Strongly minimal PD4-complexes

We consider the homotopy types of $PD_4$-complexes $X$ with fundamental group $\pi$ such that $c.d.\pi=2$ and $\pi$ has one end. Let $\beta=\beta_2(\pi;F_2)$ and $w=w_1(X)$. Our main result is that (modulo two technical conditions on $(\pi,w)$) there are at most $2^\beta$ orbits of $k$-invariants determining "strongly minimal" complexes (i.e., those with homotopy intersection pairing $\lambda_X$ trivial). The homotopy type of a $PD_4$-complex $X$ with $\pi$ a $PD_2$-group is determined by $\pi$, $w$, $\lambda_X$ and the $v_2$-type of $X$. Our result also implies that Fox's 2-knot with metabelian group is determined up to TOP isotopy and reflection by its group.Comment: 17 page

Surgery on SL~×En\widetilde{\Bbb{SL}}\times\Bbb{E}^n-manifolds

We show that although closed $\widetilde{\Bbb{SL}}\times\Bbb{E}^n$-manifolds do not admit metrics of nonpositive sectional curvature, the arguments of Farrell and Jones can be extended to show that such manifolds are topologically rigid, if $n\geq2$.Comment: 7 pages, AMS-LaTeX file, To appear in the Canadian Mathematical Bulletin

Comparison of Current Gravity Estimation and Determination Models

This paper will discuss the history of gravity estimation and determination models while analyzing methods that are in development. Some fundamental methods for calculating the gravity field include spherical harmonics solutions, local weighted interpolation, and global point mascon modeling (PMC). Recently, high accuracy measurements have become more accessible, and the requirements for high order geopotential modeling have become more stringent. Interest in irregular bodies, accurate models of the hydrological system, and on-board processing has demanded a comprehensive model that can quickly and accurately compute the geopotential with low memory costs. This trade study of current geopotential modeling techniques will reveal that each modeling technique has a unique use case. It is notable that the spherical harmonics model is relatively accurate but poses a cumbersome inversion problem. PMC and interpolation models, on the other hand, are computationally efficient, but require more research to become robust models with high levels of accuracy. Considerations of the trade study will suggest further research for the point mascon model. The PMC model should be improved through mascon refinement, direct solutions that stem from geodetic measurements, and further validation of the gravity gradient. Finally, the potential for each model to be implemented with parallel computation will be shown to lead to large improvements in computing time while reducing the memory cost for each technique.Aerospace Engineering and Engineering Mechanic

Why Performance-Based College Funding Doesn't Work

For the better part of the past century, elected officials have sought ways to improve the performance of public sector operations, such as fire departments, libraries, health clinics, job training programs, elementary schools, and traffic safety. Interest in performance management has only grown over time, to the point today that it is nearly impossible to talk about government finance without also talking about performance. The idea of attempting to measure outcomes and paying for those results is compelling because of its simple logic. Proponents believe setting clear performance goals and tying funding to them will create incentives for public organizations to operate more efficiently and effectively, ultimately resulting in better delivery of public services. Fire departments, they reason, should not be funded according to the number of engines they own, but according to the number of fires they put out. Hospitals should be funded not by the number of patients admitted, but by the health outcomes of their patients. Schools should not be funded by the number of teachers they employ, but by each teacher's contribution to student learning.In recent years, advocates seeking to increase the number of college graduates in the United States have promoted the idea that states should finance their public universities using a performance-based model. Supporters of the concept believe that the $75 billion states invest in public higher education each year will not be spent efficiently or effectively if it is based on enrollment or other input measures, because colleges have little financial incentive to organize their operations around supporting students to graduation. When states shift to performance-based funding, it is hoped, colleges will adopt innovative practices that improve student persistence in college. The appeal of performance-based funding is "intuitive," its proponents argue, "based on the logical belief that tying some funding dollars to results will provide an incentive to pursue those results."However, while pay-for-performance is a compelling concept in theory, it has consistently failed to bear fruit in actual implementation, whether in the higher education context or in other public services

Saving Multilateralism: Renovating the House of Global Economic Governance for the 21st Century

