Quantum Particle on a Quantum Circle

We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.Comment: 11 pages, LaTe

On two classical theorems in the theory of orders

AbstractThe paper contains generalizations of the Latimer-MacDuffee theorem and the Chevalley-Hasse-Noether theorem. It shows that the two theorems are closely related to each other by means of a duality, which depends on simultaneous actions of the idèle groups on maximal orders in central simple algebras and on embeddings of maximal commutative subrings into such orders

Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

Meso-Scale Hydrologic Modeling for Climate Impact Assessments: A Conceptual and A Regresssion Approach

The paper presents two different approaches to hydrologic modeling for Climate Impact Assessments: A conceptual water balance model and a non-parametric regression model. They both are designed for modeling large-scale river basins (Meso-Scale) at a monthly time step and to accept GCM-based climate scenarios defined as changes in monthly precipitation and temperature. The data requirements for the models are historical, multi-annual series of mean monthly temperature, precipitation, and runoff. These data are used to calibrate the models. GCM data or user-defined sensitivity of climatic variable must be provided for the assessment analyses. The paper describes the theoretical bases of both approaches and presents the results of a comparison of the application of the models to the Vistula River Basin in Poland

A square root of the harmonic oscillator

Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalizations.Comment: RevTex, 10 pages in preprint form, no figure

Elevated pCO2 enhances bacterioplankton removal of organic carbon.

Factors that affect the removal of organic carbon by heterotrophic bacterioplankton can impact the rate and magnitude of organic carbon loss in the ocean through the conversion of a portion of consumed organic carbon to CO2. Through enhanced rates of consumption, surface bacterioplankton communities can also reduce the amount of dissolved organic carbon (DOC) available for export from the surface ocean. The present study investigated the direct effects of elevated pCO2 on bacterioplankton removal of several forms of DOC ranging from glucose to complex phytoplankton exudate and lysate, and naturally occurring DOC. Elevated pCO2 (1000-1500 ppm) enhanced both the rate and magnitude of organic carbon removal by bacterioplankton communities compared to low (pre-industrial and ambient) pCO2 (250 -~400 ppm). The increased removal was largely due to enhanced respiration, rather than enhanced production of bacterioplankton biomass. The results suggest that elevated pCO2 can increase DOC consumption and decrease bacterioplankton growth efficiency, ultimately decreasing the amount of DOC available for vertical export and increasing the production of CO2 in the surface ocean

Voluntary Participation in Regional Fisheries Management Council Meetings

Insufficient and unrepresentative participation in voluntary public hearings and policy discussions has been problematic since Aristotle\u27s time. In fisheries, research has shown that involvement is dominated by financially resourceful and extreme-opinion stakeholders and tends to advantage groups that have a lower cost of attendance. Stakeholders may exhibit only one or all of these traits but can be still similarly advantaged. The opposites of these traits tend to characterize the disadvantaged, such as the middle-ground opinions, the less wealthy or organized, and the more remote stakeholders. Remoteness or distance is the most straightforward and objective of these characteristics to measure. We analyzed the New England Fishery Management Council\u27s sign-in sheets for 2003-2006, estimating participants\u27 travel distance and associations with the groundfish, scallop, and herring industries. We also evaluated the representativeness of participation by comparing attendance to landings and permit distributions. The distance analysis showed a significant correlation between attendance levels and costs via travel distance. These results suggest a potential bias toward those stakeholders residing closer to meeting locations, possibly disadvantaging parties who are further and must incur higher costs. However, few significant differences were found between the actual fishing industry and attendee distributions, suggesting that the geographical distribution of the meeting attendees is statistically similar to that of the larger fishery. The interpretation of these results must take into consideration the limited time span of the analysis, as policy changes may have altered the industry make-up and location prior to our study. Furthermore, the limited geographical input of stakeholders may lend bias to the Council\u27s perception of ecological and social conditions throughout the spatial range of the fishery. These factors should be further considered in the policy-formation process in order to incorporate a broader range of stakeholder input

Z3_3-graded differential geometry of quantum plane

In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.Comment: 17 page