Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.

Connectivity management and dynamic context grouping in mobile heterogenous systems

In the last 10 years the number of mobile devices has grown rapidly. Each person usually brings at least two personal devices and researchers says that in a near future this number could raise up to ten devices per person. Moreover, all the devices are becoming more integrated to our life than in the past, therefore the amount of data exchanged increases accordingly to the improvement of people's lifestyle. This is what researchers call Internet of Things. Thus, in the future there will be more than 60 billions of nodes and the current infrastructure is not ready to keep track of all the exchanges of data between them. Therefore, infrastructure improvements have been proposed in the last years, like MobileIP and HIP in order to facilitate the exchange of packets in mobility, however none of them have been optimized for the purpose. In the last years, researchers from Mid Sweden University created The MediaSense Framework. Initially, this framework was based on the Chord protocol in order to route packets in a big network, but the most important change has been the introduction of PGrids in order to create the Overlay and the persistence. Thanks to this technology, a lookup in the trie takes up to 0.5*log(N), where N is the total number of nodes in the network. This result could be improved by further optimizations on the management of the nodes, for example by the dynamic creation of groups of nodes. Moreover, since the nodes move, an underlaying support for connectivity management is needed. SCTP has been selected as one of the most promising upcoming standards for simultaneous multiple connection's management.