Evolutionary methods for self-organizing cooperation in peer-to-peer networks

The Peer-to-Peer network paradigm is drawing the attention of both final users and researchers for its features. P2P networks shift from the classic client-server approach to a high level of decentralization where there is no central control and all the nodes should be able not only to require services, but to provide them to other peers as well. While on one hand such high level of decentralization might lead to interesting properties like scalability and fault tolerance, on the other hand it implies many new problems to deal with. A key feature of many P2P systems is openness, meaning that everybody is potentially able to join a network with no need for subscription or payment systems. The combination of openness and lack of central control makes it feasible for a user to free-ride, that is to increase its own benefit by using services without allocating resources to satisfy other peers’ requests. One of the main goals when designing a P2P system is therefore to achieve cooperation between users. Given the nature of P2P systems based on simple local interactions of many peers having partial knowledge of the whole system, an interesting way to achieve desired properties on a system scale might consist in obtaining them as emergent properties of the many interactions occurring at local node level. Two methods are typically used to face the problem of cooperation in P2P networks: 1) engineering emergent properties when designing the protocol; 2) study the system as a game and apply Game Theory techniques, especially to find Nash Equilibria in the game and to reach them making the system stable against possible deviant behaviors. In this work we present an evolutionary framework to enforce cooperative behaviour in P2P networks that is alternative to both the methods mentioned above. Our approach is based on an evolutionary algorithm inspired by computational sociology and evolutionary game theory, consisting in having each peer periodically trying to copy another peer which is performing better. The proposed algorithms, called SLAC and SLACER, draw inspiration from tag systems originated in computational sociology, the main idea behind the algorithm consists in having low performance nodes copying high performance ones. The algorithm is run locally by every node and leads to an evolution of the network both from the topology and from the nodes’ strategy point of view. Initial tests with a simple Prisoners’ Dilemma application show how SLAC is able to bring the network to a state of high cooperation independently from the initial network conditions. Interesting results are obtained when studying the effect of cheating nodes on SLAC algorithm. In fact in some cases selfish nodes rationally exploiting the system for their own benefit can actually improve system performance from the cooperation formation point of view. The final step is to apply our results to more realistic scenarios. We put our efforts in studying and improving the BitTorrent protocol. BitTorrent was chosen not only for its popularity but because it has many points in common with SLAC and SLACER algorithms, ranging from the game theoretical inspiration (tit-for-tat-like mechanism) to the swarms topology. We discovered fairness, meant as ratio between uploaded and downloaded data, to be a weakness of the original BitTorrent protocol and we drew inspiration from the knowledge of cooperation formation and maintenance mechanism derived from the development and analysis of SLAC and SLACER, to improve fairness and tackle freeriding and cheating in BitTorrent. We produced an extension of BitTorrent called BitFair that has been evaluated through simulation and has shown the abilities of enforcing fairness and tackling free-riding and cheating nodes.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Sindrome da insensitività completa agli androgeni e massa ossea. Valutazione basale e longitudinale dopo oltre 12 mesi di terapia estrogenica

L’osso è un tessuto target per estrogeni ed androgeni ma l’azione singola e la sinergia tra i due non sono compresi interamente. Le donne affette da Sindrome da Insensititvità Completa agli Androgeni (CAIS) hanno un cariotipo 46XY ma presentano una completa inattività del recettore degli androgeni. Nello studio abbiamo valutato la densità minerale ossea (BMD) in un gruppo di donne adulte CAIS sottoposte a gonadectomia al momento della prima visita e dopo almeno 12 mesi di terapia estrogenica. Il principale obiettivo è stato di valutare se, nelle donne CAIS, una ottimale estrogenizzazione fosse sufficiente a mantenere/ripristinare una adeguata BMD. 24 donne CAIS sono state sottoposte a DXA lombare e femorale all'arruolamento nello studio (t1), dopo terapia estrogenica di 12mesi(t2) e oltre (t>2). Sono state valutate: BMD(g/cm2) e Zscore lombare e femorale (a t1,t2 e t>2) E’ stato considerato se fossero rilevanti l’essere (gruppo1) o meno (gruppo 2) in terapia ormonale al t1 e l’età della gonadectomia. Risultati: Al t1 BMD e Zscore lombari e femorale erano significativamente ridotti rispetto alla popolazione controllo nel campione totale (lombare 0,900+0,12; -1,976+0,07, femorale 0,831 + 0,14; -1,385+0,98), nel gruppo 1 (lombare 0,918+0,116;-1,924+0,79, femorale 0,824+0,13;-1,40+1,00) e nel gruppo 2 (lombare 0.845+0,11 -2,13+1,15, femorale 0,857+0,17;-1,348+1,05) Al t2 e t>2 la BMD lombare è risultata significativamente aumentata (p=0,05 e p=0,02). Zscore lombare, BMD e Zscore femorale non hanno dimostrato variazioni significative. L’aver effettuato la gonadectomia in età post puberale è associato a Zscore lombare e femorale più elevati al t1. Nelle donne CAIS la terapia estrogenica è indispensabile per prevenire un'ulteriore perdita di BMD ma, da sola, non sembra in grado di ripristinare normali valori di BMD.I risultati del nostro studio supportano la tesi che gli androgeni, mediante l’azione recettoriale, abbiano un' azione diretta nel raggiungere e mantenere la BMD.