Examining Point-Nonpoint Trading Ratios for Acid Mine Drainage Remediation with a Spatial-Temporal Optimization Model

A trading ratio is required for water quality trading that involves nonpoint sources to compensate for the difficulty of determining nonpoint loadings, the stochastic characteristics of nonpoint loadings, and the uncertainty inherent in nonpoint source pollution control strategies. Compensating for risk and uncertainty is one of the primary justifications that a trading ratio greater than one is commonly considered. However, the appropriate specific value of a trading ratio remains unclear because of qualitative differences between point and nonpoint sources. This study addresses a growing concern with the analytical underpinnings of point/nonpoint trading ratios in water quality trading programs. This paper considers a basic spatial-temporal optimal control model assuming that the goal of the decision maker is to maximize ecological services from the watershed over a 10-year planning horizon given a predetermined budget each year to treat acid mine drainage problems. The level of pollution is assumed to be known but declining slightly over time as the acid mine drainage sources evolve. Resources are assumed to be spent on remediation projects that produce long term but declining treatment results. The primary goal of the model is to distribute the available resources over the basin by investing in restoration projects for targeted streams each year that will maximize the ecological return on this investment. The model reflects both the spatial reality of variations in flow, in pollution, in treatment, and in the ecological benefits produced and the intertemporal constraints of limited resources and the inability to move remediation programs once the initial investment is made. The resulting optimal temporal and spatial investment strategies are derived from solutions to a mixed integer programming problem obtained using the GAMS/CPLEX mixed integer programming package. The optimal results are then manipulated to evaluate trading ratios. A hypothetical acidity trading scenario is proposed in which a point source (a new coal mine operation subject to TMDL rules) uses credits generated through remediation projects at other sites from treatment of nonpoint sources within the same basin over the 10-year planning horizon. The trading ratio is the ratio of the expected amount of pollutant removed by treating the nonpoint source divided by the amount of additional pollution allowed from the new point source. Our results indcate that point/nonpoint trading ratios in proposed trading scenarios greater than one can be justified. For example, for a point/nonpoint trade between sources in adjacent stream segments, the appropriate trading ratio is 3.66 (or 3.66 to one). We note that current regulations give a lower bound for point/nonpoint trading ratio of 1:1. The upper bound for point/nonpoint trading ratio depends on technical aspects of the relative costs of treating the point source or treating nonpoint sources and reflects the limit of how much one is willing to pay for credits. A variety of factors determine trading ratios. First, to encourage trades with less uncertainty, trades in which the credit seller and buyer are in close proximity, and in which the credit seller is upstream, lower trading ratios are recommended. Second, trading ratios should be adjusted to favor trades that contribute to strategic restoration goals such as the improvement or maintenance of water quality in a particular basin. Reduced ratios provide incentives to promote the generation of credits in priority locations. Finally, trading ratios for same-pollutant trades should be lower than those for cross-pollutant trades. Three separate trading currencies would be used to account for same-pollutant acid mine drainage trades: pounds of iron, aluminum, and manganese. There would be little uncertainty in the outcome of a trade if the credit generator and buyer were affecting the same pollutant. In contrast, cross-pollutant trades that use a common currency such as ecological indices would be measured based on their ecological effect, which is one step removed from the actual changes in pollutant loads. The higher trading ratio required for cross-pollutant trades reflects this greater uncertainty. All potential trades considered in this study are interspatial trades; trades occur in the same basin; trades could be cross-pollutant trades within acid mine draiange and same-pollutant trades as well; and the credit buyer is the new coal mining operation; credit generators could be government agencies or nonprofit organization; and abandned mine lands and bond forfeiture sites can be sites where credits are generated.point-nonpoint water quality trading, trading ratio, acid mine drainage, spatial-temporal optimization, Environmental Economics and Policy,

Combinatorial aspects of orthogonal group integrals

We study the integrals of type $I(a)=\int_{O_n}\prod u_{ij}^{a_{ij}}\,du$, depending on a matrix $a\in M_{p\times q}(\mathbb N)$, whose exact computation is an open problem. Our results are as follows: (1) an extension of the "elementary expansion" formula from the case $a\in M_{2\times q}(2\mathbb N)$ to the general case $a\in M_{p\times q}(\mathbb N)$, (2) the construction of the "best algebraic normalization" of $I(a)$, in the case $a\in M_{2\times q}(\mathbb N)$, (3) an explicit formula for $I(a)$, for diagonal matrices $a\in M_{3\times 3}(\mathbb N)$, (4) a modelling result in the case $a\in M_{1\times 2}(\mathbb N)$, in relation with the Euler-Rodrigues formula. Most proofs use various combinatorial techniques.Comment: 34 page

Algorithms for pre-microrna classification and a GPU program for whole genome comparison

MicroRNAs (miRNAs) are non-coding RNAs with approximately 22 nucleotides that are derived from precursor molecules. These precursor molecules or pre-miRNAs often fold into stem-loop hairpin structures. However, a large number of sequences with pre-miRNA-like hairpin can be found in genomes. It is a challenge to distinguish the real pre-miRNAs from other hairpin sequences with similar stem-loops (referred to as pseudo pre-miRNAs). The first part of this dissertation presents a new method, called MirID, for identifying and classifying microRNA precursors. MirID is comprised of three steps. Initially, a combinatorial feature mining algorithm is developed to identify suitable feature sets. Then, the feature sets are used to train support vector machines to obtain classification models, based on which classifier ensemble is constructed. Finally, an AdaBoost algorithm is adopted to further enhance the accuracy of the classifier ensemble. Experimental results on a variety of species demonstrate the good performance of the proposed approach, and its superiority over existing methods. In the second part of this dissertation, A GPU (Graphics Processing Unit) program is developed for whole genome comparison. The goal for the research is to identify the commonalities and differences of two genomes from closely related organisms, via multiple sequencing alignments by using a seed and extend technique to choose reliable subsets of exact or near exact matches, which are called anchors. A rigorous method named Smith-Waterman search is applied for the anchor seeking, but takes days and months to map millions of bases for mammalian genome sequences. With GPU programming, which is designed to run in parallel hundreds of short functions called threads, up to 100X speed up is achieved over similar CPU executions

Parameter Redundancy and Identifiability in Hidden Markov Models

Hidden Markov models are a flexible class of models that can be used to describe time series data which depends on an unobservable Markov process. As with any complex model, it is not always obvious whether all the parameters are identifiable, or if the model is parameter redundant; that is, the model can be reparameterised in terms of a smaller number of parameters. This paper considers different methods for detecting parameter redundancy and identifiability in hidden Markov models. We examine both numerical methods and methods that involve symbolic algebra. These symbolic methods require a unique representation of a model, known as an exhaustive summary. We provide an exhaustive summary for hidden Markov models and show how it can be used to investigate identifiability

Probabilistic Choice Models

We examine a number of probabilistic choice models in which people might form their beliefs to play their strategies in a game theoretic setting in order to propose alternative equilibrium concepts to the Nash equilibrium. In particular, we evaluate the Blavatskyy model, Returns Based Beliefs (RBB) model, Quantal Response Equilibrium (QRE) model, Boundedly Rational Nash Equilibrium (BRNE) model and the Utility Proportional Beliefs (UPB) model. We outline the foundational axioms for these models and fully explicate them in terms of probabilistic actions, probabilistic beliefs and their epistemic characterizations. We test the model predictions using empirical data and show which models perform better under which conditions. We also extend the Blavatskyy model which was developed to consider games with two actions to cases where there are three or more actions. We provide a nuanced understanding of how different types of probabilistic choice models might predict better than others