2-Selmer Parity for Hyperelliptic Curves in Quadratic Extensions

We study the 2-parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove it over quadratic extensions of the base field, providing essentially the first examples of the 2-parity conjecture in dimension greater than one. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest. Particularly surprising is the appearance in the formula of terms that govern whether or not the Cassels-Tate pairing on the Jacobian is alternating, which first appeared in a paper of Poonen and Stoll. We prove this local formula in many instances and show that in all cases it follows from standard global conjectures.Comment: 47 pages, 3 figure

Tate module and bad reduction

Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us to describe the Galois action on the l-adic Tate module of the Jacobian of C/K in terms of the special fibre of this model over F.Comment: 13 pages, final version, to appear in Proc. AM

EMPIRICALLY ANALYZING THE “FIVE PERCENT RULE OF MATERIALITY” IN FINANCIAL REPORTING DECISIONS

This study analyzes a sample of financial restatements from 2011 and 2012 as a way to assess a proposed “five percent rule of materiality” for financial reporting decisions. Such a rule claims the average investor is only influenced by income restatements greater than five percent. Market reactions are observed through stock price, volume, and bid-ask spread following the restatement in the Form 10-K/A. The study finds only some firms restating net income by more than five percent experience statistically significant reactions in two of these metrics. The study also suggests percent change in net income is a significant driver of percent change in the three metrics via a regression analysis

Quadratic twists of abelian varieties and disparity in Selmer ranks

We study the parity of 2-Selmer ranks in the family of quadratic twists of a fixed principally polarized abelian variety over a number field. Specifically, we determine the proportion of twists having odd (respectively even) 2-Selmer rank. This generalizes work of Klagsbrun–Mazur–Rubin for elliptic curves and Yu for Jacobians of hyperelliptic curves. Several differences in the statistics arise due to the possibility that the Shafarevich–Tate group (if finite) may have order twice a square. In particular, the statistics for parities of 2-Selmer ranks and 2-infinity Selmer ranks need no longer agree and we describe both

Design and testing of a position adaptation system for KUKA robots using photoelectric sensors

This thesis presents the development and analysis of a position monitoring and adaptation system to be used in conjunction with a KUKA KR16-2 articulated robot using components readily available in most manufacturing settings. This system could be beneficial in the manufacturing sector in areas such as polymer welding and spray painting. In the former it could be used to maintain an effective distance between a welding end effector laying molten plastic and the surface area of the parts being welded, or in the case of the latter the system would be useful in painting objects of unknown shape or objects with unknown variations in the surface level. In the case of spray painting if you spray to close to an object you will get an inconsistent amount of paint applied to an area. This system would maintain the programmed distance between the robot system and target object. Typically, systems that achieve this level of control rely on expensive sensors such as force torque sensors. This research proposes to take the first step in trying to address the technical problems by introducing a novel way of adapting to a target surface deformation using comparably low cost photoelectric diffuse sensors. The key outcomes of this thesis can be found in the form of a software package to interface the photo-electric sensors to the KUKA robot system. This system is operated by a custom-built algorithm which is capable of dynamically calculating robot movements based off the sensor input. Additionally, an optimum system setup is developed with different configurations of sensor mounting and speeds of robot operation discussed and tested. The viability of the photo-electric diffuses sensors used in this application is also considered with further works suggested. Finally, a secondary application is developed for recording and analysing KUKA robot movements for use in other research activities