Transformations from an oblate spheroid to a plane and vice versa: The equations used in the cartographic projection program MAP2

The relationships between the coordinates of a point on the surface on an oblate spheroid and the coordinates of the projection of that point in several common map projections are discussed. Because several of the projections are conformal, the theory of conformally mapping an oblate spheroid to the plane is summarized. For each projection considered, the equations which map the spheroid to the plane and their inverses are given

Trans-Atlantic Interactions

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Henry Brant at the Holland Festival

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Filtering and forecasting commodity futures prices under an HMM framework

We propose a model for the evolution of arbitrage-free futures prices under a regime-switching framework. The estimation of model parameters is carried out using the hidden Markov filtering algorithms. Comprehensive numerical experiments on real financial market data are provided to illustrate the effectiveness of our algorithm. In particular, the model is calibrated with data from heating oil futures and its forecasting performance as well as statistical validity is investigated. The proposed model is parsimonious, self-calibrating and can be very useful in predicting futures prices. © 2013 Elsevier B.V

Appendix: Conjunction-Problem v. Non-Conjunction-Problem Jurisdictions

This appendix presents the relevant data from our survey of jury instructions in support of the article in the print edition of the William & Mary Law Review. The Conjunction Problem and the Logic of Jury Findings (59 Wm. & Mary L. Rev. 619, 673-87 (2017)

The Conjunction Problem and the Logic of Jury Findings

For several decades, evidence theorists have puzzled over the following paradox, known as the “conjunction paradox” or “conjunction problem.” Probability theory appears to tell us that the probability of a conjunctive claim is the product resulting from multiplying the probabilities of its separate conjuncts. In a three element negligence case (breach of duty, causation, damages), a plaintiff who proves each element to a 0.6 probability will have proven her overall claim to a very low probability of 0.216. Either the plaintiff wins the verdict based on this low probability (if the jury focuses on elements), or the plaintiff loses despite having met the condition of proving each element to the stated threshold. To solve this “conjunction problem,” evidence theorists have advanced such proposals as changing the rules of probability, barring probability theory entirely from analysis of adjudicative fact-finding, abandoning the procedural principle that the defendant need not present a narrative of innocence or nonliability, or dispensing with the requirement that the overall claim meet an established burden of proof. This Article argues that the conjunction paradox in fact presents a theoretical problem of little if any consequence. Dropping the condition that proving each element is a sufficient, as opposed to merely a necessary, condition for proof of a claim makes the conjunction problem disappear. Nothing in logic or probability theory requires this “each element/sufficiency” condition, and the legal decision rules reflected in most jury instructions do not mandate it. Once this “each element/sufficiency” condition is removed, all that is left of the conjunction problem is a “probability gap,” an intuitive but ill-founded impression that the mathematical underpinnings of the conjunction problem are unfair to claimants. This probability gap is considerably narrowed by recognizing the probabilistic dependence of most facts internal to a given claim, and by applying the correct multiplication rule for probabilistically dependent events. Finally, this Article argues that solving the conjunction problem is an insufficient ground either to abandon probability theory as a useful analytical tool in the context of adjudicative fact-finding, or to reform decision rules for trial fact-finders

Wind Resource Mapping for United States Offshore Areas

A poster for the WindPower 2006 conference showing offshore resource mapping efforts in the United States

Wind Resource Mapping for United States Offshore Areas: Preprint

The U.S. Department of Energy's (DOE) National Renewable Energy Laboratory (NREL) is producing validated wind resource maps for priority offshore regions of the United States. This report describes the methodology used to validate the maps and to build a Geographic Information Systems (GIS) database to classify the offshore wind resource by state, water depth, distance from shore, and administrative unit

Wind Shear Characteristics at Central Plains Tall Towers: Preprint

Conference paper for WindPower 2006 held June 4-7, 2006, in Pittsburgh, PA, describing the wind shear characteristics at tall tower sites in the Central Plains of the United States

Wind Shear Characteristics at Central Plains Tall Towers

The objectives of this report are: (1) Analyze wind shear characteristics at tall tower sites for diverse areas in the central plains (Texas to North Dakota)--Turbines hub heights are now 70-100 m above ground and Wind measurements at 70-100+ m have been rare. (2) Present conclusions about wind shear characteristics for prime wind energy development regions