Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
We present aligned hierarchies, a novel solution to the dimension reduction problem, representing high-dimensional and noisy sequential data as a low-dimensional object that encodes relevant information. In this thesis, we motivate our presentation...
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive
Alina V. Plavsky, Class of 2010, and Dominic Klyve, mathematics graduate student, working on a translation of a document from 18th century Russian for the online Euler archive