Evolutionary game dynamics of controlled and automatic decision-making

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible, and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions where having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition, and demonstrate necessary conditions for the rise and fall of rationality.Comment: 9 pages, 7 figure

Geometric scaling in high-energy QCD at nonzero momentum transfer

We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a typical scale of the target.Comment: 4 pages, 2 figures. Talk given by G. Soyez at the "Rencontres de Moriond", 12-19 March 2005, La Thuile, Ital

Cluster approximations for infection dynamics on random networks

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasi-stationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process.Comment: the notation has been changed; Ref. [26] and a new paragraph in Section IV have been adde

Probing the Magnetized Interstellar Medium Surrounding the Planetary Nebula Sh 2-216

We present 1420 MHz polarization images of a 2.5 X 2.5 degree region around the planetary nebula (PN) Sh 2-216. The images are taken from the Canadian Galactic Plane Survey (CGPS). An arc of low polarized intensity appears prominently in the north-east portion of the visible disk of Sh 2-216, coincident with the optically identified interaction region between the PN and the interstellar medium (ISM). The arc contains structural variations down to the ~1 arcminute resolution limit in both polarized intensity and polarization angle. Several polarization-angle "knots" appear along the arc. By comparison of the polarization angles at the centers of the knots and the mean polarization angle outside Sh 2-216, we estimate the rotation measure (RM) through the knots to be -43 +/- 10 rad/m^2. Using this estimate for the RM and an estimate of the electron density in the shell of Sh 2-216, we derive a line-of-sight magnetic field in the interaction region of 5.0 +/- 2.0 microG. We believe it more likely the observed magnetic field is interstellar than stellar, though we cannot completely dismiss the latter possibility. We interpret our observations via a simple model which describes the ISM magnetic field around Sh 2-216, and comment on the potential use of old PNe as probes of the magnetized ISM.Comment: 25 pages, 4 figures. Accepted for publication in the Astrophysical Journa

Sustainable institutionalized punishment requires elimination of second-order free-riders

Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.Comment: 7 two-column pages, 3 figures; accepted for publication in Scientific Report

A Phase Front Instability in Periodically Forced Oscillatory Systems

Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where $\omega_{forcing}/\omega_{system}=2n$ ($n>1$). Stationary fronts shifting the oscillation phase by $\pi$ lose stability below a critical forcing strength and decompose into $n$ traveling fronts each shifting the phase by $\pi/n$. The instability designates a transition from stationary two-phase patterns to traveling $n$-phase patterns

A GBT Survey of the HALOGAS Galaxies and Their Environments I: Revealing the full extent of HI around NGC891, NGC925, NGC4414 & NGC4565

We present initial results from a deep neutral hydrogen (HI) survey of the HALOGAS galaxy sample, which includes the spiral galaxies NGC891, NGC925, NGC4414, and NGC4565, performed with the Robert C. Byrd Green Bank Telescope (GBT). The resulting observations cover at least four deg$^2$ around these galaxies with an average 5$\sigma$ detection limit of 1.2$\times$10$^{18}$ cm$^{-2}$ over a velocity range of 20 km s$^{-1}$ and angular scale of 9.1$'$. In addition to detecting the same total flux as the GBT data, the spatial distribution of the GBT and original Westerbork Synthesis Radio Telescope (WSRT) data match well at equal spatial resolutions. The HI mass fraction below HI column densities of 10$^{19}$ cm$^{-2}$ is, on average, 2\%. We discuss the possible origins of low column density HI of nearby spiral galaxies. The absence of a considerable amount of newly detected HI by the GBT indicates these galaxies do not have significant extended diffuse HI structures, and suggests future surveys planned with the SKA and its precursors must go \textit{at least} as deep as 10$^{17}$ cm$^{-2}$ in column density to significantly increase the probability of detecting HI associated with the cosmic web and/or cold mode accretion.Comment: Accepted for publication in The Astrophysical Journal; 28 pages, 15 figure

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file. Figures are available on request from [email protected]

Breakdown of Conformal Invariance at Strongly Random Critical Points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.Comment: 9 page

Quality versus quantity of social ties in experimental cooperative networks

Recent studies suggest that allowing individuals to choose their partners can help to maintain cooperation in human social networks; this behaviour can supplement behavioural reciprocity, whereby humans are influenced to cooperate by peer pressure. However, it is unknown how the rate of forming and breaking social ties affects our capacity to cooperate. Here we use a series of online experiments involving 1,529 unique participants embedded in 90 experimental networks, to show that there is a ‘Goldilocks’ effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors. When the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach and, hence, subjects resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties