Noncommutative String Theory, the R-Matrix, and Hopf Algebras

Motivated by the form of the noncommutative *-product in a system of open strings and Dp-branes with constant nonzero Neveu-Schwarz 2-form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its R-matrix, and comment on some of its properties. We show that the noncommutative string theory *-product is a particular example of this multiplication, and comment on other possible Hopf algebraic properties which may underlie the theory.Comment: 14 pages using LaTeX, uses amssymb.st

Surprisingly Rational: Probability theory plus noise explains biases in judgment

The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable judgments and sometimes systematic biases. This view has had a major impact in economics, law, medicine, and other fields; indeed, the idea that people cannot reason with probabilities has become a widespread truism. We present a simple alternative to this view, where people reason about probability according to probability theory but are subject to random variation or noise in the reasoning process. In this account the effect of noise is cancelled for some probabilistic expressions: analysing data from two experiments we find that, for these expressions, people's probability judgments are strikingly close to those required by probability theory. For other expressions this account produces systematic deviations in probability estimates. These deviations explain four reliable biases in human probabilistic reasoning (conservatism, subadditivity, conjunction and disjunction fallacies). These results suggest that people's probability judgments embody the rules of probability theory, and that biases in those judgments are due to the effects of random noise.Comment: 64 pages. Final preprint version. In press, Psychological Revie

Hostile Protected Persons or Extra-Conventional Persons: How Unlawful Combatants in the War on Terrorism Posed Extraordinary Challenges for Military Attorneys and Commanders

First, this Article reviews policymakers\u27 and commentators\u27 categorization of participants in Operation Enduring Freedom, the armed conflict in Afghanistan against al Qaeda and Taliban fighters. This Article concentrate specifically on the status of participants operating at the fringes of the categories of persons protected by the Geneva Conventions. It shows, for example, how al Qaeda and the Taliban fighters tested the bounds of the Conventions by employing methods of “warfare” which rendered them non-distinct and therefore made a determination of their status unclear. This Article demonstrates how policymakers and ultimately the U.S. President created a class of persons--so-called extra-conventional persons--who participated in hostilities yet failed to qualify for protection under any of the applicable Geneva Conventions. Second, this Article presents the training and education available to the judge advocates who faced these legal issues. it further presents perspectives on the law of war as it appeared from the resources, education, and training commonly available to deployed judge advocates. This Article ultimately concludes that international law and U.S. military doctrine classify many who participate in hostilities as “protected persons” under the Fourth Geneva Convention--a concept ultimately at odds with the determination made by U.S. policymakers.Third, and in concert with the two issues identified above, this Article describes the enormous challenges these issues created for U.S. military persons participating in Operation Iraqi Freedom. Specifically, it illustrates operational and legal challenges faced by military attorneys and the commanders they advised. It then explores legal issues that arose during the detention and occupation operations with respect to fighters associated with Saddam Fedayeen. Observing apparent similarities between Saddam Fedayeen and Taliban fighters earlier categorized as extra-conventional, this Article describes how, despite similarities in applicable law and attributes, judge advocates determined that these irregular fighters were protected persons under the Fourth Geneva Convention. It concludes that judge advocates dealt with these challenges responsibly, providing sound legal advice that balanced commanders\u27 mission requirements with the humanitarian spirit of the law of war

Cartan Calculus on Quantum Lie Algebras

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra, the ``Cartan Calculus''. (This is an extended version of a talk presented by P. Schupp at the XXII$^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, September 1993)Comment: 15 pages in LaTeX, LBL-34833 and UCB-PTH-93/3

Cartan Calculus for Hopf Algebras and Quantum Groups

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra. In particular we find a generalized Cartan identity that holds on the whole quantum universal enveloping algebra of the left-invariant vector fields and implicit commutation relations for a left-invariant basis of 1-forms.Comment: 15 pages (submitted to Comm. Math. Phys.