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Now showing items 1-10 of 191

#### The Gowers norm in the testing of Boolean functions

(Massachusetts Institute of Technology, 2009)

A property tester is a fast, randomized algorithm that reads only a few entries of the input, and based on the values of these entries, it distinguishes whether the input has a certain property or is "different" from any ...

#### Approximate inference : decomposition methods with applications to networks

(Massachusetts Institute of Technology, 2009)

Markov random field (MRF) model provides an elegant probabilistic framework to formulate inter-dependency between a large number of random variables. In this thesis, we present a new approximation algorithm for computing ...

#### Conformal and asymptotic properties of embedded genus-g minimal surfaces with one end

(Massachusetts Institute of Technology, 2009)

Using the tools developed by Colding and Minicozzi in their study of the structure of embedded minimal surfaces in R3 [12, 19-22], we investigate the conformal and asymptotic properties of complete, embedded minimal surfaces ...

#### Pattern-avoidance in binary fillings of grid shapes

(Massachusetts Institute of Technology, 2009)

A grid shape is a set of boxes chosen from a square grid; any Young diagram is an example. We consider a notion of pattern-avoidance for 0-1 fillings of grid shapes, which generalizes permutation pattern-avoidance. A filling ...

#### The overconvergent de Rham-Witt complex

(Massachusetts Institute of Technology, 2009)

We define the overconvergent de Rham-Witt complex ... for a smooth affine variety over a perfect field in characteristic p. We show that, after tensoring with Q, its cohomology agrees with Monsky-Washnitzer cohomology. If ...

#### Quantum proof systems and entanglement theory

(Massachusetts Institute of Technology, 2009)

Quantum complexity theory is important from the point of view of not only theory of computation but also quantum information theory. In particular, quantum multi-prover interactive proof systems are defined based on ...

#### Siegel modulator form (mod p) and algebraic modular forms

(Massachusetts Institute of Technology, 2003)

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions ... , where B is the endomorphism algebra of a ...

#### Finance without price dynamics

(Massachusetts Institute of Technology, 2003)

Traditional finance theory has addressed portfolio optimization and option pricing problems assuming specific price dynamics for securities. In this thesis we address these problems without assuming specific price dynamics. ...

#### Combinatorial properties of shifted complexes

(Massachusetts Institute of Technology, 2003)

In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face ...

#### Zariski structures and simple theories

(Massachusetts Institute of Technology, 2003)

In this thesis, I consider generalisations of geometric stability theory to minimal Lascar Strong Types definable in simple theories. Positively, we show that the conditions of linearity and 1-basedness are equivalent for ...