Reliability measures for local nodes assessment in classification trees

Most of the modem developments with classification trees are aimed at improving their predictive capacity. This article considers a curiously neglected aspect of classification trees, namely the reliability of predictions that come from a given classification tree. In the sense that a node of a tree represents a point in the predictor space in the limit, the aim of this article is the development of localized assessment of the reliability of prediction rules. A classification tree may be used either to provide a probability forecast, where for each node the membership probabilities for each class constitutes the prediction, or a true classification where each new observation is predictively assigned to a unique class. Correspondingly, two types of reliability measure will be derived-namely, prediction reliability and classification reliability. We use bootstrapping methods as the main tool to construct these measures. We also provide a suite of graphical displays by which they may be easily appreciated. In addition to providing some estimate of the reliability of specific forecasts of each type, these measures can also be used to guide future data collection to improve the effectiveness of the tree model. The motivating example we give has a binary response, namely the presence or absence of a species of Eucalypt, Eucalyptus cloeziana, at a given sampling location in response to a suite of environmental covariates, (although the methods are not restricted to binary response data).

Nodulated N-2-fixing Casuarina cunninghamiana is the sink for net N transfer from non-N-2-fixing Eucalyptus maculata via an ectomycorrhizal fungus Pisolithus sp using (NH4+)-N-15 or (NO3-)-N-15 supplied as ammonium nitrate

To determine the effects of nitrogen source on rates of net N transfer between plants connected by a common mycorrhizal network, we measured transfer of N supplied as (NH4NO3)-N-15-N-14 or (NH4NO3)-N-14-N-15 in three Casuarina/Eucalyptus treatments interconnected by a Pisolithus sp. The treatments were nonnodulated nonmycorrhizal/nonmycorrhizal; nonnodulated mycorrhizal/mycorrhizal; and nodulated mycorrhizal/mycorrhizal. Mycorrhization was 67% in Eucalyptus and 36% in Casuarina. N-2 fixation supplied 38% of the N in Casuarina. Biomass, N and N-15 contents were lowest in nonmycorrhizal plants and greatest in plants in the nodulated/mycorrhizal treatment. Nitrogen transfer was enhanced by mycorrhization and by nodulation, and was greater when N was supplied as (NH4+)-N-15 than (NO3-)-N-15. Nitrogen transfer rates were lowest in the nonmycorrhizal treatment for either N-15 source, and greatest in the nodulated, mycorrhizal treatment. Transfer was greater to Casuarina than to Eucalyptus and where ammonium rather than nitrate was the N source. Irrespective of N-15 source and of whether Casuarina or Eucalyptus was the N sink, net N transfer was low and was similar in both nonnodulated treatments. However, when Casuarina was the N sink in the nodulated, mycorrhizal treatment, net N transfer was much greater with (NH4+)-N-15 than with (NO3-)-N-15. High N demand by Casuarina resulted in greater net N transfer from the less N-demanding Eucalyptus. Net transfer of N from a non-N-2-fixing to an N-2-fixing plant may reflect the very high N demand of N-2-fixing species.

Mixed order parameters, accidental nodes and broken time reversal symmetry in organic superconductors: a group theoretical analysis

We present a group theoretical analysis of several classes of organic superconductor. We predict that highly frustrated organic superconductors, such as K-(ET)(2)Cu-2(CN)(3) (where ET is BEDT-TTF, bis(ethylenedithio) tetrathiafulvalene) and beta'-[Pd(dmit)(2)](2)X, undergo two superconducting phase transitions, the first from the normal state to a d-wave superconductor and the second to a d + id state. We show that the monoclinic distortion of K-(ET)(2)Cu(NCS)(2) means that the symmetry of its superconducting order parameter is different from that of orthorhombic-K-(ET)(2)Cu[N(CN)(2)] Br. We propose that beta'' and theta phase organic superconductors have d(xy) + s order parameters.