Evolving networks for social optima in the “weakest link game”

Previous models have applied evolving networks based on node-level “copy and rewire” rules to simple two player games (e.g. the Prisoner’s Dilemma). It was found that such models tended to evolve toward socially optimal behavior. Here we apply a similar technique to a more tricky co-ordination game (the weakest link game) requiring interactions from several players (nodes) that may play several strategies. We define a variant of the game with several equilibria—each offering increasing social benefit. We found that the evolving network functions to select and spread more optimal equilibria while resisting invasion by lower ones. Hence the network acts as a kind of “social ratchet” selecting for increasing social benefit. Such networks have applications in peer-to-peer computing and may have implications for understanding social systems.

Sphere packings, I

We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite configurations called Delaunay stars. A score, which is related to the density of packings, is assigned to each Delaunay star. We conjecture that the score of every Delaunay star is at most the score of the stars in the face-centered cubic and hexagonal close packings. This conjecture implies the Kepler conjecture. To complete the first step of the program, we show that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.     

Sphere Packings, II

An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of R ³ into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining class have density at most that of a regular octahedron (about 0.7209). Received April 24, 1995, and in revised form April 11, 1996.     

Two-photon spectroscopy and analysis with a white-light continuum probe

We present a powerful experimental tool and analysis for characterization of two-photon absorption (2PA) spectra. We demonstrate this method with ZnS and then apply it to organic dyes in solution. We also compare the results with those from other methods such as two-photon fluorescence spectroscopy. This femtosecond pump-probe method uses a white-light continuum (WLC) as the probe to produce a nondegenerate 2PA spectrum. The extreme chirp of the WLC requires that transmittance data be collected over a range of temporal delays between pump and probe pulses. These data then need to be corrected for the effects of this chirp as well as for the temporal walk-off of the pulses in the sample that result from the frequency nondegenerate nature of the experiment. We present a simple analytic solution for the transmitted fluence through the sample, which is applicable for most practical cases.     

Meaning and Control: Social Aspects of Science and Technology

Journal of the Operational Research Society -     

The role of column switching in analysing complex samples

Our objective in using column switching is primarily to achieve the desired separation in the minimum analysis time. Complimentary to this aim is the need for sample and column cleanup followed by column re-equilibration. Finally, all operations should be capable of automation. Fundamental to column switching methodology is the concept of Zone cutting, where part of the chromatogram is transferred to another column. This forms the basis of sample cleanup and is a very versatile and powerful methods. Multiple zone cutting is also possible to further increase to scope of cleanup or to minimise analysis time. Zone cutting is also complimentary to the techniques of trace enrichment and recycling. Examples will be given involving the use of these techniques in the analysis of complex matrices such as urine, plant extracts, wine and serum. The latter will be used to propose a novel approach to the quantitative analysis of anti-convulsants in serum using hexobarbital as internal standard.