Globally Convergent Parallel Algorithm for Zeros of Polynomial Systems

Certain classes of nonlinear systems of equations, such as polynomial systems, have properties that make them particularly amenable to solution on distributed computing systems. Some algorithms, considered unfavorably on a single processor serial computer, may be excellent on a distributed system. This paper considers the solution of polynomial systems of equations via a globally convergent homotopy algorithm on a hypercube. Some computational results are reported

Automatic Tail-Cutter

Essity commissioned Olivet Senior Design Team #9 with the creation of a device that will expedite the roll change time on Machine #515 while maintaining the safety standards that Essity has set forth. The current process is manual, with inefficiencies due to operators entering and leaving the machine area along with a slow manual cut time. Our goal is to optimize this process with the addition of a new process and/or devices. The solution provided to Essity was the addition of a lowering device and a cutting device which were to be used alongside an existing piece of equipment on Machine #515

A comparison of recombinant thrombin to bovine thrombin as a hemostatic ancillary in patients undergoing peripheral arterial bypass and arteriovenous graft procedures

ObjectivesRecombinant thrombin (rThrombin) is a potential hemostatic alternative to bovine and human plasma-derived thrombin. This report examines the clinical results for the vascular surgery subgroup of patients enrolled in a larger double-blind, randomized, multicenter trial, which evaluated the comparative safety and efficacy of rThrombin and bovine plasma-derived thrombin (bThrombin) when used as adjuncts to surgical hemostasis.MethodsData from the 164 vascular patients who underwent either a peripheral arterial bypass (PAB) or arteriovenous graft (AV) procedure are included in this analysis. Time to hemostasis at proximal and distal anastomotic sites at 1.5-, 3-, 6-, and 10-minute intervals was determined by procedure (PAB or AV) and overall (PAB + AV). Baseline and day 29 immunologic sera were analyzed. The incidences of postoperative adverse events were compared between treatment groups. Categorical adverse events were evaluated in relation to thrombin product antibody formation.ResultsPatients were randomized to either bThrombin (n = 82) or rThrombin (n = 82). Procedures included PAB (n = 88) and AV (n = 76). The bThrombin and rThrombin groups were well matched for demographics and baseline characteristics. A comparable incidence of anastomotic hemostasis was observed in both treatment groups at 10 minutes (94% bThrombin, 91% rThrombin). The incidence of hemostasis was lower at all time points for PAB procedures compared with AV procedures. In the PAB group, a significantly greater proportion of patients receiving rThrombin (55%) achieved hemostasis at 3 minutes compared with bThrombin (39%; P < .05). Adverse event profiles and laboratory findings were similar between groups. No patients in the rThrombin group developed anti-rThrombin product antibodies at day 29, whereas 27% of patients in the bThrombin group developed antibodies to bThrombin product (P < .0001).ConclusionsrThrombin or bThrombin used as a hemostatic ancillary for anastomotic bleeding was equally effective at 10 minutes; however, rThrombin compared with bThrombin may provide a more rapid onset of hemostasis at 3 minutes in PAB procedures. Adverse events were similar between the two thrombins. In patients undergoing vascular surgery, both treatments were similarly well tolerated, although rThrombin demonstrated a superior immunogenicity profile

The Trail, 1965-05-07

https://soundideas.pugetsound.edu/thetrail_all/4038/thumbnail.jp

The Trail, 1965-02-18

https://soundideas.pugetsound.edu/thetrail_all/1902/thumbnail.jp

Finding All Isolated Solutions To Polynomial Systems Using Hompack

Although the theory of polynomial continuation has been established for over a decade (following the work of Garcia, Zangwill, and Drexler), it is difficult to solve polynomial systems using continuation in practice. Divergent paths (solutions at infinity), singular solutions, and extreme scaling of coefficients can create catastrophic numerical problems. Further, the large number of paths that typically arise can be discouraging. In this paper we summarize polynomial-solving homotopy continuation and report on the performance of three standard path-tracking algorithms (as implemented in HOMPACK) in solving three physical problems of varying degrees of difficulty. Our purpose is to provide useful information on solving polynomial systems; including specific guidelines for homotopy construction and parameter settings. The m-homogeneous strategy for constructing polynomial homotopies is outlined, along with more tradition approaches. Computational comparisons are included to illustrate and contrast the major HOMPACK options. The conclusions summarize our numerical experience and discuss areas for future research