Extracting useful information from large data sets can be a daunting task. Topological
methods for analysing data sets provide a powerful technique for extracting such …

We study the ℓ1-low rank approximation problem, where for a given nxd matrix A and
approximation factor α≤ 1, the goal is to output a rank-k matrix  for which‖ A-Â‖ 1≤ α …

The classical low rank approximation problem is: given a matrix A, find a rank-k matrix B
such that the Frobenius norm of A− B is minimized. It can be solved efficiently using, for …

Switch-like responses arising from bistability have been linked to cell signaling processes
and memory. Revealing the shape and properties of the set of parameters that lead to …

Topological data analysis offers a robust way to extract useful information from noisy,
unstructured data by identifying its underlying structure. Recently, an efficient quantum …

In 2015, Guth proved that if S is a collection of n g-dimensional semialgebraic sets in R^d
and if D≧1 is an integer, then there is a d-variate polynomial P of degree at most D so that …

We present a massively parallel framework for computing tropicalizations of algebraic
varieties which can make use of symmetries using the workflow management system GPI …

We give partial generalizations of the classical Descartes' rule of signs to multivariate
polynomials (with real exponents), in the sense that we provide upper bounds on the …

The matrix plays an essential role in many theoretical computer science and machine
learning problems. In this thesis, we develop a better understanding of matrices with a view …

We consider the problem of finding the best memoryless stochastic policy for an infinite-
horizon partially observable Markov decision process (POMDP) with finite state and action …