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

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

Decision Support Design for Workload Mitigation in Human Supervisory Control of Multiple Unmanned Aerial Vehicles

As UAVs become increasingly autonomous, the multiple personnel currently required to operate a single UAV may eventually be superseded by a single operator concurrently managing multiple UAVs. Instead of lower-level tasks performed by today’s UAV teams, the sole operator would focus on high-level supervisory control tasks such as monitoring mission timelines and reacting to emergent mission events. A key challenge in the design of such single-operator systems will be the need to minimize periods of excessive workload that could arise when critical tasks for several UAVs occur simultaneously. To a certain degree, it is possible to predict and mitigate such periods in advance. However, actions that mitigate a particular period of high workload in the short term may create long term episodes of high workload that were previously non-existent. Thus some kind of decision support is needed that facilitates an operator’s ability to evaluate different options for managing a mission schedule in real-time. This paper describes two decision support visualizations designed for supervisory control of four UAVs performing a time-critical targeting mission. A configural display common to both visualizations, named the StarVis, was designed to highlight potential periods of high workload corresponding to the current mission timeline, as well as “what if” projections of possible high workload periods based upon different operator options. The first visualization design allows an operator to compare different high workload mitigation options for individual UAVs. This is termed the local visualization. The second visualization is indicates the combined effects of multiple high workload mitigation decisions on the timeline. This is termed the global visualization. The main advantage of the local visualization is that options can be compared directly; however, the possible effects of these options on the mission timeline are only indicated for the individual UAV primarily affected by the decision. For the global visualization, different decisions can be combined to show possible effects on the system propagated across all UAVs, but the different alternatives of a single decision option alternative cannot be directly compared. An experiment was conducted testing these visualizations against a control with no visualization. Results showed that subject using the local visualization had better performance, higher situational awareness, and no significant increase in workload over the other two experimental conditions. This occurred despite the fact that the local and global StarVis displays were very similar. Not only did the Global StarVis produce degraded results as compared to the local StarVis, but those participants with no visualization performed as well as those with the global StarVis. This disparity in performance despite strong visual similarities in the StarVis designs is attributed to operators’ inability to process all the information presented in the global StarVis as well as the fact that participants with the local StarVis were able to rapidly develop effective cognitive problem strategies. This research effort highlights a very important design consideration, in that a single decision support design can produce very different performance results when applied at different levels of abstraction.Prepared for Kevin Burns, The MITRE Corporatio

Metric On Quantum Spaes

We introduce the analogue of the metric tensor in case of $q$-deformed differential calculus. We analyse the consequences of the existence of such metric, showing that this enforces severe restrictions on the parameters of the theory. We discuss in detail the examples of the Manin plane and the $q$-deformation of $SU(2)$. Finally we touch the topic of relations with the Connes' approach.Comment: 7 pages (LaTeX), preprint TPJU 14/9

Dirac Operator on the Quantum Sphere

We construct a Dirac operator on the quantum sphere $S^2_q$ which is covariant under the action of $SU_q(2)$. It reduces to Watamuras' Dirac operator on the fuzzy sphere when $q\to 1$. We argue that our Dirac operator may be useful in constructing $SU_q(2)$ invariant field theories on $S^2_q$ following the Connes-Lott approach to noncommutative geometry.Comment: 13 page

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

SUq(2)SU_q(2) Lattice Gauge Theory

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters - the deformation parameter $\lambda$ and the lattice spacing $a$. We show that the system of Kogut and Susskind is recovered when $\lambda \rightarrow 0$, while QCD is recovered in the continuum limit (for any $\lambda$). We thus have the possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil

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

Case Report: Positive outcome of medical leeches (hirudotherapy) for venous congestion

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