Rule-Based Application Development using Webdamlog

We present the WebdamLog system for managing distributed data on the Web in a peer-to-peer manner. We demonstrate the main features of the system through an application called Wepic for sharing pictures between attendees of the sigmod conference. Using Wepic, the attendees will be able to share, download, rate and annotate pictures in a highly decentralized manner. We show how WebdamLog handles heterogeneity of the devices and services used to share data in such a Web setting. We exhibit the simple rules that define the Wepic application and show how to easily modify the Wepic application.Comment: SIGMOD - Special Interest Group on Management Of Data (2013

Introducing Access Control in Webdamlog

We survey recent work on the specification of an access control mechanism in a collaborative environment. The work is presented in the context of the WebdamLog language, an extension of datalog to a distributed context. We discuss a fine-grained access control mechanism for intentional data based on provenance as well as a control mechanism for delegation, i.e., for deploying rules at remote peers.Comment: Proceedings of the 14th International Symposium on Database Programming Languages (DBPL 2013), August 30, 2013, Riva del Garda, Trento, Ital

Stabilisation of stochastic single-file dynamics using port-Hamiltonian systems

This study revisits a recently proposed symmetric port-Hamiltonian single-file model in one dimension. The uniform streaming solutions are stable in the deterministic model. However, the introduction of white noise into the dynamics causes the model to exhibit divergence. In response, we introduce a control term in a port-Hamiltonian framework. Our results show that this control term effectively stabilises the dynamics even in the presence of noise, providing valuable insights for the control of road traffic flows

Submanifolds with boundary and Stokes' Theorem in Heisenberg groups

We introduce and study the notion of $C^1_\mathbb{H}$-regular submanifold with boundary in sub-Riemannian Heisenberg groups. As an application, we prove a version of Stokes' Theorem for $C^1_\mathbb{H}$-regular submanifolds with boundary that takes into account Rumin's complex of differential forms in Heisenberg groups.Comment: 30 page

On sets with unit Hausdorff density in homogeneous groups

It is a longstanding conjecture that given a subset E of a metric space, if E has unit $\mathscr {H}^{\alpha }\llcorner E$ -density almost everywhere, then E is an $\alpha$ -rectifiable set. We prove this conjecture under the assumption that the ambient metric space is a homogeneous group with a smooth-box norm