The optimism bias : a cognitive neuroscience perspective

The optimism bias is a well-established psychological phenomenon. Its study has implications that are far reaching in fields as diverse as mental health and economic theory. With the emerging field of cognitive neuroscience and the advent of advanced neuroimaging techniques, it has been possible to investigate the neural basis of the optimism bias and to understand in which neurological conditions this natural bias fails. This review first defines the optimism bias, discusses its implications and reviews the literature that investigates its neural basis. Finally some potential pitfalls in experimental design are discussed.peer-reviewe

Zoll Metrics, Branched Covers, and Holomorphic Disks

We strengthen our previous results regarding the moduli spaces of Zoll metrics and Zoll projective structures on S^2. In particular, we describe a concrete, open condition which suffices to guarantee that a totally real embedding of RP^2 in CP_2 arises from a unique Zoll projective structure on the 2-sphere. Our methods ultimately reflect the special role such structures play in the initial value problem for the 3-dimensional Lorentzian Einstein-Weyl equations.Comment: 21 pages, LaTeX2

Yamabe Invariants and Spin^c Structures

The Yamabe Invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using spin^c Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Laplacian. These results dovetail perfectly with those derived from the perturbed Seiberg-Witten equations, but the present method is much more elementary in spirit.Comment: Standard LaTeX fil

Zoll Manifolds and Complex Surfaces

We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to previous work, our approach is twistor-theoretic, and depends fundamentally on the fact that, up to biholomorphism, there is only one complex structure on CP2

Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks

We develop a global twistor correspondence for pseudo-Riemannian conformal structures of signature (++--) with self-dual Weyl curvature. Near the conformal class of the standard indefinite product metric on S^2 x S^2, there is an infinite-dimensional moduli space of such conformal structures, and each of these has the surprising global property that its null geodesics are all periodic. Each such conformal structure arises from a family of holomorphic disks in CP_3 with boundary on some totally real embedding of RP^3 into CP_3. An interesting sub-class of these conformal structures are represented by scalar-flat indefinite K\"ahler metrics, and our methods give particularly sharp results in this more restrictive setting.Comment: 56 pages, LaTeX2

The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks

We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence.Comment: 11 pages, LaTeX2e. Revised version strengthens result and completes proo

Radiative cooling of swept up gas in AGN-driven galactic winds and its implications for molecular outflows

We recently used hydro-chemical simulations to demonstrate that molecular outflows observed in luminous quasars can be explained by molecule formation within the AGN wind. However, these simulations cover a limited parameter space, due to their computational cost. We have therefore developed an analytic model to follow cooling in the shocked ISM layer of an AGN wind. We explore different ambient densities ($1-10^{4} \, \rm{cm}^{-3}$), density profile slopes ($0-1.5$), AGN luminosities ($10^{44}-10^{47} \, \rm{erg} \, \rm{s}^{-1}$), and metallicities ($0.1-3 \rm{Z}_{\odot}$). The swept up gas mostly cools within ~1 Myr. Based on our previous simulations, we predict that this gas would produce observable molecular outflows. The instantaneous momentum boost initially increases as the outflow decelerates. However, it reaches a maximum of $\approx$20, due to work done against the gravitational potential. The predicted time-averaged observational estimate of the molecular outflow momentum boost reaches a maximum of $\approx1-2$, partly due to our assumed molecular fraction, 0.2, but also because the instantaneous and observational, time-averaged definitions are not equivalent. Thus recent observational estimates of order unity momentum boosts do not necessarily rule out energy-driven outflows. Finally, we find that dust grains are likely to re-form by accretion of metals after the shocked ISM layer has cooled, assuming that a small fraction of dust grains swept up after this layer has cooled are able to mix into the cool phase, and assuming that grain growth remains efficient in the presence of the strong AGN radiation field. This would enable rapid molecule formation, as assumed in our models.Comment: 22 pages, 16 figures (including appendices). Accepted for publication in MNRA