DEVELOPMENT OF A CONCEPTUAL MODEL AND PARAMETERIZATION OF A MATHEMATICAL MODEL FOR SEDIMENT PHOSPHORUS DIAGENESIS, SORPTION AND RELEASE FROM ONONDAGA LAKE SYRACUSE, NEW YORK

Eutrophication is a persistent problem in many fresh water lakes. Delay in lake recovery following reductions in external loading of phosphorus, the limiting nutrient in fresh water ecosystems, is often observed. Models have been created to assist with lake remediation efforts, however, the application of management tools to sediment diagenesis is often neglected due to conceptual and mathematical complexity. SED2K (Chapra et al. 2012) is proposed as a "middle way", offering engineering rigor while being accessible to users. An objective of this research is to further support the development and application SED2K for sediment phosphorus diagenesis and release to the water column of Onondaga Lake. Application of SED2K has been made to eutrophic Lake Alice in Minnesota. The more homogenous sediment characteristics of Lake Alice, compared with the industrially polluted sediment layers of Onondaga Lake, allowed for an invariant rate coefficient to be applied to describe first order decay kinetics of phosphorus. When a similar approach was attempted on Onondaga Lake an invariant rate coefficient failed to simulate the sediment phosphorus profile. Therefore, labile P was accounted for by progressive preservation after burial and a rate coefficient which gradual decreased with depth was applied. In this study, profile sediment samples were chemically extracted into five operationally-defined fractions: CaCO3-P, Fe/Al-P, Biogenic-P, Ca Mineral-P and Residual-P. Chemical fractionation data, from this study, showed that preservation is not the only mechanism by which phosphorus may be maintained in a non-reactive state in the profile. Sorption has been shown to contribute substantially to P burial within the profile. A new kinetic approach involving partitioning of P into process based fractions is applied here. Results from this approach indicate that labile P (Ca Mineral and Organic P) is contributing to internal P loading to Onondaga Lake, through diagenesis and diffusion to the water column, while the sorbed P fraction (Fe/Al-P and CaCO3-P) is remaining consistent. Sediment profile concentrations of labile and total phosphorus at time of deposition were also modeled and compared with current labile and total phosphorus, to quantify the extent to which remaining phosphorus which will continue to contribute to internal P loading and influence the trophic status of Onondaga Lake. Results presented here also allowed for estimation of the depth of the active sediment layer and the attendant response time as well as the sediment burden of labile P and associated efflux.

DISTRIBUTED APPROACH FOR SOLVING OPTIMAL POWER FLOW PROBLEMS IN THREE-PHASE UNBALANCED DISTRIBUTION NETWORK

The objective of this report is to study distributed (decentralized) three phase optimal power flow (OPF) problem in unbalanced power distribution networks. A full three phase representation of the distribution networks is considered to account for the highly unbalance state of the distribution networks. All distribution network’s series/shunt components, and load types/combinations had been modeled on commercial version of General Algebraic Modeling System (GAMS), the high-level modeling system for mathematical programming and optimization. The OPF problem has been successfully implemented and solved in a centralized approach and distributed approach, where the objective is to minimize the active power losses in the entire system. The study was implemented on the IEEE-37 Node Test Feeder. A detailed discussion of all problem sides and aspects starting from the basics has been provided in this study. Full simulation results have been provided at the end of the report.

Incorporating Latent Variables into Discrete Choice Models - A Simultaneous Estimation Approach Using SEM Software

Integrated choice and latent variable (ICLV) models represent a promising new class of models which merge classic choice models with the structural equation approach (SEM) for latent variables. Despite their conceptual appeal, applications of ICLV models in marketing remain rare. We extend previous ICLV applications by first estimating a multinomial choice model and, second, by estimating hierarchical relations between latent variables. An empirical study on travel mode choice clearly demonstrates the value of ICLV models to enhance the understanding of choice processes. In addition to the usually studied directly observable variables such as travel time, we show how abstract motivations such as power and hedonism as well as attitudes such as a desire for flexibility impact on travel mode choice. Furthermore, we show that it is possible to estimate such a complex ICLV model with the widely available structural equation modeling package Mplus. This finding is likely to encourage more widespread application of this appealing model class in the marketing field.

Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.

Cost-effectiveness of different strategies to monitor adults on antiretroviral treatment: a combined analysis of three mathematical models

Background: WHO's 2013 revisions to its Consolidated Guidelines on antiretroviral drugs recommend routine viral load monitoring, rather than clinical or immunological monitoring, as the preferred monitoring approach on the basis of clinical evidence. However, HIV programmes in resource-limited settings require guidance on the most cost-effective use of resources in view of other competing priorities such as expansion of antiretroviral therapy coverage. We assessed the cost-effectiveness of alternative patient monitoring strategies. Methods: We evaluated a range of monitoring strategies, including clinical, CD4 cell count, and viral load monitoring, alone and together, at different frequencies and with different criteria for switching to second-line therapies. We used three independently constructed and validated models simultaneously. We estimated costs on the basis of resource use projected in the models and associated unit costs; we quantified impact as disability-adjusted life years (DALYs) averted. We compared alternatives using incremental cost-effectiveness analysis. Findings: All models show that clinical monitoring delivers significant benefit compared with a hypothetical baseline scenario with no monitoring or switching. Regular CD4 cell count monitoring confers a benefit over clinical monitoring alone, at an incremental cost that makes it affordable in more settings than viral load monitoring, which is currently more expensive. Viral load monitoring without CD4 cell count every 6—12 months provides the greatest reductions in morbidity and mortality, but incurs a high cost per DALY averted, resulting in lost opportunities to generate health gains if implemented instead of increasing antiretroviral therapy coverage or expanding antiretroviral therapy eligibility. Interpretation: The priority for HIV programmes should be to expand antiretroviral therapy coverage, firstly at CD4 cell count lower than 350 cells per μL, and then at a CD4 cell count lower than 500 cells per μL, using lower-cost clinical or CD4 monitoring. At current costs, viral load monitoring should be considered only after high antiretroviral therapy coverage has been achieved. Point-of-care technologies and other factors reducing costs might make viral load monitoring more affordable in future. Funding: Bill & Melinda Gates Foundation, WHO.

A case of distinct difference between the measured blood Ethanol concentration and the concentration estimated by Widmark's equation

In the last century, several mathematical models have been developed to calculate blood ethanol concentrations (BAC) from the amount of ingested ethanol and vice versa. The most common one in the field of forensic sciences is Widmark's equation. A drinking experiment with 10 voluntary test persons was performed with a target BAC of 1.2 g/kg estimated using Widmark's equation as well as Watson's factor. The ethanol concentrations in the blood were measured using headspace gas chromatography/flame ionization and additionally with an alcohol Dehydrogenase (ADH)-based method. In a healthy 75-year-old man a distinct discrepancy between the intended and the determined blood ethanol concentration was observed. A blood ethanol concentration of 1.83 g/kg was measured and the man showed signs of intoxication. A possible explanation for the discrepancy is a reduction of the total body water content in older people. The incident showed that caution is advised when using the different mathematical models in aged people. When estimating ethanol concentrations, caution is recommended with calculated results due to potential discrepancies between mathematical models and biological systems