Last December, the eyes of all those with a stake in international affairs turned to Europe. First they looked to Geneva, for signs that the long-running Doha Round of multilateral trade negotiations at the World Trade Organization (WTO) would get back on track after years of stalemate. Then observers turned to Copenhagen, hoping to see a binding and comprehensive agreement reflecting a commitment on the part of the world’s governments to address the pressing global challenge of climate change. They were to be sorely disappointed. Inscribed on the faces of those struggling to reach agreements was a deep frustration with multilateral processes that were proving incapable of delivery. Instead of agreement, the images playing out on television screens and in newspapers around the world were of fractiousness and division, due in part to the large number of participants and contentiousness of the issues faced; of anger, on the part of all those who felt marginalized by the process; and of concern, from those looking for signs that the world still has the capacity to reach accords when it really matters. The failure of these meetings to produce formal agreements—or even specific paths to reaching agreements in the future—despite the high stakes and the political capital that had been invested in advance left many questioning the ability of the world’s leaders to meet global challenges, shedding a spotlight on the institutions and fora that were established for the purpose of achieving multilateral solutions to the most pressing collective problems of the 21st century. Why did these meetings fail? Many had assumed that the most significant economic crisis since the Great Depression and the overwhelming scientific and circumstantial evidence of damaging changes to our climate would compel world leaders to set aside their differences and reach meaningful agreements. But it did not happen. It is not that the problems are not big enough or urgent enough. The failure to reach agreements can best be seen as part of a long-term trend toward increased complexity in the world that makes it nearly impossible to reach traditional multilateral binding accords, combined with a waning of faith on the part of many countries in multilateralism and multilateral institutions

Multilateral Economic Institutions and U.S. Foreign Policy: Hearing Before the Subcomm. on Multilateral Int\u27l Dev., Multilateral Insts., & Int\u27l Econ., Energy, & Envtl. Pol\u27y of the S. Comm. on Foreign Relations, 115th Cong., Nov. 27, 2018 (Statement of Jennifer A. Hillman)

Virtually every major international gathering of world leaders recently has ended in failure—or at least failure to reach enough agreement to issue a concluding statement or communique. These failures come at a time when many have been looking for signs that world leaders would come together to address the most pressing problems facing the world—including climate change, the breakdown in the rules of the international trading system, the need everywhere for good jobs that pay a living wage, and rapidly growing income inequality. The failure of these meetings to produce formal agreements—or even specific paths to reaching agreements in the future—despite the high stakes has left many questioning the ability of the world’s leaders to meet global challenges, shedding a spotlight on the institutions and fora that were established for the purpose of achieving multilateral solutions—particularly the World Trade Organization (WTO), the World Bank and the International Monetary Fund (IMF). The failure to reach agreements can best be seen as part of a long-term trend toward increased complexity in the world that makes it nearly impossible to reach traditional multilateral binding accords, combined with a waning of faith on the part of many countries in multilateralism and multilateral institutions. A number of clear trends emerge from the failures to reach accords at virtually all recent international gatherings: 1) Government policies and international arrangements for collective decision-making have not kept pace with changes in the world, especially the high degree of international economic integration and interdependence. Much of the increasing complexity in the international economic order stems from the explosive growth in the number and size of multinational corporations and financial institutions, many of which now dwarf the size of most of the nations in the world. Added to the complexity is the increase in the speed at which goods, money and technology moves around the globe in our digital age. 2) Learning to operate in this vastly more complex world will require more multilateralism, not less. As countries emerged from the era of colonialization and began opening their markets, the number of players on global stage increased, making reaching consensus among a much larger group of disparate interests more difficult. But because the most significant problems facing the world cross many international boundaries, solving them will require that countries come together to find regional, plurilateral, or global solutions. 3) It is essential that the international economic institutions be updated and improved, not destroyed or left to wither. Because it is clear that reaching major new binding accords or creating new international institutions is quite difficult, the best and most achievable solution is to renovate our existing institutions. Each needs to modernize and improve their governance structures to ensure that work can get done despite the increases in complexities and to update their mandates to ensure the ability to address the problems of the 21st century, many of which are quite different from those that existed in the 1940s when these institutions were created. Given that the crisis is most acute at the WTO, this testimony will focus on what must be done to renovate the World Trade Organization and why doing so is critical, both for the trading system and for the continued existence of a rules-based international economic order. The need for the WTO and its dispute settlement system to remain viable is particularly critical if we are to address the challenges presented by the explosive growth of China and its transformation into the largest exporter of goods in the world