Scholarly Works  Pure Mathematics and Mathematical Statistics
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Homological stability for moduli spaces of high dimensional manifolds. I
We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S$^{n}$ x S$^{n}$ . This is analogous to Harer's stability theorem ... 
Highdimensional change point estimation via sparse projection
Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study highdimensional time series in which, at certain time points, the mean structure changes in a sparse ... 
Critical surface of the 12 model
The 12 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It ...