Separability of Rotational Effects on a Gravitational Lens

We derive the deflection angle up to $O(m^2a)$ due to a Kerr gravitational lens with mass $m$ and specific angular momentum $a$. It is known that at the linear order in $m$ and $a$ the Kerr lens is observationally equivalent to the Schwarzschild one because of the invariance under the global translation of the center of the lens mass. We show, however, nonlinear couplings break the degeneracy so that the rotational effect becomes in principle separable for multiple images of a single source. Furthermore, it is distinguishable also for each image of an extended source and/or a point source in orbital motion. In practice, the correction at $O(m^2a)$ becomes $O(10^{-10})$ for the supermassive black hole in our galactic center. Hence, these nonlinear gravitational lensing effects are too small to detect by near-future observations.Comment: 12 pages (RevTeX); accepted for publication in Phys. Rev.

Binary Collisions and the Slingshot Effect

We derive the equations for the gravity assist manoeuvre in the general 2D case without the constraints of circular planetary orbits or widely different masses as assumed by Broucke, and obtain the slingshot conditions and maximum energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the geometric view developed in an earlier paper by the authors the possible trajectories are computed for both attractive or repulsive interactions yielding a further insight on the slingshot mechanics and its parametrization. The general slingshot manoeuvre for arbitrary masses is explained as a particular case of the possible outcomes of attractive or repulsive binary collisions, and the correlation between asymptotic information and orbital parameters is obtained in general.Comment: 12 pages, 7 figures, accepted for publication Dec'07, Celestial Mechanics and Dynamical Astronom

The normative underpinnings of population-level alcohol use: An individual-level simulation model

Background. By defining what is “normal,” appropriate, expected, and unacceptable, social norms shape human behavior. However, the individual-level mechanisms through which social norms impact population-level trends in health-relevant behaviors are not well understood. Aims. To test the ability of social norms mechanisms to predict changes in population-level drinking patterns. Method. An individual-level model was developed to simulate dynamic normative mechanisms and behavioral rules underlying drinking behavior over time. The model encompassed descriptive and injunctive drinking norms and their impact on frequency and quantity of alcohol use. A microsynthesis initialized in 1979 was used as a demographically representative synthetic U.S. population. Three experiments were performed in order to test the modelled normative mechanisms. Results. Overall, the experiments showed limited influence of normative interventions on population-level alcohol use. An increase in the desire to drink led to the most meaningful changes in the population’s drinking behavior. The findings of the experiments underline the importance of autonomy, that is, the degree to which an individual is susceptible to normative influence. Conclusion. The model was able to predict theoretically plausible changes in drinking patterns at the population level through the impact of social mechanisms. Future applications of the model could be used to plan norms interventions pertaining to alcohol use as well as other health behaviors

Protecting the conformal symmetry via bulk renormalization on Anti deSitter space

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.Comment: 40 page

On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group $\Gamma$, will construct explicit finite models for the skeleta of $K(\Gamma,1)$ and hence compute the integral homology and cohomology of $\Gamma$.Comment: 21 pages, 4 figure

A bacterial-based algorithm to simulate complex adaptive systems

Following a bacterial-based modeling approach, we want to model and analyze the impact of both decentralization and heterogeneity on group behavior and collective learning. Inspired by bacterial conjugation, we have defined an artificial society in which agents' strategies adapt to changes in resources location, allowing migration and survival in a dynamic sugarscape-like scenario. To study the impact of these variables we have simulated a scenario in which resources are limited and localized. We also have defined three constraints in genetic information processing (inhibition of plasmid conjugation, inhibition of plasmid reproduction and inhibition of plasmid mutation). Our results affirmed the hypothesis that efficiency of group adaptation to dynamic environments is better when societies are varied and distributed than when they are homogeneous and centralized

Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Can social norms explain long-term trends in alcohol use? Insights from inverse generative social science

Social psychological theory posits entities and mechanisms that attempt to explain observable differences in behavior. For example, dual process theory suggests that an agent's behavior is influenced by intentional (arising from reasoning involving attitudes and perceived norms) and unintentional (i.e., habitual) processes. In order to pass the generative sufficiency test as an explanation of alcohol use, we argue that the theory should be able to explain notable patterns in alcohol use that exist in the population, e.g., the distinct differences in drinking prevalence and average quantities consumed by males and females. In this study, we further develop and apply inverse generative social science (iGSS) methods to an existing agent-based model of dual process theory of alcohol use. Using iGSS, implemented within a multi-objective grammar-based genetic program, we search through the space of model structures to identify whether a single parsimonious model can best explain both male and female drinking, or whether separate and more complex models are needed. Focusing on alcohol use trends in New York State, we identify an interpretable model structure that achieves high goodness-of-fit for both male and female drinking patterns simultaneously, and which also validates successfully against reserved trend data. This structure offers a novel interpretation of the role of norms in formulating drinking intentions, but the structure's theoretical validity is questioned by its suggestion that individuals with low autonomy would act against perceived descriptive norms. Improved evidence on the distribution of autonomy in the population is needed to understand whether this finding is substantive or is a modeling artefact