Cohen-Macaulayness of Rees Algebras of Diagonal Ideals

Given two determinantal rings over a field k. We consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the join variety. When the Rees algebra and the Symmetric algebra coincide, we show that the Rees algebra is Cohen-Macaulay.Comment: This work is based on author's Ph. D. thesis from Purdue University under the direction of Professor Bernd Ulric

Science and Risk Analysis in CPTPP/SPS-Plus: Role Model or Unbearable Burden?

Trade in food and agricultural products accounts for a major part of global trade, and the trade continues to alert domestic consumers to the risks associated with modern food processing and production methods. The Trans-Pacific Partnership Agreement (TPP), now rebranded as the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), represents a new model of mega-regional trade pacts posed to set higher standards for promoting and streamlining trade liberalization. Because of concerns with national food safety regulations that could constitute forms of non-tariff barriers, the CPTPP, in contrast to the World Trade Organization (WTO), stipulates further rules on parties’ sanitary and phytosanitary measures (SPS), achieving a type of role model of SPS-plus. This article explores the legal implications and progressiveness of the SPS-plus design, particularly focusing on the requirements of scientific evidence and risk analysis. The SPS-plus that sets hurdles for national regulatory regimes largely reflects WTO jurisprudence, international health standards, and the national regulations of the United States. I argue that the role model may provide momentum to modernize parties’ food safety regimes, but the cost of full compliance could be high. Genuine collaboration, experience-sharing, and technological and financial support between developed countries and less developed countries may alleviate the difficulties of implementation and promote coherence

Width and mode of the profile for some random trees of logarithmic height

We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise estimates for expected width, central moments of the width and almost sure convergence. It is widely applicable to random trees of logarithmic height, including recursive trees, binary search trees, quad trees, plane-oriented ordered trees and other varieties of increasing trees.Comment: Published at http://dx.doi.org/10.1214/105051606000000187 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Local limit theorems for finite and infinite urn models

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.Comment: Published in at http://dx.doi.org/10.1214/07-AOP350 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org