â€” Recently, Baker and Norine (Advances in Mathematics, 215(2): 766-788, 2007) found new analogies between graphs and Riemann surfaces by developing a Riemann-Roch machinery on a finite graph G. Inâ€¦ (More)

We consider the subgraph counting problem in data streams and develop the first non-trivial algorithm for approximately counting cycles of an arbitrary but fixed size. Previous non-trivial algorithmsâ€¦ (More)

The Riemann-Roch theorem on a graph G is closely related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whoseâ€¦ (More)

Given a set of points in a Hilbert space that can be separated from the origin. The slab support vector machine (slab SVM) is an optimization problem that aims at finding a slab (two parallelâ€¦ (More)

In this thesis we deal with two geometric optimization problems: Minimizing Absolute Gaussian Curvatue Locally in Meshes and the Solution path of the Slab Support Vector Machine. In the first part,â€¦ (More)

Wire Bonding is a well known method used for interconnecting integrated circuit (IC) die and the leads of its package. In this paper, the effect of current on the temperature of the gold (Au) ribbonâ€¦ (More)

We study the problem of computing the rank of a divisor on a finite graph, a quantity that arises in the Riemann-Roch theory on the finite graph developed by Baker and Norine (Advances inâ€¦ (More)

Chemical Reactions networks are widely studied in a variety of fields, including Systems Biology, Medicine, and Chemical Engineering. Analyzing chemical reaction networks is a widely studied problemâ€¦ (More)