Combinatorics in N = 1 Heterotic Vacua

We briefly review an algorithmic strategy to explore the landscape of heterotic E8 \times E8 vacua, in the context of compactifying smooth Calabi-Yau three-folds with vector bundles. The Calabi-Yau three-folds are algebraically realised as hypersurfaces in toric varieties and a large class of vector bundles are constructed thereon as monads. In the spirit of searching for Standard-like heterotic vacua, emphasis is placed on the integer combinatorics of the model-building programme.Comment: 14 pages. An introductory review prepared for the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physic

Correlation Structures Corresponding to Forward Rates

In finance, there is a constant effort to model future prices of stocks, bonds, and commodities; the ability to predict future behaviour provides important information about the underlying structure of these securities. While it has become common to model a single stock using the Black-Scholes formulation, the modelling of bond prices requires one to simulate the change of interest rates as a function of their maturity, which requires one to model the movement of an entire yield curve. If one studies the spectral decomposition of the correlation matrix corresponding to the spot rates from this curve, then one finds that the top three components can explain nearly all of the data; in addition, this same structure is observed for any bond or commodity. In his 2000 paper, Ilias Lekkos [4] proposes that such results are an artefact due to the implicit correlation between spot rates, and that the analysis should instead be performed using forward rates. In this paper, we discuss the results obtained for the spectral structure of the correlation matrices of forward rates, and investigate a model for this associated structure. The paper is divided into four parts, covering forward rates background material, principal components analysis, yield curve modelling, and conclusions and research extensions

Pieri rule for the affine flag variety

We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumar's work on the equivariant cohomology of the affine flag variety. We show that the cap operators for Pieri elements are the same as Pieri operators defined by Berg, Saliola and Serrano. This establishes the affine Pieri rule.Comment: 14 pages, Fixed typo

Exploring the effect of group polarisation on perceived invulnerability in general aviation pilots : a thesis presented in partial fulfilment of the requirements for the degree of Master of Aviation at Massey University

Although both perceived invulnerability and group polarisation are well known psychological phenomena, there has not been any research conducted to examine the effect of group polarisation on the level of perceived invulnerability amongst general aviation pilots. Two studies were conducted to measure the level of perceived invulnerability amongst general aviation pilots and to test whether the level of perceived invulnerability was affected due to group polarisation. The first study tested 34 pilots. Although the majority of the pilots exhibited perceived invulnerability, there was no evidence suggesting that low level group interaction induced group polarisation leading to an increase in individual's level of perceived invulnerability. The second study examined 78 pilots. Although the majority of the participants displayed perceived invulnerability, there was no evidence suggesting that high level group interaction resulted in group polarisation leading to an increase in individual's level of perceived invulnerability. There was no evidence that the two experimental manipulations (low group interaction and high group interaction) differed in effectiveness, as the effect size between studies I and II did not significantly differ. Although it is of some concern to general aviation safety that the majority of the pilots in both studies exhibited perceived invulnerability, the level of perceived invulnerability does not appear to be increased by a group polarisation effect. The latter finding is consistent with safe operations, having found no evidence that multi-crew operations lead to increased levels of perceived invulnerability. In addition to the implication of the current findings, limitations of the present study, possible areas for further research and recommendations are presented

Under the Queen’s Throne: Analysis of \u3cem\u3eThe Lily of Life\u3c/em\u3e

This essay explores one of the older fairy tales that is not widely known by many people. The Lily of Life, published in 1913 and written by Queen Marie of Romania, touches on several topics that are still in effect in today’s society. The fairy tale is about a royal family with beautiful twin sisters and happily married queen and king; however, a brave young prince challenges the happiness. The adventure one of the sisters takes to save the prince reveals the hidden meanings, morals, and values of the story. The further research of author Seth Lerer has been applied to the analysis to connect to find similar contents in The Lily of Life and Puritanism. This also serves the purpose to discover further into Queen Marie’s psychology and the culture. The findings create another dimension of analysis by reading the magical fairy tales through realistic lenses