Analytical properties of Einasto dark matter haloes

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the S\'ersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.Comment: 10 pages, 2 figures. Accepted for publication in Astronomy and Astrophysic

Spike pattern recognition by supervised classification in low dimensional embedding space

© The Author(s) 2016. This article is published with open access at Springerlink.com under the terms of the Creative Commons Attribution License 4.0, (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.Epileptiform discharges in interictal electroencephalography (EEG) form the mainstay of epilepsy diagnosis and localization of seizure onset. Visual analysis is rater-dependent and time consuming, especially for long-term recordings, while computerized methods can provide efficiency in reviewing long EEG recordings. This paper presents a machine learning approach for automated detection of epileptiform discharges (spikes). The proposed method first detects spike patterns by calculating similarity to a coarse shape model of a spike waveform and then refines the results by identifying subtle differences between actual spikes and false detections. Pattern classification is performed using support vector machines in a low dimensional space on which the original waveforms are embedded by locality preserving projections. The automatic detection results are compared to experts’ manual annotations (101 spikes) on a whole-night sleep EEG recording. The high sensitivity (97 %) and the low false positive rate (0.1 min−1), calculated by intra-patient cross-validation, highlight the potential of the method for automated interictal EEG assessment.Peer reviewedFinal Published versio

MULTISEASONAL TREE CROWN STRUCTURE MAPPING WITH POINT CLOUDS FROM OTS QUADROCOPTER SYSTEMS

OTF (Off The Shelf) quadro copter systems provide a cost effective (below 2000 Euro), flexible and mobile platform for high resolution point cloud mapping. Various studies showed the full potential of these small and flexible platforms. Especially in very tight and complex 3D environments the automatic obstacle avoidance, low copter weight, long flight times and precise maneuvering are important advantages of these small OTS systems in comparison with larger octocopter systems. This study examines the potential of the DJI Phantom 4 pro series and the Phantom 3A series for within-stand and forest tree crown 3D point cloud mapping using both within stand oblique imaging in different altitude levels and data captured from a nadir perspective. On a test site in Brandenburg/Germany a beach crown was selected and measured with 3 different altitude levels in Point Of Interest (POI) mode with oblique data capturing and deriving one nadir mosaic created with 85/85 % overlap using Drone Deploy automatic mapping software. Three different flight campaigns were performed, one in September 2016 (leaf-on), one in March 2017 (leaf-off) and one in May 2017 (leaf-on) to derive point clouds from different crown structure and phenological situations – covering the leaf-on and leafoff status of the tree crown. After height correction, the point clouds where used with GPS geo referencing to calculate voxel based densities on 50 × 10 × 10 cm voxel definitions using a topological network of chessboard image objects in 0,5 m height steps in an object based image processing environment. Comparison between leaf-off and leaf-on status was done on volume pixel definitions comparing the attributed point densities per volume and plotting the resulting values as a function of distance to the crown center. In the leaf-off status SFM (structure from motion) algorithms clearly identified the central stem and also secondary branch systems. While the penetration into the crown structure is limited in the leaf-on status (the point cloud is a mainly a description of the interpolated crown surface) – the visibility of the internal crown structure in leaf-off status allows to map also the internal tree structure up to and stopping at the secondary branch level system. When combined the leaf-on and leaf-off point clouds generate a comprehensive tree crown structure description that allows a low cost and detailed 3D crown structure mapping and potentially precise biomass mapping and/or internal structural differentiation of deciduous tree species types. Compared to TLS (Terrestrial Laser Scanning) based measurements the costs are neglectable and in the range of 1500–2500 €. This suggests the approach for low cost but fine scale in-situ applications and/or projects where TLS measurements cannot be derived and for less dense forest stands where POI flights can be performed. This study used the in-copter GPS measurements for geo referencing. Better absolute geo referencing results will be obtained with DGPS reference points. The study however clearly demonstrates the potential of OTS very low cost copter systems and the image attributed GPS measurements of the copter for the automatic calculation of complex 3D point clouds in a multi temporal tree crown mapping context

Dipole estimation errors due to skull conductivity perturbations: Simulation study in spherical head models

Electroencephalogram (EEG) dipole source localization is a non-invasive technique used in the pre-surgical diagnosis of epilepsy. In the present study we investigated the dipole location and orientation errors due to skull conductivity perturbations, in seven 3-shell concentric spherical head models with brain-to-skull conductivity ratio (R-sigma) ranging from 10 to 40. Each head model was compared to the baseline head model with R-sigma = 20. It is noted that perturbations in the skull conductivity generate dipole location and orientation errors: the more R-sigma deviates from the baseline value the greater the errors and the larger the error ranges. Results show that the estimated dipole location is radially shifted away from the center of the head model if the skull conductivity is larger than that of the baseline head model (11, = 10, 15), while it is radially shifted towards the center in case the skull conductivity is less than that of the baseline head model (R, = 25,30,35,40). The dipole orientation error due to skull conductivity perturbations is not significant (maximal mean 6 mm, standard deviation = 3 mm), especially when the dipoles are near the skull the maximal mean can reach 8 mm. Therefore, accurate estimation of the skull conductivity of the head model is necessary to enhance the reliability in EEG dipole source localization

Multi-Modal and Multi-Temporal Data Fusion: Outcome of the 2012 GRSS Data Fusion Contest

The 2012 Data Fusion Contest organized by the Data Fusion Technical Committee (DFTC) of the IEEE Geoscience and Remote Sensing Society (GRSS) aimed at investigating the potential use of very high spatial resolution (VHR) multi-modal/multi-temporal image fusion. Three different types of data sets, including spaceborne multi-spectral, spaceborne synthetic aperture radar (SAR), and airborne light detection and ranging (LiDAR) data collected over the downtown San Francisco area were distributed during the Contest. This paper highlights the three awarded research contributions which investigate (i) a new metric to assess urban density (UD) from multi-spectral and LiDAR data, (ii) simulation-based techniques to jointly use SAR and LiDAR data for image interpretation and change detection, and (iii) radiosity methods to improve surface reflectance retrievals of optical data in complex illumination environments. In particular, they demonstrate the usefulness of LiDAR data when fused with optical or SAR data. We believe these interesting investigations will stimulate further research in the related areas