The discovery that many trans‐Neptunian objects exist in pairs, or binaries, is proving invaluable for shedding light on the formation, evolution and structure of the outer Solar system. Based on recent systematic searches it has been estimated that up to 10 per cent of Kuiper‐belt objects might be binaries. However, all examples discovered to date are unusual, as compared with near‐Earth and main‐belt asteroid binaries, for their mass ratios of the order of unity and their large, eccentric orbits. In this article we propose a common dynamical origin for these compositional and orbital properties based on four‐body simulations in the Hill approximation. Our calculations suggest that binaries are produced through the following chain of events. Initially, long‐lived quasi‐bound binaries form by two bodies getting entangled in thin layers of dynamical chaos produced by solar tides within the Hill sphere. Next, energy transfer through gravitational scattering with a low‐mass intruder nudges the binary into a nearby non‐chaotic, stable zone of phase space. Finally, the binary hardens (loses energy) through a series of relatively gentle gravitational scattering encounters with further intruders. This produces binary orbits that are well fitted by Kepler ellipses. Dynamically, the overall process is strongly favoured if the original quasi‐bound binary contains comparable masses. We propose a simplified model of chaotic scattering to explain these results. Our findings suggest that the observed preference for roughly equal‐mass ratio binaries is probably a real effect; that is, it is not primarily due to an observational bias for widely separated, comparably bright objects. Nevertheless, we predict that a sizeable population of very unequal‐mass Kuiper‐belt binaries is probably awaiting discovery.

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

he reason w hy atomic physicists are i nterested i n celestial m echani cs is simple: the gravi tati ona l and C oulom bic potenti als are mathemati cally i denti cal and a one-electron atom is, therefore, governed by the same Hami ltoni an as is the Kepler problem . However, once one goes beyon d the two-bod y Kepler problem the connecti ons between atomi c physi cs and celesti al mechanics become less di rect. For exam ple, the three-body problem , arguab ly the raison d' eà tre of celestial mechani cs for several centuries, has recei ved relatively little attenti on from atomic physi cists because i t does not have a direct quantu m counterpart: three quantu m parti cles canno t m utually attract one anothe r and at the same ti me interact throug h a purely Coulombi c force law . Nevertheless, i n the last ® ve years several research groups have di scovered that quantu m analogues of a parti cular limi t of the three-bod y problem, the restricted three-body problem , not only exist but contain dramati cally new physics. Thi s arti cle will describe this work and in parti cular will demonstrate the possibi lity of producing locali zed electroni c states in atom s that are di rect analog s of the coherent states of the harm oni c osci llator. These coherent wavepackets behave i n a simi lar way to the coherent states of the harmonic osci llator and the resulti ng atom mi mi cs a`classi cal' or Bohr atom althoug h external ® elds must be used to m aintain thei r i ntegri ty. Such w avepacket states are of as much funda mental interest i n laser chemi stry as they are i n atomi c, m olecular, opti cal, and soli d state physi cs. T he potenti al applicati ons of ti me-evolving quantu m wavepackets seem limi tless; some exam ples of thei r uses i nclude: the explorati on of the bounda ry between classi cal and quantu m m echani cs, the i nvesti gation of the i nterpretati on of quantu m mechanics by creating experi mental reali zations of such classi c experim ents as SchroÈ di nger' s Cat, the control of chemi cal reacti on dynam ics to achieve laser i sotope separation, the storage of coherence for quantu m computational or com municati ons purposes, and the constructi on of opti cal switches and m odulato rs.

Feature selection is an important challenge in many classification problems, especially if the number of features greatly exceeds the number of examples available. We have developed a procedure--GenForest--which controls feature selection in random forests of decision trees by using a genetic algorithm. This approach was tested through our entry into the Comparative Evaluation of Prediction Algorithms 2006 (CoEPrA) competition (accessible online at: http://www.coepra.org). CoEPrA was a modeling competition organized to provide an objective testing for various classification and regression algorithms via the process of blind prediction. In the competition GenForest ranked 10/23, 5/16 and 9/16 on CoEPrA classification problems 1, 3 and 4, respectively, which involved the classification of type I MHC nonapeptides i.e. peptides containing nine amino acids. These problems each involved the classification of different sets of nonapeptides. Associated with each amino acid was a set of 643 features for a total of 5787 features per peptide. The method, its application to the CoEPrA datasets, and its performance in the competition are described.