Neighbor selection and hitting probability in small-world graphs

Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very little knowledge of the graph itself. In an attempt to understand how such graphs arise we introduce a different criterion for graphs to be navigable in this sense, relating the neighbor selection of a vertex to the hitting probability of routed walks. In several models starting from both discrete and continuous settings, this can be shown to lead to graphs with the desired properties. It also leads directly to an evolutionary model for the creation of similar graphs by the stepwise rewiring of the edges, and we conjecture, supported by simulations, that these too are navigable.Comment: Published in at http://dx.doi.org/10.1214/07-AAP499 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Book review: young British muslims: identity, culture, politics and the media

In Britain’s highly politicised social climate in the aftermath of the 7/7 London bombings, this book provides an in-depth understanding of British Muslim identity through migration history, family settlement, socio-economic status, religion and culture, and the wider societal environment. Russell Sandberg finds that Nahid Afrose Kabir‘s emphasis on the importance of biculturalism is an important contribution to that literature

Energetics of the brain and AI

Does the energy requirements for the human brain give energy constraints that give reason to doubt the feasibility of artificial intelligence? This report will review some relevant estimates of brain bioenergetics and analyze some of the methods of estimating brain emulation energy requirements. Turning to AI, there are reasons to believe the energy requirements for de novo AI to have little correlation with brain (emulation) energy requirements since cost could depend merely of the cost of processing higher-level representations rather than billions of neural firings. Unless one thinks the human way of thinking is the most optimal or most easily implementable way of achieving software intelligence, we should expect de novo AI to make use of different, potentially very compressed and fast, processes

The biopsychosocial context of ADHD.

attention-deficit/hyperactivity disorder (adhd) represents adaptation to defective neurotransmission – an adaptation seldom with benefit. the resulting behavioural style not only increases vulnerability to adverse experiences, but also creates a context in which encountering adversity is more likely. furthermore, the fact that adhd is a highly heritable condition increases the probability of a child with a compromised neurobiological disposition being raised by caregivers with suboptimal resources

Generalized cylindrical coordinates for characteristic boundary conditions and characteristic interface conditions

The aim of this report is to derive generalized coordinates for the specific case of mapping only the streamwise and radial coordinate of a cylindrical coordinate system, while leaving the azimuthal coordinate unchanged. The characteristic equations and the required matrices for the transformation from conservative to characteristic form are presented for this specific case. All equations and procedures are based on previous work on generalized characteristic boundary conditions (Kim &amp; Lee, 2000) and characteristic interface conditions (Kim &amp; Lee, 2003).<br/

Tensor spherical harmonics on S^2 and S^3 as eigenvalue problems

Tensor spherical harmonics for the 2‐sphere and 3‐sphere are discussed as eigenfunction problems of the Laplace operators on these manifolds. The scalar, vector, and second‐rank tensor harmonics are given explicitly in terms of known functions and their properties summarized