Vertex operators, Weyl determinant formulae and Littlewood duality

Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof of the duality between the universal orthogonal and symplectic Schur functions using vertex operators.Comment: 18 pages; revised version, reference adde

Three Essays on the Empirical Market Microstructure of Money Market Derivatives

This thesis is the first directly to study the entire limit order book of a large market. Herein, I conduct a population study on the microstructure of the Eurodollar future market, to my knowledge this is a) the first study of its type and b) the largest microstructure study ever conducted. I will build a data-drive model that incorporates information from the entire population of quotes updates and transactions on this type of future market. This thesis aims to provide a comprehensive understanding of the market microstructure on money market derivatives and the impact of high-speed algorithmic trading activity on the market characteristics and quality. I apply a broad battery of market volatility and liquidity measurements, and gauge the proportion of high-frequency algorithmic traders in the market. This thesis provides a standard asymmetric information based theoretical model to predict the relation on the term structure of Eurodollar future contracts. The prediction is a non-linear relation between the saturation of algorithmic traders (ATs) versus the impacts on the quality of the market. Therefore, I develop a novel semi-parametric estimator and model the non-linear relation between the impact of the fraction of algorithmic trading and a large set of different market quality indicators including volatility, liquidity and price informativeness. Finally, I consider the efficiency and the speed of high-frequency prices formation by implementing the return autocorrelations and vector autoregression, and also make a contribution to the trade classification algorithm using the order book data. My findings are fourfold. First, the impact of high-frequency trading (HFT) on market quality is a non-linear by implementing the semi-parametric model. This may partially explain why prior studies have found contradictory results regarding the impact of high-frequency traders (HFTs) on market characteristics. Second, prior studies only including the inside quotes or best bid best ask are limited to reflect all the information in the market. My findings suggest that the second level quoting in the limit order book is by far the most rapidly quoted element of the order book. Furthermore, I find that wavelet variance covariance of the bid and the ask side changes substantially over the term structure; providing further supporting evidence of the non-linear impact of HFTs. Finally, the adjustment time of the trade prices formation process is within one second, and the quote prices are even faster within 200 milliseconds (ms). The mid-quoted return autocorrelation is positive and gradually increase from the shortest time interval to the longest time interval. The trade prices are less sensitive to new information as the contract approaches its maturity

Seasonal Variations in Nutrient and Total Suspended Solids Sources and Fluxes in Rivers of Northern New Jersey and Newark Bay, USA

In recent decades, aquatic systems have experienced major problems with water quality due to high nutrient concentrations from both point and non-point sources resulting from industrialization, urbanization, and population growth. While nutrient pollution due to land use change cannot be ignored, point sources such as combined sewer overflows and discharging sites have also contributed to the problem. Integrated hydrodynamic, chemical, and biological models have been developed to simulate nutrient transportation from both sources. This paper reviews and analyzes water quality data from published literature to evaluate nutrient pollution in aquatic systems and emphasizes the need for a continuously developed integrated monitoring and management plan to regulate nutrient discharges. Two studies were conducted in northern New Jersey, USA, to examine the impact of land use change on water quality in the Passaic River and to estimate nutrient fluxes from the Passaic and Hackensack Rivers into Newark Bay. The first study used long-term water quality monitoring and land-use data to show that urban land use is a significant contributor to water quality problems in the Passaic River, while natural landscapes dominate the area. The second study collected bi-weekly total inorganic nitrogen and orthophosphate concentration data over 15 years to estimate the annual nutrient loading from both rivers, which varied seasonally due to weather conditions such as hurricane events. Another study investigated the relationship between total suspended solids (TSS) loadings and Land Use Land Cover (LULC) type across six drainage basin areas in New Jersey, using 16 years of published monitoring data. The study found that water discharge has a strong correlation with the area of a drainage basin and that TSS concentration is positively correlated with medium and high developed LULC types and negatively impacted by forests and wetlands. The study also used the ARIMA model to forecast future TSS loading trends and fluctuations over time, indicating its effectiveness in capturing cyclic patterns, especially with seasonal variations in time series data