Molecular phenotyping using networks, diffusion, and topology: soft tissue sarcoma.

Many biological datasets are high-dimensional yet manifest an underlying order. In this paper, we describe an unsupervised data analysis methodology that operates in the setting of a multivariate dataset and a network which expresses influence between the variables of the given set. The technique involves network geometry employing the Wasserstein distance, global spectral analysis in the form of diffusion maps, and topological data analysis using the Mapper algorithm.

To infinity and some glimpses of beyond.

When mathematical and computational dynamic models reach infinity in finite time, extending analysis and numerics beyond it becomes a notorious challenge. We suggest how, upon suitable transformations, it may become possible to go beyond infinity with the solution becoming again well behaved and the computations continuing normally. In our Ordinary Differential Equation examples the crossing of infinity occurs instantaneously.