In recent years there has been a great deal of new activity at the interface of biology and computation. This has largely been driven by the massive in flux of data from new experimental technologies, particularly ...

(cont.) yield a new proof of a result of Mochizuki yield a new proof of a result of Mochizuki Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.

In this thesis, I studied the stability of local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood ...

The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this category and that the morphisms ...

Recently Bruno and Vaynblat introduced a new mathematical model to describe shock induced martensitic phase transitions. This model is much simpler than prior ones -- requiring, essentially, no quantities that cannot be ...

In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...

This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical ...