Exploring Interpolation Techniques in Enumerative Geometry

In this paper we examine the invariant subsets A of a vector space V , when we act by a group, G. Gathering some of the information about A in the equivariant cohomology ring H*G(V) is an important area of study in enumerative geometry. The descriptions we seek to find for an invariant subspace satisfies certain universal properties. A notable example of this is given a vector bundle with fiber V and structure group G over a compact manifold M looking at some cohomological data for A-points of a section can be done in the equivariant cohomology ring instead of the cohomology ring of M. The fundamental cohomology class and Segre-Schwartz- MacPherson class are two such objects that are the same in both cohomology rings. Since these classes are universal in the above sense, we expect that it is very difficult to determine the fundamental class and the Chern-Schwartz-MacPherson class. However, it is possible in certain situations. In this paper we find the fundamental class and the CSM/SSM classes in the equivariant cohomology rings for two separate groups actions. Before we make our way through calculations, we give some intuitive definition of what these classes are. The basis for the computations we do is from interpolation characterizations of the CSM class and the fundamental classes, which are stated in a way applicable to our situation. We then work through the computation one of these for two seperate group actions. The culmination of the first section is the statement and the proof of a well-known result called the Porteous identity. The second section ends with some conjectures based on the lower-dimensional results.Bachelor of Scienc

Investigation of Aromatic/Aliphatic Polyimides as Dispersants for Single Wall Carbon Nanotubes

Novel aromatic/aliphatic polyimides were prepared from 2,7-diamino-9,9'- dioctylfluorene (AFDA) and aromatic dianhydrides. Upon investigating the effectiveness of these polyimides for dispersing single wall carbon nanotubes (SWNTs) in solution, three were discovered to disperse SWNTs in N,N-dimethylacetamide (DMAc). Two of these polyimides, one from 3,3',4,4'-oxydiphthalic anhydride (ODPA) and one from symmetric 3,3',4,4'-biphenyltetracarboxylic dianhydride (s-BPDA), were used to prepare nanocomposites. Homogeneous polyimide/SWNT suspensions from both polymers were used in the preparation of films and fibers containing up to 1 wt% SWNTs. The samples were thermally treated to remove residual solvent and the films were characterized for SWNT dispersion by optical and high resolution scanning electron microscopy (HRSEM). Electrical and mechanical properties of the films were also determined. Electrospun fibers were examined by HRSEM to characterize SWNT alignment and orientation

Reductions in cardiovascular, cerebrovascular, and respiratory mortality following the national Irish smoking ban: Interrupted time-series analysis

Copyright @ 2013 Stallings-Smith et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.Background: Previous studies have shown decreases in cardiovascular mortality following the implementation of comprehensive smoking bans. It is not known whether cerebrovascular or respiratory mortality decreases post-ban. On March 29, 2004, the Republic of Ireland became the first country in the world to implement a national workplace smoking ban. The aim of this study was to assess the effect of this policy on all-cause and cause-specific, non-trauma mortality. Methods: A time-series epidemiologic assessment was conducted, utilizing Poisson regression to examine weekly age and gender-standardized rates for 215,878 non-trauma deaths in the Irish population, ages ≥35 years. The study period was from January 1, 2000, to December 31, 2007, with a post-ban follow-up of 3.75 years. All models were adjusted for time trend, season, influenza, and smoking prevalence. Results: Following ban implementation, an immediate 13% decrease in all-cause mortality (RR: 0.87; 95% CI: 0.76-0.99), a 26% reduction in ischemic heart disease (IHD) (RR: 0.74; 95% CI: 0.63-0.88), a 32% reduction in stroke (RR: 0.68; 95% CI: 0.54-0.85), and a 38% reduction in chronic obstructive pulmonary disease (COPD) (RR: 0.62; 95% CI: 0.46-0.83) mortality was observed. Post-ban reductions in IHD, stroke, and COPD mortalities were seen in ages ≥65 years, but not in ages 35-64 years. COPD mortality reductions were found only in females (RR: 0.47; 95% CI: 0.32-0.70). Post-ban annual trend reductions were not detected for any smoking-related causes of death. Unadjusted estimates indicate that 3,726 (95% CI: 2,305-4,629) smoking-related deaths were likely prevented post-ban. Mortality decreases were primarily due to reductions in passive smoking. Conclusions: The national Irish smoking ban was associated with immediate reductions in early mortality. Importantly, post-ban risk differences did not change with a longer follow-up period. This study corroborates previous evidence for cardiovascular causes, and is the first to demonstrate reductions in cerebrovascular and respiratory causes

Registration and analysis of multispectral images acquired during uterine transplantation surgery

Organ transplant success is dependent on blood supply health. A multispectral imaging laparoscope has been used to monitor tissue oxygenation changes during a rabbit uterine transplant. A feature tracking algorithm was used to compensate for movement. © OSA 2012

Multispectral Imaging of Organ Viability during Uterine Transplantation Surgery

Uterine transplantation surgery has been proposed as a treatment for permanent absolute uterine factor infertility (AUFI) in the case of loss of the uterus. Due to the complexity of the vasculature correct reanastomosis of the blood supply during transplantation surgery is a crucial step to ensure reperfusion and viability of the organ. While techniques such as fluorescent dye imaging have been proposed to visualise perfusion there is no gold standard for intraoperative visualisation of tissue oxygenation. In this paper results from a liquid crystal tuneable filter (LCTF)-based multispectral imaging (MSI) laparoscope are described. The system was used to monitor uterine oxygen saturation (SaO) before and after transplantation. Results from surgeries on two animal models (rabbits and sheep) are presented. A feature-based registration algorithm was used to correct for misalignment induced by breathing or peristalsis in the tissues of interest prior to analysis. An absorption spectrum was calculated at each spatial pixel location using reflectance data from a reference standard, and the relative contributions from oxy- and deoxyhaemoglobin were calculated using a least squares regression algorithm with non-negativity constraints. Results acquired during animal surgeries show that cornual oxygenation changes are consistent with those observed in point measurements taken using a pulse oximeter, showing reduced SaO following reanastomosis. Values obtained using the MSI laparoscope were lower than those taken with the pulse oximeter, which may be due to the latter’s use of the pulsatile arterial blood signal. Future work incorporating immunological test results will help to correlate SaO levels with surgical outcomes

Successful Medical Management of Status Post-Roux-en-Y-Gastric-Bypass Hyperinsulinemic Hypoglycemia

Roux-en-Y gastric bypass (RYGBP) is the most commonly performed type of bariatric surgery, which is used in the treatment of obesity and type 2 diabetes. Recent case reports and case series have described a rare complication of RYGBP, status post-gastric-bypass hyperinsulinemic hypoglycemia, which was mainly managed successfully with pancreatectomy. In this letter, we describe the first successful management of status post-gastric-bypass hyperinsulinemic hypoglycemia with diazoxide

Use of biomedical photonics in gynecological surgery: a uterine transplantation model

Aim: Uterine transplantation (UTx) has been proposed as a treatment for permanent absolute uterine factor infertility. The study aims were to compare pulse oximetry and multispectral imaging (MSI), for intraoperative tracking of uterine oxygen saturation in animal UTx models (rabbit and sheep). Results/methodology: Imaging results confirmed the re-establishment of adequate perfusion in the transplanted organ after surgery. Comparison of oxygen saturation values between the pre-UTx donor and post-UTx recipient, and pre-UTx and post-UTx recipient reveals a statistically significant decrease in saturation levels post-UTx. Conclusion: The use of MSI is the first case in gynecology and has demonstrated promise of possible future human use. MSI technique has advantages over pulse oximetry - it provides spatial information in a real-time, noncontact manner