1. What is a scheme?: 8/31/16 1 2. But really, what is a scheme?: 9/7/16 4 3. Algebraic Groups, a De nition: 9/14/16 8 4. Nice Properties of Algebraic Groups: 9/21/16 9 5. Examples of Algebraic Groups: 9/28/16 12 6. More Examples: 10/5/16 14 7. Hopf Algebras and A ne Algebraic Groups 14 8. Some Representation Theory: 10/19/16 16 9. More Representation Theory and Chevalley’s Theorem: 10/26/16 19...

Plant oils containing ω-7 fatty acids (FAs; palmitoleic 16:1Δ(9) and cis-vaccenic 18:1Δ(11)) have potential as sustainable feedstocks for producing industrially important octene via metathesis chemistry. Engineering plants to produce seeds that accumulate high levels of any unusual FA has been an elusive goal. We achieved high levels of ω-7 FA accumulation by systematic metabolic engineering of...

Background: Human papillomavirus (HPV) is responsible for the development of cervical neoplasia.  Infection with human papillomavirus type 16 (HPV-16) is a major risk factor for the development of cervical cancer. The virus encodes three oncoproteins (E5, E6 and E7), of which, the E7 oncoprotein is the major protein involved in cell immortalization and transformation o...

In the title compound, C(16)H(15)NO, the dihedral angle between the outer benzene rings is 51.88 (6)°, and each of the central six-membered rings has a boat conformation. The hy-droxy and amino groups are syn, and the hy-droxy H atom forms an intra-molecular O-H⋯N hydrogen bond. In the crystal, mol-ecules assemble via C-H⋯O and C-H⋯π inter-actions, consolidating a three-dimensional architecture.

My lab has shown that Stat3, an oncogenic protein constitutively-activated in tumor cells, is also persistently activated in tumor stromal cells, including diverse immune subsets. We have further demonstrated that Stat3 signaling coordinates multiple levels of interactions between tumor cells and their microenvironment, affecting tumor growth, apoptosis and angiogenesis. Importantly, our recent...

Intracranial arterial disease includes thromboembolic events, vascular stenoses, and aneurysms. Endovascular techniques have been investigated for treatment of intracranial arterial disease, as an alternative to intravenous tissue plasminogen activator and supportive care for acute stenosis and as an alternative to risk factor modification for chronic stenosis. For cerebral aneurysms, stentassi...

An analysis on the algebraic decoding of the (31, 16, 7) quadratic residue (QR) code with reducib le generator polynomial that uses the inverse-free Berlekamp-Massey (IFBM) algorithm to determine the error-locator polynomial is presented in this paper. The primary known syndrome S1 will be equal to zero for some weight-3 error patterns. However, the zero S1 does not cause a decoding failure whi...

BACKGROUND Many studies document a robust and consistent relationship between gang membership and elevated delinquency, with gang members disproportionately involved in crime compared to non-gang peers. Research also indicates that both delinquent youth and youth who join gangs often show a wide range of deficient or distorted social-cognitive processes compared to non-delinquent peers. Cogniti...

Assume that we are given a rooted tree with n leaves. All leaves have the same distance ` from the root and all nodes except for the leaves have three children. A problem instance consists of such a tree and a boolean value for each leaf. The value of each inner node is defined as the majority value of its children. Initially, the values of inner nodes are not given. The objective is to compute...

1 Executive Summary We started with an introduction to the notion of percolation over random graphs with a 2-D lattice as an example. We then studied branching processes over random trees and proved conditions under which the such a process continues forever with positive probability. Finally, we defined the probability space of a random graph over a 2-D lattice. 2 Introduction to Percolation C...