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#### Relative Hilbert scheme methods in pseudoholomorphic geometry

(Massachusetts Institute of Technology, 2004)

This thesis takes up a program initiated by S. Donaldson and I. Smith aimed at using symplectic Lefschetz fibration techniques to obtain information about pseudoholomorphic curves in symplectic 4-manifolds. Donaldson and ...

#### Facility location and the analysis of algorithms through factor-revealing programs

(Massachusetts Institute of Technology, 2004)

In the metric uncapacitated facility location problem (UFLP), we are given a set of clients, a set of facilities, an opening cost for each facility, and a connection cost between each client and each facility satisfying ...

#### Generalized long-wave evolution equations

(Massachusetts Institute of Technology, 1998)

#### Studies in projective combinatorics

(Massachusetts Institute of Technology, 1998)

#### Testing and learning Boolean functions

(Massachusetts Institute of Technology, 2009)

Given a function f on n inputs, we consider the problem of testing whether f belongs to a concept class C, or is far from every member of C. An algorithm that achieves this goal for a particular C is called a property ...

#### Matrix probing, skeleton decompositions, and sparse Fourier transform

(Massachusetts Institute of Technology, 2013)

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 ...

#### Domino tiling, gene recognition and mice

(Massachusetts Institute of Technology, 1999)

#### Computer-assisted proofs in geometry and physics

(Massachusetts Institute of Technology, 2013)

In this dissertation we apply computer-assisted proof techniques to two problems, one in discrete geometry and one in celestial mechanics. Our main tool is an effective inverse function theorem which shows that, in favorable ...

#### The cohomology of weight varities

(Massachusetts Institute of Technology, 1999)

#### On evasiveness, permutation embeddings, and mappings on sequences.

(Massachusetts Institute of Technology, 1975)