Monomial Complete Intersections, The Weak Lefschetz Property and Plane Partitions

We characterize the monomial complete intersections in three variables satisfying the Weak Lefschetz Property (WLP), as a function of the characteristic of the base field. Our result presents a surprising, and still combinatorially obscure, connection with the enumeration of plane partitions. It turns out that the rational primes p dividing the number, M(a,b,c), of plane partitions contained inside an arbitrary box of given sides a,b,c are precisely those for which a suitable monomial complete intersection (explicitly constructed as a bijective function of a,b,c) fails to have the WLP in characteristic p. We wonder how powerful can be this connection between combinatorial commutative algebra and partition theory. We present a first result in this direction, by deducing, using our algebraic techniques for the WLP, some explicit information on the rational primes dividing M(a,b,c).Comment: 16 pages. Minor revisions, mainly to keep track of two interesting developments following the original posting. Final version to appear in Discrete Mat

Inference for Two-stage Experiments under Covariate-Adaptive Randomization

This paper studies inference in two-stage randomized experiments with covariate-adaptive randomization. Here, by a two-stage randomized experiment, we mean one in which clusters (e.g., households, schools, or graph partitions) are first randomly assigned to different levels of treated fraction and then units within each treated clusters are randomly assigned to treatment or control according to its selected treated fraction; by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve ``balance'' within each stratum. We study estimation and inference of this design under two different asymptotic regimes: ``small strata'' and ``large strata'', which enable us to study a wide range of commonly used designs from the empirical literature. We establish conditions under which our estimators are consistent and asymptotically normal and construct consistent estimators of their corresponding asymptotic variances. Combining these results establishes the asymptotic validity of tests based on these estimators. We argue that ignoring covariate information at the design stage can lead to efficiency loss, and commonly used inference methods that ignore or improperly use covariate information can lead to either conservative or invalid inference. Then, we apply our results to studying optimal use of covariate information in two-stage designs, and show that a certain generalized matched-pair design achieves minimum asymptotic variance for each proposed estimator. A simulation study and empirical application confirm the practical relevance of our theoretical results

A Policy Overview, and Implications for the EU

The post-Cold War international security environment has changed dramatically however, the proliferation of Weapons of Mass Destruction (WMD) continues to be one of the major global challenges and threats to security. In 2003, the European Union declared in the European Security Strategy (ESS) its aim to promote 'effective multilateralism', and established a strategic partnership with China. Focusing on major current multilateral regimes in export controls, this policy paper uses China as a case country and provides an overview of China's export control policies.It then discusses the implications of promoting European norms and paradigms such as multilateralism to China, especially in the area of international export controls

Indium growth and island height control on Si submonolayer phases

The quantum size effects (QSE) make it possible to control the dimensions of self-assembled nanostructures. An important goal in present day surface science is to grow uniform sized self-assembled nanostructures. One system which has displayed a number of interesting surface structures is Pb/In grown on a Si(111) substrate. The first part of the thesis discussed Pb islands grown on the anisotropic Si(111)-In(4x1) substrate. In addition to a preferred height of 4 monolayers due to QSE, these islands grow as nanowires with a preferred width of 660nm due to strain driven growth from the anisotropic substrate. Islands grown on the In(4x1) substrate also retain their preferred height to room temperature in contrast to previously observed critical temperatures of 250 K or less for islands grown on other substrates. Then In islands were grown on Si(111)-Pb-alpha-sqrt3 x sqrt3 substrate. The In islands in face-centered cubic (FCC) structure were found to have a preferred height of 4 monolayers due to QSE. With further depositions, an FCC to body-centered tetragonal(BCT) structure transition is observed. The In bct islands was found to have unexpected fast growth rate compared to FCC structure, which indicate the extra high mobility of In atoms. In the last part In islands were grown on varies of In phases at low temperature. Conversion between submonolayer In phases are observed. Due to the highly mobility of In atoms, the QSE effects observed on the Pb alpha phase is not observed

High Enthalpy Storage Thermoset Network with Giant Stress and Energy Output in Rubbery State and Associated Applications

In this study, a new shape memory thermoset network with giant stress and energy output in rubbery state is synthesized and studied firstly since the low output in stress and energy in rubbery state has been a bottleneck for wide-spread applications of thermoset shape memory polymers (SMPs). Traditionally, stress or energy storage in thermoset network is through entropy reduction by mechanical deformation or programming. We here report another mechanism for energy storage, which stores energy primarily through enthalpy increase by stretched bonds during programming. As compared to entropy-driven counterparts, which usually have a stable recovery stress from tenths to several MPa and energy output of several tenths MJ/m3, our rubbery network achieved a recovery stress of 17.0 MPa and energy output of 2.12 MJ/m3 in bulk form. Subsequently, this new shape memory thermoset polymer is fabricated into powder and particle for to serve as the expansive additive of the cement used in petroleum industry. Shape memory polymer has been identified and studied as a new generation of the expansive additive for the cement from our previous study. It has showed a good expansion ability and the preservation of the mechanical property. However, for the deeper unground, the higher temperature as the trigger of shape memory effect is necessary. Here we report the new shape memory polymer with the giant stress and energy output can achieve a 1.2% circumferential expansion by adding 6% weight percent in particle form. Moreover, it can enhance the mechanical property in terms of compressive strength, Young’s modulus and the compressive strain at the same time which is a rare accomplishment by single type additive. Moreover, the E-glass fiber FRP rebar and the reinforced concrete can be obtained. The curved FRP can produce 77.8 MPa bending recovery stress

VISUAL SEMANTIC SEGMENTATION AND ITS APPLICATIONS

This dissertation addresses the difficulties of semantic segmentation when dealing with an extensive collection of images and 3D point clouds. Due to the ubiquity of digital cameras that help capture the world around us, as well as the advanced scanning techniques that are able to record 3D replicas of real cities, the sheer amount of visual data available presents many opportunities for both academic research and industrial applications. But the mere quantity of data also poses a tremendous challenge. In particular, the problem of distilling useful information from such a large repository of visual data has attracted ongoing interests in the fields of computer vision and data mining. Structural Semantics are fundamental to understanding both natural and man-made objects. Buildings, for example, are like languages in that they are made up of repeated structures or patterns that can be captured in images. In order to find these recurring patterns in images, I present an unsupervised frequent visual pattern mining approach that goes beyond co-location to identify spatially coherent visual patterns, regardless of their shape, size, locations and orientation. First, my approach categorizes visual items from scale-invariant image primitives with similar appearance using a suite of polynomial-time algorithms that have been designed to identify consistent structural associations among visual items, representing frequent visual patterns. After detecting repetitive image patterns, I use unsupervised and automatic segmentation of the identified patterns to generate more semantically meaningful representations. The underlying assumption is that pixels capturing the same portion of image patterns are visually consistent, while pixels that come from different backdrops are usually inconsistent. I further extend this approach to perform automatic segmentation of foreground objects from an Internet photo collection of landmark locations. New scanning technologies have successfully advanced the digital acquisition of large-scale urban landscapes. In addressing semantic segmentation and reconstruction of this data using LiDAR point clouds and geo-registered images of large-scale residential areas, I develop a complete system that simultaneously uses classification and segmentation methods to first identify different object categories and then apply category-specific reconstruction techniques to create visually pleasing and complete scene models