We study the phase diagram of a minority game where three classes of agents are present. Two types of agents play a risk-loving game that we model by the standard Snowdrift Game. The behaviour of the third type of agents is coded by indifference with respect to the game at all: their dynamics is designed to account for risk-aversion as an innovative behavioral gambit. From this point of view, the choice of this solitary strategy is enhanced when innovation starts, while is depressed when it becomes the majority option. This implies that the payoff matrix of the game becomes dependent on the global awareness of the agents measured by the relevance of the population of the indifferent players. The resulting dynamics is nontrivial with different kinds of phase transition depending on a few model parameters. The phase diagram is studied on regular as well as complex networks.

The spectrum of anomalous dimensions of gauge-invariant operators in maximally super- symmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2) subsector spanned by the twist-two single- trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow ana- lytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

In this paper, which is a sequel to Beccaria et al (2010 J. Phys. A: Math. Theor. 43 165402), we compute the one-loop correction to the energy of pulsating string solutions in AdS5 ×S5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can also be put into the single-gap Lame ́ form. A novel aspect of pulsating solutions is that the one- loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the ‘short-string’ limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of ‘small’ semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS3 part of AdS5×S5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lam ́e form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.

Epidemic evolution on complex networks strongly depends on their topology and the infection dynamical properties, as highly connected nodes and individuals exposed to the contagion have competing roles in the disease spreading. In this spirit, we propose a new immunization strategy exploiting the knowledge of network geometry and dynamical information about the spreading infection. The flexibility and effectiveness of the proposed scheme are successfully tested with numerical simulations on a wide set of complex networks.

We study the leading quantum string correction to the dressing phase in the asymptotic Bethe Ansatz system for superstring in AdS3 × S3 × T 4 supported by RR flux. We find that the phase should be different from the phase appearing in the AdS5 ×S5 case. We use the simplest example of a rigid circular string with two equal spins in S3 and also consider the general approach based on the algebraic curve description. We also discuss the case of the AdS3 × S3 × S3 × S1 theory and find the dependence of the 1-loop correction to the effective string tension function h(λ) (expected to enter the magnon dispersion relation) on the parameters α related to the ratio of the two 3-sphere radii. This correction vanishes intheAdS3×S3×T4 case.

We consider integrable superstring theory on AdS3 × S3 × M4 where M4 = T4 or M4 = S3 × S1 with generic ratio of the radii of the two 3-spheres. We compute the one- loop energy of a short folded string spinning in AdS3 and rotating in S3. The computation is performed by world-sheet small spin perturbation theory as well as by quantizing the classical algebraic curve characterizing the finite-gap equations. The two methods give equal results up to regularization contributions that are under control. One important byproduct of the calculation is the part of the energy which is due to the dressing phase in the Bethe Ansatz. Remarkably, this contribution Edressing turns out to be independent 1 on the radii ratio. In the M4 = T4 limit, we discuss how Edressing relates to a recent 1 proposal for the dressing phase tested in the su(2) sector. We point out some difficulties suggesting that quantization of the AdS3 classical finite-gap equations could be subtler than the easier AdS5 × S5 case.

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent of the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks.

We analyze the higher conserved charges of type IIB superstring on from the perspective of a recently discovered generalized Gribov-Lipatov reciprocity. We provide several evidences that reciprocity holds for all the higher charges and not only for the energy. This is discussed in the simple case of twist , and operators in the sl subsector at (a) multi-loop level in weak coupling, (b) classical level at strong coupling for the dual folded string.

The most general large N = 4 superconformal W∞ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the W∞ algebra is uniquely determined by the levels of the two su(2) algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.