Introduction to Gromov-Witten Theory

The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference aimed at introducing graduate students to the subject which took place during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.Comment: 21 Page

Quasi-modularity of generalized sum-of-divisors functions

In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that they are quasi-modular forms.Comment: 11 page

Three Steps Towards More Effective Development Assistance

There are three steps New Zealand can take to make its bilateral development assistance more effective in reducing poverty. These steps are ‘easy’ because they are unilateral: they improve the effectiveness of development assistance without requiring changes in the politics or policies of developing countries. By far the most important of these three steps is to focus New Zealand’s bilateral aid on those poor countries that are democracies pursing policies of market-led growth. One of the major findings of recent research is that development aid only reinforces what is already there. New Zealand should accept the developing countries as it finds them and pick and choose so that it helps those already helping themselves.aid effectiveness, autocracy, democracy, development, New Zealand

MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms

We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute these functions, as well as proving a conjecture of MacMahon about their general form by relating them to quasi-modular forms. These functions arise as solutions to a curve-counting problem on Abelian surfaces.Comment: 6 Page

Pirate plunder: game-based computational thinking using scratch blocks

Policy makers worldwide argue that children should be taught how technology works, and that the ‘computational thinking’ skills developed through programming are useful in a wider context. This is causing an increased focus on computer science in primary and secondary education. Block-based programming tools, like Scratch, have become ubiquitous in primary education (5 to 11-years-old) throughout the UK. However, Scratch users often struggle to detect and correct ‘code smells’ (bad programming practices) such as duplicated blocks and large scripts, which can lead to programs that are difficult to understand. These ‘smells’ are caused by a lack of abstraction and decomposition in programs; skills that play a key role in computational thinking. In Scratch, repeats (loops), custom blocks (procedures) and clones (instances) can be used to correct these smells. Yet, custom blocks and clones are rarely taught to children under 11-years-old. We describe the design of a novel educational block-based programming game, Pirate Plunder, which aims to teach these skills to children aged 9-11. Players use Scratch blocks to navigate around a grid, collect items and interact with obstacles. Blocks are explained in ‘tutorials’; the player then completes a series of ‘challenges’ before attempting the next tutorial. A set of Scratch blocks, including repeats, custom blocks and clones, are introduced in a linear difficulty progression. There are two versions of Pirate Plunder; one that uses a debugging-first approach, where the player is given a program that is incomplete or incorrect, and one where each level begins with an empty program. The game design has been developed through iterative playtesting. The observations made during this process have influenced key design decisions such as Scratch integration, difficulty progression and reward system. In future, we will evaluate Pirate Plunder against a traditional Scratch curriculum and compare the debugging-first and non-debugging versions in a series of studies

Studies on antibody to gastric intrinsic factor

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