Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface

We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d (assumed coprime) on a Riemann surface of genus g greater than or equal to 2. We also use these formulas for intersection numbers to obtain a proof of the Verlinde formula for the dimension of the space of holomorphic sections of a line bundle over M(n,d).Comment: 77 pages, LaTeX version 2.09. This is the text of the revised version which will appear in Annals of Mathematics. An error in Section 2 of the previous version has been correcte

Pseudo-scheduling: A New Approach to the Broadcast Scheduling Problem

The broadcast scheduling problem asks how a multihop network of broadcast transceivers operating on a shared medium may share the medium in such a way that communication over the entire network is possible. This can be naturally modeled as a graph coloring problem via distance-2 coloring (L(1,1)-labeling, strict scheduling). This coloring is difficult to compute and may require a number of colors quadratic in the graph degree. This paper introduces pseudo-scheduling, a relaxation of distance-2 coloring. Centralized and decentralized algorithms that compute pseudo-schedules with colors linear in the graph degree are given and proved.Comment: 8th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (ALGOSENSORS 2012), 13-14 September 2012, Ljubljana, Slovenia. 12 page

How Different are Universities from Companies? Financial Reporting Perspectives and the Market for Vice Chancellors (Part 2)

The oldest university still in operation is approximately 1,750 years old (wordiQ.com, 2004). When compared to firms, universities have stood the test of time, while firms seem to lack longevity. The oldest listed firm still operating is around 225 years old (O’Hara and Mandel, 2004), a lifespan of approximately one-eighth that of the oldest university. Whilst this comparison involves extremes, it is still the case that the average university is much older than the average company. What distinctive features of universities promote their long lifespans? Summers (2003) argues that it is the importance placed on knowledge and ideas in universities that help them withstand the test of time. He goes further to suggest that corporations may do better in meeting their challenges if they adopt some of the features of the university model. However, over time, we have seen universities moving away from their traditional positions as nonprofit organisations to institutions that are concerned with their financial viability. To what extent are universities becoming transformed into corporations? There is evidence suggesting that earnings quality for universities has improved over time, consistent with the theory that universities face increased pressure to become more like corporates and for greater public accountability as they seek to raise revenue from non-traditional sources in the face of federal funding cuts to higher education. We look at two dimensions of earnings quality for Australian universities: one based on the adherence of financial statements to prescribed requirements and the second based on accruals and earnings persistence. Although universities are nominally nonprofit organisations, there is evidence that they behave like companies and have incentives to avoid reporting negative earnings results. However, there is little evidence of opportunistic accruals earnings management. How does leadership affect the dynamics of these organisations? We investigate this by looking at the workings of the market for Vice-Chancellors. A picture of the typical Vice-Chancellor emerges. We see that they are appointed at relatively older ages than CEOs in the private sector, although they do not have shorter tenure. On an international comparison between Vice-Chancellors, Australian Vice-Chancellors enjoy the highest real remuneration, favourable taxation arrangements and a better quality of life relative to their counterparts in the United States and the United Kingdom. There is also a large disparity between the remuneration of Vice-Chancellors and CEOs, with the discount associated with university top management positions at 60 percent relative to the private sector. The evidence suggests that on the spectrum of organisation type from nonprofits to corporates, the traditional way in which we view universities as predominantly nonprofits is not consistent with the underlying behaviour of these institutions. This raises interesting implications for the future of higher education in Australia and the quality of the public good provided.

How Different are Universities from Companies? Financial Reporting Perspectives and the Market for Vice Chancellors (Part 4)

The oldest university still in operation is approximately 1,750 years old (wordiQ.com, 2004). When compared to firms, universities have stood the test of time, while firms seem to lack longevity. The oldest listed firm still operating is around 225 years old (O’Hara and Mandel, 2004), a lifespan of approximately one-eighth that of the oldest university. Whilst this comparison involves extremes, it is still the case that the average university is much older than the average company. What distinctive features of universities promote their long lifespans? Summers (2003) argues that it is the importance placed on knowledge and ideas in universities that help them withstand the test of time. He goes further to suggest that corporations may do better in meeting their challenges if they adopt some of the features of the university model. However, over time, we have seen universities moving away from their traditional positions as nonprofit organisations to institutions that are concerned with their financial viability. To what extent are universities becoming transformed into corporations? There is evidence suggesting that earnings quality for universities has improved over time, consistent with the theory that universities face increased pressure to become more like corporates and for greater public accountability as they seek to raise revenue from non-traditional sources in the face of federal funding cuts to higher education. We look at two dimensions of earnings quality for Australian universities: one based on the adherence of financial statements to prescribed requirements and the second based on accruals and earnings persistence. Although universities are nominally nonprofit organisations, there is evidence that they behave like companies and have incentives to avoid reporting negative earnings results. However, there is little evidence of opportunistic accruals earnings management. How does leadership affect the dynamics of these organisations? We investigate this by looking at the workings of the market for Vice-Chancellors. A picture of the typical Vice-Chancellor emerges. We see that they are appointed at relatively older ages than CEOs in the private sector, although they do not have shorter tenure. On an international comparison between Vice-Chancellors, Australian Vice-Chancellors enjoy the highest real remuneration, favourable taxation arrangements and a better quality of life relative to their counterparts in the United States and the United Kingdom. There is also a large disparity between the remuneration of Vice-Chancellors and CEOs, with the discount associated with university top management positions at 60 percent relative to the private sector. The evidence suggests that on the spectrum of organisation type from nonprofits to corporates, the traditional way in which we view universities as predominantly nonprofits is not consistent with the underlying behaviour of these institutions. This raises interesting implications for the future of higher education in Australia and the quality of the public good provided.