An elementary approach to some aspects of Heegaard Floer homology

Heegaard Floer homology is a new invariant for 3-manifolds and links introduced by Ozsvath and Szabo. It counts pseudo-holomorphic Whitney disks in the symmetric product of the Heegaard surface of the underlying manifold. This thesis is about showing the existence of a natural complex structure on the symmetric product Sym9 (E9) of a surface E9 and mainly studying the moduli space of the set of holomorphic representatives of Whitney disks for special cases of domains from the Heegaard diagram which are bigons and squares. These moduli spaces are relevant for the computation of the boundary map in Heegaard Floer Homology. All of this is done using basic tools from differential topology and complex analysis. We will end this thesis by briefly describing some of the analysis required to ground this work in the more general theory of J-holomorphic curves and partial differential operators

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 3.

Diagram of the movement of a pendulum-like object. Pg 48.https://digitalcommons.usu.edu/visionsofscience/1050/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 10.

Table of contents and chapter introductory page.https://digitalcommons.usu.edu/visionsofscience/1057/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 4.

Diagram of a time-telling instrument. Pg 52.https://digitalcommons.usu.edu/visionsofscience/1051/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 6.

Several geometric diagrams -- one based on a circle, one a rectangle, and several on a triangle. Pg. 160.https://digitalcommons.usu.edu/visionsofscience/1053/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 9.

Geometric drawings alongside a mechanical diagram of a scientific instrument. Pg. 776.https://digitalcommons.usu.edu/visionsofscience/1056/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 1.

Author portrait in an illustrated frame. To the left, there is a smaller pasted image of the author -- likely of him at an older age.https://digitalcommons.usu.edu/visionsofscience/1048/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 8.

Diagrams of some of Huygens\u27 mechanical inventions -- used for things such as time-telling and measuring. Pg. 286.https://digitalcommons.usu.edu/visionsofscience/1055/thumbnail.jp

Christiani Hugenii Zulichemii, dum viveret Zelemii Toparchae, Opera Varia. Image 2.

Title page/frontispiece.https://digitalcommons.usu.edu/visionsofscience/1049/thumbnail.jp