Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

Automated Portal Placement for Arthroscopic Hip Surgery

Placing portal incisions during arthroscopic hip surgery presents challenges for surgeons in terms of anatomic accessibility and patient safety. Based on key anatomic landmarks and portal placement information from recent literature, suggested portal incisions were determined. Guidance in the placement of the three most common portal incision locations (anterior, anterolateral, and posterolateral) for arthroscopic surgery; in addition to visual feedback on tool trajectory to the hip joint is provided in real time by a computer aided system for hip arthroscopy. By simplifying the portal placement process, one of the most challenging aspects of arthroscopic hip surgery, an increased use of this minimally invasive technique could be possible. In addition to portal information, improvements to an existing computer aided system for arthroscopic hip surgery, including a new hip model and redesigned mechanical tracking linkage, were completed.