Quasi-tree expansion for the Bollob\'as-Riordan-Tutte polynomial

Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. The Bollob\'as-Riordan-Tutte polynomial is a three-variable polynomial that extends the Tutte polynomial to oriented ribbon graphs. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We generalize the spanning tree expansion of the Tutte polynomial to a quasi-tree expansion of the Bollob\'as-Riordan-Tutte polynomial.Comment: This version to be published in the Bulletin of the London Mathematical Society. 17 pages, 4 figure

Form removal aspects on the waviness parameters for steel sheet in automotive applications : fourier filtering versus polynomial regression

Premium car makers attach great importance to the visual appearance of the painted car skin as an indication of product quality. The “orange peel” phenomenon constitutes a major problem here. It is not only depending on the paint’s chemical composition and application method, but also on possible waviness components in the sheet substrate. Therefore one is searching hard for a valuable waviness parameter to quantify the substrate’s fitness for purpose. A technically emerging problem is how to remove the form from the measured signal, which is indeed not significant to the orange peel phenomenon. This paper will compare two commonly used approaches: i.e. Fourier filtering versus polynomial regression and will reveal and quantify some common aspects in terms of wavelengths

Form removal aspects on the waviness parameters for steel sheet in automotive applications : fourier filtering versus polynomial regression

Premium car makers attach great importance to the visual appearance of the painted car skin as an indication of product quality. The “orange peel” phenomenon constitutes a major problem here. It is not only depending on the paint’s chemical composition and application method, but also on possible waviness components in the sheet substrate. Therefore one is searching hard for a valuable waviness parameter to quantify the substrate’s fitness for purpose. A technically emerging problem is how to remove the form from the measured signal, which is indeed not significant to the orange peel phenomenon. This paper will compare two commonly used approaches: i.e. Fourier filtering versus polynomial regression and will reveal and quantify some common aspects in terms of wavelengths

The 1997 event in the Crab pulsar revisited

A complex event observed in the radio pulses from the Crab pulsar in 1997 included echoes, a dispersive delay, and large changes in intensity. It is shown that these phenomena were due to refraction at the edge of a plasma cloud in the outer region of the Crab Nebula. Several similar events have been observed, although in less detail. It is suggested that the plasma cloud is in the form of filaments with diameter around 3 x 10^11m and electron density of order 10^4 cm-3Comment: 5 pages 4 figs Accepted by MNRA

The limits of spatial resolution achievable using a 30kHz multibeam sonar: model predictions and field results

A Simrad EM300 multibeam sonar was used to attempt to resolve small (-5m high) targets in 450m of water. The targets had previously been surveyed using a deeply towed 59 kHz sidescan sonar. Using multisector active yaw, pitch and roll compensation, together with dynamically altering angular sectors, the sonar is capable of maintaining sounding densities of as tight as 10m spacing in these water depths. This is significantly smaller than the largest dimension of the projected beam footprints (1 6-64m). The observed data suggest that the targets are intermittently resolved. The field results compare well to the output of a numerical model which reproduces the imaging geometry. Possible variations in the imaging geometry are implemented in the model, comparing equiangular and equidistant beam spacings, differing angular sectors and all the different combinations of transmit and receive beam widths that are available for this model of sonar. While amplitude detection is significantly aliased by targets smaller than the across track beam footprint, under conditions where the signal to noise ratio is favorable, phase detection can be used to reduce the minimum size of target observed to about the scale of the across track beam width. Thus having the beam spacing at the scale is justifiable. The phase distortion due to smaller targets, however, is generally averaged out

Development of a land use regression model for black carbon using mobile monitoring data and its application to pollution-avoiding routing

Black carbon is often used as an indicator for combustion-related air pollution. In urban environments, on-road black carbon concentrations have a large spatial variability, suggesting that the personal exposure of a cyclist to black carbon can heavily depend on the route that is chosen to reach a destination. In this paper, we describe the development of a cyclist routing procedure that minimizes personal exposure to black carbon. Firstly, a land use regression model for predicting black carbon concentrations in an urban environment is developed using mobile monitoring data, collected by cyclists. The optimal model is selected and validated using a spatially stratified cross-validation scheme. The resulting model is integrated in a dedicated routing procedure that minimizes personal exposure to black carbon during cycling. The best model obtains a coefficient of multiple correlation of R = 0.520. Simulations with the black carbon exposure minimizing routing procedure indicate that the inhaled amount of black carbon is reduced by 1.58% on average as compared to the shortest-path route, with extreme cases where a reduction of up to 13.35% is obtained. Moreover, we observed that the average exposure to black carbon and the exposure to local peak concentrations on a route are competing objectives, and propose a parametrized cost function for the routing problem that allows for a gradual transition from routes that minimize average exposure to routes that minimize peak exposure