Three-dimensional track reconstruction for directional Dark Matter detection

Directional detection of Dark Matter is a promising search strategy. However, to perform such detection, a given set of parameters has to be retrieved from the recoiling tracks : direction, sense and position in the detector volume. In order to optimize the track reconstruction and to fully exploit the data of forthcoming directional detectors, we present a likelihood method dedicated to 3D track reconstruction. This new analysis method is applied to the MIMAC detector. It requires a full simulation of track measurements in order to compare real tracks to simulated ones. We conclude that a good spatial resolution can be achieved, i.e. sub-mm in the anode plane and cm along the drift axis. This opens the possibility to perform a fiducialization of directional detectors. The angular resolution is shown to range between 20$^\circ$ to 80$^\circ$, depending on the recoil energy, which is however enough to achieve a high significance discovery of Dark Matter. On the contrary, we show that sense recognition capability of directional detectors depends strongly on the recoil energy and the drift distance, with small efficiency values (50%-70%). We suggest not to consider this information either for exclusion or discovery of Dark Matter for recoils below 100 keV and then to focus on axial directional data.Comment: 27 pages, 20 figure

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Executive stock option exercise with full and partial information on a drift change point

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration $\widehat{\mathbb{F}}$ in which the stock drift becomes a diffusion driven by the innovations process, an $\widehat{\mathbb{F}}$-Brownian motion also driving the stock under $\widehat{\mathbb{F}}$, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.Comment: 48 pages, final version, accepted for publication in SIAM Journal on Financial Mathematic

Interest communities and flow roles in directed networks: the Twitter network of the UK riots

Directionality is a crucial ingredient in many complex networks in which information, energy or influence are transmitted. In such directed networks, analysing flows (and not only the strength of connections) is crucial to reveal important features of the network that might go undetected if the orientation of connections is ignored. We showcase here a flow-based approach for community detection in networks through the study of the network of the most influential Twitter users during the 2011 riots in England. Firstly, we use directed Markov Stability to extract descriptions of the network at different levels of coarseness in terms of interest communities, i.e., groups of nodes within which flows of information are contained and reinforced. Such interest communities reveal user groupings according to location, profession, employer, and topic. The study of flows also allows us to generate an interest distance, which affords a personalised view of the attention in the network as viewed from the vantage point of any given user. Secondly, we analyse the profiles of incoming and outgoing long-range flows with a combined approach of role-based similarity and the novel relaxed minimum spanning tree algorithm to reveal that the users in the network can be classified into five roles. These flow roles go beyond the standard leader/follower dichotomy and differ from classifications based on regular/structural equivalence. We then show that the interest communities fall into distinct informational organigrams characterised by a different mix of user roles reflecting the quality of dialogue within them. Our generic framework can be used to provide insight into how flows are generated, distributed, preserved and consumed in directed networks.Comment: 32 pages, 14 figures. Supplementary Spreadsheet available from: http://www2.imperial.ac.uk/~mbegueri/Docs/riotsCommunities.zip or http://rsif.royalsocietypublishing.org/content/11/101/20140940/suppl/DC