We consider a natural generalization of the eigenvalue problem for the Laplacian with homogeneous Dirichlet boundary conditions. This corresponds to look for the critical values of the Dirichlet integral, constrained to the unit Lq sphere. We collect some results, present some counter-examples and compile a list of open problems.

Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non-constant resolution of the jet representation. We develop a dynamic mesh- refinement method for the numerical study of the electro-hydrodynamic behavior of charged jets using discrete element methods. To this purpose, we import ideas and techniques from the string method originally developed in the framework of free-energy landscape simulations.

In recent years we are witnessing a continuous growth in the amount of data that both public and private organizations collect and profit by. Search engines are the most common tools used to retrieve information, and more recently, clustering techniques showed to be an effective tool in helping users to skim query results.

Trust and reputation systems are decision support tools used to drive parties' interactions on the basis of parties' reputation. In such systems, parties rate with each other after each interaction.

Parties of reputation systems rate each other and use ratings to compute reputation scores that drive their interactions. When deciding which reputation model to deploy in a network environment, it is important to find the most suitable model and to determine its right initial configuration. This calls for an engineering approach for describing, implementing and evaluating reputation systems while taking into account specific aspects of both the reputation systems and the networked environment where they will run.

The anonymous marketplaces ecosystem represents a new channel for black market/goods and services, offering a huge variety of illegal items.

The popularity of the cloud computing paradigm is opening new opportunities for collaborative computing. In this paper we tackle a fundamental problem in open-ended cloud-based distributed computing platforms, i.e., the quest for potential collaborators. We assume that cloud participants are willing to share their computational resources for shared distributed computing problems, but they are not willing to disclose the details of their resources. Lacking such information, we advocate to rely on reputation scores obtained by evaluating the interactions among participants.

The amount of traffic data collected by automatic number plate reading systems constantly incrseases. It is therefore important, for law enforcement agencies, to find convenient techniques and tools to analyze such data. In this paper we propose a scalable and fully automated procedure leveraging the Apache Accumulo technology that allows an effective importing and processing of traffic data. We discuss preliminary results obtained by using our application for the analysis of a dataset containing real traffic data provided by the Italian National Police.

Two conflicting high-level goals govern the enforcement of security policies, abridged in the phrase ``high security at a low cost''. While these drivers seem irreconcilable, formal modelling languages and automated verification techniques can facilitate the task of finding the right balance. We propose a modelling language and a framework in which security checks can be relaxed or strengthened to save resources or increase protection, on the basis of trust relationships among communicating parties.