Organised crime uses information technology systems to communicate, work or expand its influence. The EU FP7 Security Research Project CAPER (Collaborative information, Acquisition, Processing, Exploitation and Reporting for the prevention of organised crime), created in cooperation with European Law Enforcement Agencies (LEAs), aims to build a common collaborative and information sharing platform for the detection and prevention of organised crime, which exploits Open Source Intelligence (OSINT). LEAs are becoming more inclined to using OSINT tools, and particularly tools able to manage Online Social Networks (OSNs) data. This paper presents the CAPER Facebook crawling and analysis subsystem. Heuristic algorithms have been implemented in order to extract specific properties of Facebook's social graph, in particular user interactions. To support analysis tasks specifically, extensive effort has been spent on the analysis of textual user generated content and on the recognition of named-entities, in particular person names, locations and organisations. Relationships between users and entities mentioned in posts and in related comments are created and merged into the users networks extracted from the social graph. All entity relationships are finally visualised in userfriendly network graphs.

We comment on a challenge raised by Newson more than a century ago and present an expression for the volume of the convex hull of a convex closed space curve with four vertex points.

Given a smooth distribution D of m-dimensional planes along a smooth regular curve γ in R m+n , we consider the following problem: To find an m-dimensional developable submanifold of R m+n , that is, a ruled submanifold with constant tangent space along the rulings, such that its tangent bundle along γ coincides with D. In particular, we give sufficient conditions for the local well-posedness of the problem, together with a parametric description of the solution.

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We study submanifolds of arbitrary codimension in a Lie group G equipped with a bi-invariant metric. In particular, we show that, if the normal bundle of M ⊂ G is abelian, then the normal Jacobi operator of M equals the square of its invariant shape operator. This allows us to obtain geometric conditions which are necessary and sufficient for the submanifold M to be curvature adapted to G.