Universal Behavior in Large-scale Aggregation of Independent Noisy Observations

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a protypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.Comment: 10 pages, 3 figure

Minimizing Unsatisfaction in Colourful Neighbourhoods

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional explanatio

The Supershell-Molecular Cloud Connection in the Milky Way and Beyond

The role of large-scale stellar feedback in the formation of molecular clouds has been investigated observationally by examining the relationship between HI and 12CO(J=1-0) in supershells. Detailed parsec-resolution case studies of two Milky Way supershells demonstrate an enhanced level of molecularisation over both objects, and hence provide the first quantitative observational evidence of increased molecular cloud production in volumes of space affected by supershell activity. Recent results on supergiant shells in the LMC suggest that while they do indeed help to organise the ISM into over-dense structures, their global contribution to molecular cloud formation is of the order of only ~10%.Comment: Proceedings of IAUS 292 - Molecular Gas, Dust, and Star Formation in Galaxies, eds. T. Wong & J. Ott. 4 pages, 3 figure

Spin-Electromagnetic Hydrodynamics and Magnetization Induced by Spin-Magnetic Interaction

The hydrodynamic model including the spin degree of freedom and the electromagnetic field was discussed. In this derivation, we applied electromagnetism for macroscopic medium proposed by Minkowski. For the equation of motion of spin, we assumed that the hydrodynamic representation of the Pauli equation is reproduced when the many-body effect is neglected. Then the spin-magnetic interaction in the Pauli equation was converted to a part of the magnetization. The fluid and spin stress tensors induced by the many-body effect were obtained by employing the algebraic positivity of the entropy production in the framework of the linear irreversible thermodynamics, including the mixing effect of the irreversible currents. We further constructed the constitutive equation of the polarization and the magnetization. Our polarization equation is more reasonable compared to another result obtained using electromagnetism for macroscopic medium proposed by de Groot-Mazur.Comment: 24 pages, no figure, the discussion for the modifed thermodynamic relation is added, several errors are corrected, accepted for publication in PR

Supergiant Shells and Molecular Cloud Formation in the LMC

We investigate the influence of large-scale stellar feedback on the formation of molecular clouds in the Large Magellanic Cloud (LMC). Examining the relationship between HI and 12CO(J=1-0) in supergiant shells (SGSs), we find that the molecular fraction in the total volume occupied by SGSs is not enhanced with respect to the rest of the LMC disk. However, the majority of objects (~70% by mass) are more molecular than their local surroundings, implying that the presence of a supergiant shell does on average have a positive effect on the molecular gas fraction. Averaged over the full SGS sample, our results suggest that ~12-25% of the molecular mass in supergiant shell systems was formed as a direct result of the stellar feedback that created the shells. This corresponds to ~4-11% of the total molecular mass of the galaxy. These figures are an approximate lower limit to the total contribution of stellar feedback to molecular cloud formation in the LMC, and constitute one of the first quantitative measurements of feedback-triggered molecular cloud formation in a galactic system.Comment: 14 pages, 6 figures. Accepted for publication in Ap

Trajectory generation for road vehicle obstacle avoidance using convex optimization

This paper presents a method for trajectory generation using convex optimization to find a feasible, obstacle-free path for a road vehicle. Consideration of vehicle rotation is shown to be necessary if the trajectory is to avoid obstacles specified in a fixed Earth axis system. The paper establishes that, despite the presence of significant non-linearities, it is possible to articulate the obstacle avoidance problem in a tractable convex form using multiple optimization passes. Finally, it is shown by simulation that an optimal trajectory that accounts for the vehicle’s changing velocity throughout the manoeuvre is superior to a previous analytical method that assumes constant speed

How to Find More Supernovae with Less Work: Object Classification Techniques for Difference Imaging

We present the results of applying new object classification techniques to difference images in the context of the Nearby Supernova Factory supernova search. Most current supernova searches subtract reference images from new images, identify objects in these difference images, and apply simple threshold cuts on parameters such as statistical significance, shape, and motion to reject objects such as cosmic rays, asteroids, and subtraction artifacts. Although most static objects subtract cleanly, even a very low false positive detection rate can lead to hundreds of non-supernova candidates which must be vetted by human inspection before triggering additional followup. In comparison to simple threshold cuts, more sophisticated methods such as Boosted Decision Trees, Random Forests, and Support Vector Machines provide dramatically better object discrimination. At the Nearby Supernova Factory, we reduced the number of non-supernova candidates by a factor of 10 while increasing our supernova identification efficiency. Methods such as these will be crucial for maintaining a reasonable false positive rate in the automated transient alert pipelines of upcoming projects such as PanSTARRS and LSST.Comment: 25 pages; 6 figures; submitted to Ap