Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln2_2InSbO7_7 family

The lanthanide pyrochlore oxides Ln$_2$B$_2$O$_7$ are one of the most intensely studied classes of materials within condensed matter physics, firmly centered as one of the pillars of frustrated magnetism. The extensive chemical diversity of the pyrochlores, coupled with their innate geometric frustration, enables realization of a wide array of exotic and complex magnetic ground states. Thus, the discovery of new pyrochlore compositions has been a persistent theme that continues to drive the field in exciting directions. The recent focus on the mixed B-site pyrochlores offers a unique route towards tuning both local coordination chemistry and sterics, while maintaining a nominally pristine magnetic sublattice. Here, we present a broad overview of the pyrochlore stability field, integrating recent synthetic efforts in mixed B-site systems with the historically established Ln$_2$B$_2$O$_7$ families. In parallel, we present the discovery and synthesis of the entire Ln$_2$InSbO$_7$ family (Ln: La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) located near the boundary of the pyrochlore stability field using a rapid, hybrid mechanicochemical/microwave-assisted synthesis technique. Magnetic characterization on the entire class of compounds draws striking parallels to the stannate analogs, suggesting that these compounds may host a breadth of exotic magnetic ground states

Computer simulation of glioma growth and morphology

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion

Neural Embeddings of Graphs in Hyperbolic Space

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into applications in domains other than language. One such domain is graph-structured data, where embeddings of vertices can be learned that encapsulate vertex similarity and improve performance on tasks including edge prediction and vertex labelling. For both NLP and graph based tasks, embeddings have been learned in high-dimensional Euclidean spaces. However, recent work has shown that the appropriate isometric space for embedding complex networks is not the flat Euclidean space, but negatively curved, hyperbolic space. We present a new concept that exploits these recent insights and propose learning neural embeddings of graphs in hyperbolic space. We provide experimental evidence that embedding graphs in their natural geometry significantly improves performance on downstream tasks for several real-world public datasets.Comment: 7 pages, 5 figure