Pure Nash Equilibria: Hard and Easy Games

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems

Anisotropies in momentum space at finite Shear Viscosity in ultrarelativistic heavy-ion collisions

Within a parton cascade we investigate the dependence of anisotropies in momentum space, namely the elliptic flow $v_2=$ and the $v_4=$, on both the finite shear viscosity $\eta$ and the freeze-out (f.o.) dynamics at the RHIC energy of 200 AGeV. In particular it is discussed the impact of the f.o. dynamics looking at two different procedures: switching-off the collisions when the energy density goes below a fixed value or reducing the cross section according to the increase in $\eta/s$ from a QGP phase to a hadronic one. We address the relation between the scaling of $v_2(p_T)$ with the eccentricity $\epsilon_x$ and with the integrated elliptic flow. We show that the breaking of the $v_2(p_T)/\epsilon_x$ scaling is not coming mainly from the finite $\eta/s$ but from the f.o. dynamics and that the $v_2(p_T)$ is weakly dependent on the f.o. scheme. On the other hand the $v_4(p_T)$ is found to be much more dependent on both the $\eta/s$ and the f.o. dynamics and hence is indicated to put better constraints on the properties of the QGP. A first semi-quantitative analysis show that both $v_2$ and $v_4$ (with the smooth f.o.) consistently indicate a plasma with $4\pi \eta/s \sim 1-2$.Comment: 7 pages. Proceedings of the International School of Nuclear Physics in Erice, Sicily, to appear in Progress in Particle and Nuclear Physic

A comparison between different optimization criteria for tuned mass dampers design

Tuned mass sampers (TMDs) are widely used strategies for vibration control in many engineering applications, so that many TMD optimization criteria have been proposed till now. However, they normally consider only TMD stiffness and damping as design variables and assume that the tuned mass is a pre-selected value. In this work a more complete approach is proposed and then also TMD mass ratio is optimized. A standard single degree of freedom system is investigated to evaluate TMD protection efficiency in case of excitation at the support. More precisely, this model is used to develop two different optimizations criteria which minimize the main system displacement or the inertial acceleration. Different environmental conditions described by various char- acterizations of the input, here modelled by a stationary filtered stochastic process, are considered. Results show that all solutions obtained considering also the mass of the TMD as design variable are more efficient if compared with those obtained without it. However, in many cases these solutions are inappropriate because the optimal TMD mass is greater than real admissible values in practical technical applications for civil and mechanical engineering. Anyway, one can deduce that there are some interesting indications for applications in some actual contexts. In fact, the results show that there are some ranges of environmental parameters ranges where results attained by the displacement criterion are compatible with real applications requiring some percent of main system mass. Finally, the present research gives promising indications for complete TMD optimization application in emerging technical contexts, as micro- mechanical devices and nano resonant beam

Dye diffusion during laparoscopic tubal patency tests may suggest a lymphatic contribution to dissemination in endometriosis: A prospective, observational study

Aim Women with adenomyosis are at higher risk of endometriosis recurrence after surgery. This study was to assess if the lymphatic vessel network drained from the uterus to near organs where endometriosis foci lied. Methods A prospective, observational study, Canadian Task Force Classification II-2, was conducted at Sacro Cuore Don Calabria Hospital, Negrar, Italy. 104 white women aged 18–43 years were enrolled consecutively for this study. All patients underwent laparoscopy for endometriosis and a tubal dye test was carried out. Results Evidence of dye dissemination through the uterine wall and outside the uterus was noted in 27 patients (26%) with adenomyosis as it permeated the uterine wall and a clear passage of the dye was shown in the pelvic lymphatic vessels regardless whether the tubes were unobstructed. Histological assessment of the uterine biopsies confirmed adenomyosis. Conclusion Adenomyosis is characterized by ectatic lymphatics that allow the drainage of intrauterine fluids (the dye and, perhaps, menstrual blood) at minimal intrauterine pressure from the uterine cavity though the lymphatic network to extrauterine organs. Certainly, this may not be the only explanation for endometriosis dissemination but the correlation between the routes of the dye drainage and location of endometriosis foci is highly suggestive

Energy density fluctuations in Early Universe

The primordial nucleosinthesys of the element can be influenced by the transitions of phase that take place after the Big Bang, such as the QCD transition. In order to study the effect of this phase transition, in this work we compute the time evolution of thermodynamical quantities of the early universe, focusing on temperature and energy density fluctuations, by solving the relevant equations of motion using as input the lattice QCD equation of state to describe the strongly interacting matter in the early universe plasma. We also study the effect of a primordial strong magnetic field by means of a phenomenological equation of state. Our results show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during the crossover.Comment: 4 pages, 2 figures. Talk given at Sventh European Summer School on Experimental Nuclear Astrophysics, 15-27 September 2013, Santa Tecla (CT) - Ital