## Search

Now showing items 1-10 of 15

#### A geometric theory of outliers and perturbation

(Massachusetts Institute of Technology, 2002)

We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a ...

#### Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions

(Massachusetts Institute of Technology, 2002)

Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in ...

#### Running in circles : packet routing on ring networks

(Massachusetts Institute of Technology, 2002)

I analyze packet routing on unidirectional ring networks, with an eye towards establishing bounds on the expected length of the queues. Suppose we route packets by a greedy "hot potato" protocol. If packets are inserted ...

#### Affine quantum algebras, Weyl groups and constructible functions

(Massachusetts Institute of Technology, 2002)

This thesis consists of two parts. In the first part we study the affine quantum group of type A, giving a geometric description of its natural inner product, and studying the theory of cells attached to the canonical ...

#### The instability of time-dependent jets

(Massachusetts Institute of Technology, 2002)

The central focus of my thesis is to study the instability jets of various complexity by analyzing the linear and nonlinear dynamics. We applied this methodology to four different situations in order to learn the following. ...

#### Equivariant cohomology, homogeneous spaces and graphs

(Massachusetts Institute of Technology, 2002)

The focus of this thesis is manifolds with group actions, in particular symplectic manifolds with Hamiltonian torus actions. We investigate the relationship between the equivariant cohomology of the manifold M and the fixed ...

#### A complexity theoretic approach to learning

(Massachusetts Institute of Technology, 2002)

This thesis details a new vantage point for attacking longstanding problems in machine learning. We use tools from computational complexity theory to make progress on problems from computational learning theory. Our methods ...

#### Rational families of vector bundles on curves

(Massachusetts Institute of Technology, 2002)

We find and describe the irreducible components of the space of rational curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the ...

#### The homotopy type of the matroid Grassmannian

(Massachusetts Institute of Technology, 2002)

In this thesis, I establish a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert ...

#### [rho]-compact groups as framed manifolds

(Massachusetts Institute of Technology, 2002)

We describe a natural way to associate to any [rho]-compact group an element of the [rho]-local stable stems, which, applied to the [rho]-completion of a compact Lie group G, coincides with the element represented by the ...