A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Temperature Prediction Model for Bone Drilling Based on Density Distribution and In Vivo Experiments for Minimally Invasive Robotic Cochlear Implantation

Surgical robots have been proposed ex vivo to drill precise holes in the temporal bone for minimally invasive cochlear implantation. The main risk of the procedure is damage of the facial nerve due to mechanical interaction or due to temperature elevation during the drilling process. To evaluate the thermal risk of the drilling process, a simplified model is proposed which aims to enable an assessment of risk posed to the facial nerve for a given set of constant process parameters for different mastoid bone densities. The model uses the bone density distribution along the drilling trajectory in the mastoid bone to calculate a time dependent heat production function at the tip of the drill bit. Using a time dependent moving point source Green's function, the heat equation can be solved at a certain point in space so that the resulting temperatures can be calculated over time. The model was calibrated and initially verified with in vivo temperature data. The data was collected in minimally invasive robotic drilling of 12 holes in four different sheep. The sheep were anesthetized and the temperature elevations were measured with a thermocouple which was inserted in a previously drilled hole next to the planned drilling trajectory. Bone density distributions were extracted from pre-operative CT data by averaging Hounsfield values over the drill bit diameter. Post-operative [Formula: see text]CT data was used to verify the drilling accuracy of the trajectories. The comparison of measured and calculated temperatures shows a very good match for both heating and cooling phases. The average prediction error of the maximum temperature was less than 0.7 °C and the average root mean square error was approximately 0.5 °C. To analyze potential thermal damage, the model was used to calculate temperature profiles and cumulative equivalent minutes at 43 °C at a minimal distance to the facial nerve. For the selected drilling parameters, temperature elevation profiles and cumulative equivalent minutes suggest that thermal elevation of this minimally invasive cochlear implantation surgery may pose a risk to the facial nerve, especially in sclerotic or high density mastoid bones. Optimized drilling parameters need to be evaluated and the model could be used for future risk evaluation.

Size-frequency distribution of boulders ≥7 m on comet 67P/Churyumov-Gerasimenko

Aims. We derive for the first time the size-frequency distribution of boulders on a comet, 67P/Churyumov-Gerasimenko (67P), computed from the images taken by the Rosetta/OSIRIS imaging system. We highlight the possible physical processes that lead to these boulder size distributions. Methods. We used images acquired by the OSIRIS Narrow Angle Camera, NAC, on 5 and 6 August 2014. The scale of these images (2.44−2.03 m/px) is such that boulders ≥7 m can be identified and manually extracted from the datasets with the software ArcGIS. We derived both global and localized size-frequency distributions. The three-pixel sampling detection, coupled with the favorable shadowing of the surface (observation phase angle ranging from 48° to 53°), enables unequivocally detecting boulders scattered all over the illuminated side of 67P. Results. We identify 3546 boulders larger than 7 m on the imaged surface (36.4 km2), with a global number density of nearly 100/km2 and a cumulative size-frequency distribution represented by a power-law with index of −3.6 +0.2/−0.3. The two lobes of 67P appear to have slightly different distributions, with an index of −3.5 +0.2/−0.3 for the main lobe (body) and −4.0 +0.3/−0.2 for the small lobe (head). The steeper distribution of the small lobe might be due to a more pervasive fracturing. The difference of the distribution for the connecting region (neck) is much more significant, with an index value of −2.2 +0.2/−0.2. We propose that the boulder field located in the neck area is the result of blocks falling from the contiguous Hathor cliff. The lower slope of the size-frequency distribution we see today in the neck area might be due to the concurrent processes acting on the smallest boulders, such as i) disintegration or fragmentation and vanishing through sublimation; ii) uplifting by gas drag and consequent redistribution; and iii) burial beneath a debris blanket. We also derived the cumulative size-frequency distribution per km2 of localized areas on 67P. By comparing the cumulative size-frequency distributions of similar geomorphological settings, we derived similar power-law index values. This suggests that despite the selected locations on different and often opposite sides of the comet, similar sublimation or activity processes, pit formation or collapses, as well as thermal stresses or fracturing events occurred on multiple areas of the comet, shaping its surface into the appearance we see today.

Online Reputation Systems and Cumulative Advantage

The study of online reputation systems and their importance for promoting trust and cooperation and, therefore, the smooth functioning of online markets has received considerable attention over the last few years. In the first part of our talk we will try to give a brief overview of the existing theoretical and empirical work in this field, summarize the main findings from this research and identify open questions where results are either controversial or do not yet exist. The second part of our talk will focus on one of these issues that deserve further research, namely the relation between online reputation systems and processes of "cumulative advantage." Cumulative advantage is the mechanism where a favorable relative position of having a good reputation becomes a resource for further relative gains. The process leads to increased status inequality and a heavily skewed distribution of number of feedbacks, i.e. the ties in the reputation network. We present empirical evidence for direct and indirect reputation effects on the micro level of an auction reputation system and discuss the distributional consequences for the market level.