Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit

Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_

Automated analysis of AODV using UPPAAL

This paper describes an automated, formal and rigorous analysis of the Ad hoc On-Demand Distance Vector (AODV) routing protocol, a popular protocol used in wireless mesh networks. We give a brief overview of a model of AODV implemented in the UPPAAL model checker. It is derived from a process-algebraic model which reflects precisely the intention of AODV and accurately captures the protocol specification. Furthermore, we describe experiments carried out to explore AODV's behaviour in all network topologies up to 5 nodes. We were able to automatically locate problematic and undesirable behaviours. This is in particular useful to discover protocol limitations and to develop improved variants. This use of model checking as a diagnostic tool complements other formal-methods-based protocol modelling and verification techniques, such as process algebra

Cryovolcanic Features on Titan

International audienceWe present evidence to support the cryovolcanic origin of some features, which includes the deepest pit known on Titan (Sotra Patera) and some of the highest mountains (Doom and Erebor Montes). We interpret this region to be a cryovolcanic complex of multiple cones, craters, and flows. Elsewhere, a circular feature, approximately 100 km across, is morphologically similar to a laccolith, showing a cross pattern interpreted to be extensional fractures. However, we find that some other previously supposed cryovolcanic features were likely formed by other processes. We discuss implications for eruption style and composition of cryovolcanism on Titan. Our analysis shows the great value of combining data sets when interpreting Titan's geology and in particular stresses the value of topographic dat

3D Surface Reconstruction and Registration for Image Guided Medialization Laryngoplasty

The purpose of our project is to develop an image guided system for the medialization laryngoplasty. One of the fundamental challenges in our system is to accurately register the preoperative 3D CT data to the intraoperative 3D surfaces of the patient. In this paper, we will present a combined surface and fiducial based registration method to register the preoperative 3D CT data to the intraoperative surface of larynx. To accurately model the exposed surface area, an active illumination based stereo vision technique is used for the surface reconstruction. To register the point clouds from the intraoperative stage to the preoperative 3D GT data, a shape priori based ICPmethod is proposed to quickly register the two surfaces. The proposed approach is capable of tracking the fiducial markers and reconstructing the surface of larynx with no damage to the anatomical structure. Although, the proposed method is specifically designed for the image guided laryngoplasty, it can be applied to other image guided surgical areas. We used off-the-shelf digital cameras, LCD projector and rapid 3D prototyper to develop our experimental system. The final RMS error in the registration is less than 1mm. © Springer-Verlag Berlin Heidelberg 2006

Titan’s surface at 2.18-cm wavelength imaged by the Cassini RADAR radiometer: Results and interpretations through the first ten years of observation

International audienceA comprehensive calibration and mapping of the thermal microwave emission from Titan’s surface is reported based on radiometric data obtained at 2.18-cm wavelength by the passive radiometer included in the Cassini RADAR instrument. Compared to previous work, the present results incorporate the much larger data set obtained in the approximately ten years following Saturn Orbit Insertion. Brightness temperature data including polarization were accumulated by segments in Titan passes from Ta (October 2004) through T98 (February 2014). The observational segments were analyzed to produce a mosaic of effective dielectric constant based on the measurement of thermal polarization covering 76% of the surface, and brightness temperature at normal incidence covering Titan’s entire surface. As part of the mosaicking process we also solved for the seasonal variation of physical temperature with latitude, which we found to be smaller by a factor of 0.87 ± 0.05 in relative amplitude compared to that reported in the thermal infrared by Cassini’s Composite Infrared Spectrometer (CIRS). We used the equatorial temperature obtained by the Huygens probe and the seasonal dependence with latitude from CIRS to convert the brightness mosaic to absolute emissivity, from which we could infer global thermophysical properties of the surface in combination with the dielectric mosaic. We see strong evidence for subsurface (volume) scattering as a dominant cause of the radar reflectivity in bright regions, and elsewhere a surface composition consistent with the slow deposition and processing of organic compounds from the atmosphere. The presence of water ice in the near subsurface is strongly indicated by the high degree of volume scattering observed in radar-bright regions (e.g., Hummocky/mountainous terrains) constituting ∼ 10% of Titan’s surface. A thermal analysis allowed us to infer a mean 2.18-cm emission depth in the range 40 to 100 cm for the dominant radar-dark terrains (the remainder of Titan’s surface) at all latitudes of Titan, consistent with the deposition and possible processing and redistribution of tholin-like atmospheric photochemical products

Geometrical transformation approximation for 2D/3D intensity-based registration of portal images and CT scan

Conformal radiotherapy treatments need accurate patient positioning in order to spare normal tissues. Patient pose can be evaluated by registering portal images (PI) with Digitally Reconstructed Radiographs (DRR). Several methods involve segmentation which is known to be a dicult task for noisy PI. In this paper, we study another approach by using a fully 3D intensity-based registration method, without segmentation. Our approach uses the correlation ratio as similarity measure and replace DRR generation with a treatment on pre-computed DRR. A specic geometrical transformation is applied to approximate a given projection by the composition of out-of-plane rotations and inplane transformation. Some preliminary experiments on both simulated and real portal images, lead to good results (RMS error lower than 2 mm). 1 Medical contex