On a Centrality Maximization Game

The Bonacich centrality is a well-known measure of the relative importance of nodes in a network. This notion is, for example, at the core of Google's PageRank algorithm. In this paper we study a network formation game where each player corresponds to a node in the network to be formed and can decide how to rewire his m out-links aiming at maximizing his own Bonacich centrality, which is his utility function. We study the Nash equilibria (NE) and the best response dynamics of this game and we provide a complete classification of the set of NE when m=1 and a fairly complete classification of the NE when m=2. Our analysis shows that the centrality maximization performed by each node tends to create undirected and disconnected or loosely connected networks, namely 2-cliques for m=1 and rings or a special "Butterfly"-shaped graph when m=2. Our results build on locality property of the best response function in such game that we formalize and prove in the paper.Comment: 10 pages, 11 figure

On a Network Centrality Maximization Game

We study a network formation game where $n$ players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player $i$ consists in the wiring of a predetermined number $d_i$ of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node $i$ to link to other nodes that are at incoming distance more than $d_i$ from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number $d$ of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases $d=1$ and $d=2$, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks.Comment: 42 pages, 11 figure

Analysis of DTC nutrigenetic services in Italy: state of the art, agreement to the ESHG statement and future outlooks

Background: In both USA and Europe operate companies selling Direct-to-consumer genetic tests (DTC). These tests are offered to healthy people aiming to identify predispositions to complex diseases and to take preventive measures. Several DTC-nutrigenetic tests (DNTs) are available on the market. They propose the definition of a personalized diet, on the basis of the investigated genetic variants, which would reduce the risk of developing those diseases which have been associated to specific genetic markers. However, the risk/benefit balance of exposing unselected population to genetic testing without any medical surveillance is far from be established. Furthermore, it lacks an accepted procedure to select which genetic markers needs to be investigated, to evaluate their specific role and, as consequence, to define a personalized diet. Within this context, the European Society of Human Genetics (ESHG) released a statement regarding the DTC tests that has been ratified by several national societies including the Italian one. 
In the present study we analyzed the DNT offered in Italy, the state of the art and the abidance with the ESHG statement. 
Methods: We queried web search engine for the DNT offered to italian population, portraying a non-specialized customer. We examined the DNTs vendor websites and/or directly contacted the companies to collect information on: 1) genetic marker essayed, 2) diseases and phenotypes considered and 3) kind of dietary advices provided. Finally, we evaluated the abidance to the ESHG statement. The study was conducted between November, 2010 and May, 2011.
Results: Six companies operate in Italy with a total of seven different DNTs offered. Both studied phenotypes and investigated genetic markers were very different among companies, with a relative higher level of agreement for phenotype than for genes. None of the companies described the methods used to select markers and to define diet advices. None of the companies showed a complete agreement to the statement of the ESHG. 
Conclusion: Although DNT companies' efforts are worthy, a standardization of methods and a more strictly agreement with ESHG statement should be encouraged

EVALUATION BY TEST OF TIGHTENING TORQUE FOR PRELOADED STAIN-LESS STEEL BOLTING ASSEMBLIES

Preloaded stain-less steel bolting assemblies are currently used in minor and secondary structures such as ventilated facades, but the national and international regulations condition their use on the execution of specific tests to determine the sliding resistance. This approach is justified by the dif-ferent viscoplastic behaviour compared to carbon steel, which can lead to a greater loss of preload over time and by the galling, that is a formation of streaks during tightening with damage of the bolt. This study investigates the use of bolted joints in stainless steel and hypothesizes, based on labora-tory tests, valid formulations in the project for the definition of the preload and the consequent sliding resistance of the joint. Using non-lubricated stainless-steel bolts with geometries according to UNI EN ISO 4014, 4017 standards, tests were carried out on the suitability for preloading, on the possible presence of galling and on the sliding resistance of joints. The preload suitability tests were carried out following the current regulations for preloaded carbon steel bolting, UNI EN 14399 2 and 3, and the achievable preloads were found to be lower than those defined for common steel. The most important conclusion is that it is possible to use these preloaded bolts, with a design preload equal to 50% of that defined in the case of carbon steel. On the other hand, for the factor k, laboratory tests have shown that the values for these bolts are included in a range between 0.25-0.40, higher than carbon steel preloaded bolting. Since the interval is quite wide, further laboratory tests are therefore necessary to define the k factor of these joints made by stainless steel, to avoid over-tightening or in the other hand, having a too low preload. The study constitutes further investigation with laboratory tests on the application of the correct tightening torque without damaging the bolt, compared to the previous publication dealt with in 2019 Bologna’s conference, which was limited to sliding tests of the joint