Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant

The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange functions that are uniformly bounded and decay away from their center at an exponential rate. An immediate corollary is that the corresponding Lebesgue constant will be uniformly bounded with a constant whose only dependence on the set of data sites is reflected in the mesh ratio, which measures the uniformity of the data. The analysis needed for these results was inspired by some fundamental work of Matveev where the Sobolev decay of Lagrange functions associated with certain kernels on \Omega \subset R^d was obtained. With a bit more work, one establishes the following: Lebesgue constants associated with surface splines and Sobolev splines are uniformly bounded on R^d provided the data sites \Xi are quasi-uniformly distributed. The non-Euclidean case is more involved as the geometry of the underlying surface comes into play. In addition to establishing bounded Lebesgue constants in this setting, a "zeros lemma" for compact Riemannian manifolds is established.Comment: 33 pages, 2 figures, new title, accepted for publication in SIAM J. on Math. Ana

Israel and Palestine - Looking Ahead Twenty Five Years: A Symposium Report

This article summarizes the findings of symposia conducted at the University of Bridgeport between 2005 and 2007 on the ways in which in changes in political economy, religion, and demographics will affect Israel and the Palestinian territories by the year 2030

A Seat at the UN Security Council for India? How the Indian Diaspora in the US may be key...

Prime Minister Narendara Modi assumed his role as India’s Head of Government in May 2014. One of his initiatives has been his appeal for United Nations reform with a specific focus on India assuming a broader role, including a permanent seat in the UN Security Council. While President Obama announced both in April and in September 2015 that he would support India having a permanent seat at the UN, the road to permanent Security Council membership for India, in spite of many reasons why this would make sense, will face obstacles because of the processes required to effect UN reform. The Indian diaspora notably in the United States may play a key role in allowing this to happen in the coming decade

How the Shanghai Rankings have transformed France’s System of Higher Education

Dr. Ward's poster discussing the impact of China's Shanghai ranking on education in France and to the United States

IR Inflation from Multiple Branes

In this paper we examine the IR inflation scenario using the DBI action, where we have $N$ multiple branes located near the tip of a warped geometry. At large $N$ the solutions are similar in form to the more traditional single brane models, however we find that it is difficult to simultaneously satisfy the WMAP bounds on the scalar amplitude and the scalar spectral index. We go on to examine two new solutions where N=2 and N=3 respectively, which both have highly non-linear actions. The sound speed in both cases is dramatically different from previous works, and for the N=3 case it can actually be zero. We show that inflation is possible in both frameworks, and find that the scalar spectral index is bounded from above by unity. The level of non-gaussian fluctuations are smaller in the N=2 case compared to the single brane models, whilst those in the N=3 case are much larger

The Comfort Women Controversy (cont.) Korea vs. Taiwan

Thomas Ward and William Lay's poster on why the Taiwanese experience of Japanese enforced comfort women in World War II differed from the Korean experience

Can a Park Statue Destabilize Northeast Asia’s Inter-State Relations?

In 1991, after fifty years of silence, the forced sexual enslavement of Korean women and girls at the hands of Japan’s Imperial Army during World War II emerged as an embarrassing blight upon Japan’s otherwise enviable profile as a political and economic miracle. The case against Japan’s alleged trafficking of women meandered through the courts of Japan and the United States. It also became an issue for United Nations Human Rights Commissioner Navi Pillay in August 2014. However, no satisfactory solution has been found. Beginning in 2005 efforts began in the United States to raise public awareness of the conditions that Korean women were subjected to at the hands of Japan. Strong resistance emerged in certain Japanese-American communities to the Korean and Korean-American accounting of events but especially from Japanese government officials who have visited the United States. Japan does not dispute that Korean women and girls served as Comfort Women; however, its disputes the methods of recruitment and the numbers of women indicated in the Korean narrative. We thus find two competing narratives, that of Japan and that of Korea, being disputed in the United States. In most places the Korean narrative has prevailed but in places such as Buena Vista, California and Queens, New York, it has not. This text argues that the “Comfort Women” controversy may undermine Korea-Japan-US relations in Northeast Asia. The President of Korea made it clear in December 2014 that relations with Japan will not improve without addressing this. This article speaks of ways to do indicating the need for an objective review of both narratives and, most likely, the articulation of an American narrative