains presented in various structural arrangements to expand the functional repertoire of RNA-binding proteins. Furthermore, predicting RNA-binding residues in a RNA-binding protein can help biologists reveal important site-directed mutagenesis in wet-lab experiments.</p

Discovery of two new hypervelocity stars from the LAMOST spectroscopic surveys

We report the discovery of two new unbound hypervelocity stars (HVSs) from the LAMOST spectroscopic surveys. They are respectively a B2V type star of ~ 7 M$_{\rm \odot}$ with a Galactic rest-frame radial velocity of 502 km/s at a Galactocentric radius of ~ 21 kpc and a B7V type star of ~ 4 M$_{\rm \odot}$ with a Galactic rest-frame radial velocity of 408 km/s at a Galactocentric radius of ~ 30 kpc. The origins of the two HVSs are not clear given their currently poorly measured proper motions. However, the future data releases of Gaia should provide proper motion measurements accurate enough to solve this problem. The ongoing LAMOST spectroscopic surveys are expected to yield more HVSs to form a statistical sample, providing vital constraint on understanding the nature of HVSs and their ejection mechanisms.Comment: 5 pages, 3 figures, 1 table, accepted for publication in ApJ