Bounds on the multipartite entanglement of superpositions

We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.Comment: 4 pages, 2 figure. few typos correcte

Two essays on monetary union and international finance

This dissertation studies the Economic and Monetary Union (EMU) and its effects on foreign exchange markets and corporate cash holdings. These two potential effects are examined in the dissertation in two separate essays. The first essay examines the validity of the purchasing power parity (PPP) condition during three distinct exchange rate regimes (floating-rate, target-zone arrangement, and fixed-rate or common currency) from January 1973 through January 2004. My results support PPP, but I find that PPP during the common currency regime holds in fewer EMU countries than during the alternative exchange rate regimes. In addition, PPP between currency blocs holds for all countries examined during the first two regimes, but deteriorates after the introduction of the euro for the EMU countries as opposed to the non-EMU countries. I do not obtain strong evidence supporting PPP for the EMU countries since the euro adoption, but the faster mean reversion I observe in the few EMU countries where PPP does hold, may signal higher market efficiency and economic integration in the future. The second essay investigates corporate liquidity (cash holdings of firms) from 15 European Union (EU) countries [12 Economic and Monetary Union (EMU) countriesthat adopted the euro, and 3 non-EMU countries] from 1993 to 2002 using a dynamic panel data model. My main contributions to the corporate liquidity literature are fourfold. First, I provide evidence that creditor rights also affect corporate liquidity and their effect is more consistent than that of shareholder rights. Second, I show that the recent formation of EMU affects corporate liquidity. Debt and net working capital are better substitutes for cash in EMU countries than non-EMU countries. The adoption of a common currency reduces cash holdings in EMU countries. Third, my results suggest that agency theory plays an important role in explaining corporate liquidity. In particular, the agency view explains corporate liquidity better for EMU firms, probably because of an enhanced capital market integration that weakens the transaction and precautionary motives of holding cash. Fourth, I show that dealing with the endogeneity problem in corporate liquidity studies is important

Goodness-of-Fit Test Issues in Generalized Linear Mixed Models

Linear mixed models and generalized linear mixed models are random-effects models widely applied to analyze clustered or hierarchical data. Generally, random effects are often assumed to be normally distributed in the context of mixed models. However, in the mixed-effects logistic model, the violation of the assumption of normally distributed random effects may result in inconsistency for estimates of some fixed effects and the variance component of random effects when the variance of the random-effects distribution is large. On the other hand, summary statistics used for assessing goodness of fit in the ordinary logistic regression models may not be directly applicable to the mixed-effects logistic models. In this dissertation, we present our investigations of two independent studies related to goodness-of-fit tests in generalized linear mixed models. First, we consider a semi-nonparametric density representation for the random effects distribution and provide a formal statistical test for testing normality of the random-effects distribution in the mixed-effects logistic models. We obtain estimates of parameters by using a non-likelihood-based estimation procedure. Additionally, we not only evaluate the type I error rate of the proposed test statistic through asymptotic results, but also carry out a bootstrap hypothesis testing procedure to control the inflation of the type I error rate and to study the power performance of the proposed test statistic. Further, the methodology is illustrated by revisiting a case study in mental health. Second, to improve assessment of the model fit in the mixed-effects logistic models, we apply the nonparametric local polynomial smoothed residuals over within-cluster continuous covariates to the unweighted sum of squares statistic for assessing the goodness-of-fit of the logistic multilevel models. We perform a simulation study to evaluate the type I error rate and the power performance for detecting a missing quadratic or interaction term of fixed effects using the kernel smoothed unweighted sum of squares statistic based on the local polynomial smoothed residuals over x-space. We also use a real data set in clinical trials to illustrate this application

Comparison of the Synoptic Environments Conducive to Eastward versus Southeastward Transport of Asian Dust Events

Asian dust events that travel eastward and southeastward in the lower troposphere affect different areas near the coastal East Asia. To understand the synoptic differences between the two types of dust events, four dust events from 2006 to 2009 are selected for each type and the synoptic environment is compared. Surface measurements, trajectory analyses, and a regional dust model are also applied to further analyze each type. Results show that the strength of the low-level trough and the surface anticyclonic system are important in determining the transport route of dust event. A deep 700–850 hPa trough extending far south beyond 30°N associated with an intense surface anticyclone with maximum pressure greater than 1020 hPa over coastal East Asia favors southeastward movement of dust event. The prevailing northwesterlies or northerlies behind the deep trough and ahead of the intense surface anticyclone promote the southeastward movement of dust event. Since intense surface anticyclones often associated with strong dust events, severe dust activities tend to move southeastward. In contrast, a shallow trough accompanied by a weak surface high locating north of 30°N over the coastal East Asia favors an eastward transport route

Single-step growth of graphene and graphene-based nanostructures by plasma-enhanced chemical vapour deposition

The realization of many promising technological applications of graphene and graphene-based nanostructures depends on the availability of reliable, scalable, high-yield and low-cost synthesis methods. Plasma enhanced chemical vapor deposition (PECVD) has been a versatile technique for synthesizing many carbon-based materials, because PECVD provides a rich chemical environment, including a mixture of radicals, molecules and ions from hydrocarbon precursors, which enables graphene growth on a variety of material surfaces at lower temperatures and faster growth than typical thermal chemical vapor deposition. Here we review recent advances in the PECVD techniques for synthesis of various graphene and graphene-based nanostructures, including horizontal growth of monolayer and multilayer graphene sheets, vertical growth of graphene nanostructures such as graphene nanostripes with large aspect ratios, direct and selective deposition of monolayer and multi-layer graphene on nanostructured substrates, and growth of multi-wall carbon nanotubes. By properly controlling the gas environment of the plasma, it is found that no active heating is necessary for the PECVD growth processes, and that high-yield growth can take place in a single step on a variety of surfaces, including metallic, semiconducting and insulating materials. Phenomenological understanding of the growth mechanisms are described. Finally, challenges and promising outlook for further development in the PECVD techniques for graphene-based applications are discussed

Direct Large-Area Growth of Graphene on Silicon for Potential Ultra-Low-Friction Applications and Silicon-Based Technologies

Deposition of layers of graphene on silicon has the potential for a wide range of optoelectronic and mechanical applications. However, direct growth of graphene on silicon has been difficult due to the inert, oxidized silicon surfaces. Transferring graphene from metallic growth substrates to silicon is not a good solution either, because most transfer methods involve multiple steps that often lead to polymer residues or degradation of sample quality. Here we report a single-step method for large-area direct growth of continuous horizontal graphene sheets and vertical graphene nano-walls on silicon substrates by plasma-enhanced chemical vapor deposition (PECVD) without active heating. Comprehensive studies utilizing Raman spectroscopy, x-ray/ultraviolet photoelectron spectroscopy (XPS/UPS), atomic force microscopy (AFM), scanning electron microscopy (SEM) and optical transmission are carried out to characterize the quality and properties of these samples. Data gathered by the residual gas analyzer (RGA) during the growth process further provide information about the synthesis mechanism. Additionally, ultra-low friction (with a frictional coefficient ~0.015) on multilayer graphene-covered silicon surface is achieved, which is approaching the superlubricity limit (for frictional coefficients <0.01). Our growth method therefore opens up a new pathway towards scalable and direct integration of graphene into silicon technology for potential applications ranging from structural superlubricity to nanoelectronics, optoelectronics, and even the next-generation lithium-ion batteries