A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction (``bond'') in the system can be satisfied at the same time. Such systems are common in all areas of physical and biological science. In the most extreme cases they can have a disordered ground state with ``macroscopic'' degeneracy, that is, one that comprises a huge number of equivalent states of the same energy. Pauling's description of the low temperature proton disorder in water ice was perhaps the first recognition of this phenomenon, and remains the paradigm. In recent years a new class of magnetic substance has been characterised, in which the disorder of the magnetic moments at low temperatures is precisely analogous to the proton disorder in water ice. These substances, known as spin ice materials, are perhaps the ``cleanest'' examples of such highly frustrated systems yet discovered. They offer an unparalleled opportunity for the study of frustration in magnetic systems at both an experimental and a theoretical level. This article describes the essential physics of spin ice, as it is currently understood, and identifies new avenues for future research on related materials and models.Comment: 5 POSTSCRIPT figures included. Contact: gingras@gandalf.uwaterloo.ca for access to Science PDF fil

Within the past 20 years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type A 3+ 2 B 4+ 2 O 7 where A is a rare-earth ion and B is usually a transition metal. Both the A and B sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long range ordered ground states in accord with the Third Law is frustrated, resulting in some novel short range ordered alternatives such as spin glasses, spin ices and spin liquids and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.

BACKGROUND Major issues in the implementation of screening for lung cancer by means of low-dose computed tomography (CT) are the definition of a positive result and the management of lung nodules detected on the scans. We conducted a population-based prospective study to determine factors predicting the probability that lung nodules detected on the first screening low-dose CT scans are malignant or will be found to be malignant on follow-up. METHODS We analyzed data from two cohorts of participants undergoing low-dose CT screening. The development data set included participants in the Pan-Canadian Early Detection of Lung Cancer Study (PanCan). The validation data set included participants involved in chemoprevention trials at the British Columbia Cancer Agency (BCCA), sponsored by the U.S. National Cancer Institute. The final outcomes of all nodules of any size that were detected on baseline low-dose CT scans were tracked. Parsimonious and fuller multivariable logistic-regression models were prepared to estimate the probability of lung cancer. RESULTS In the PanCan data set, 1871 persons had 7008 nodules, of which 102 were malignant, and in the BCCA data set, 1090 persons had 5021 nodules, of which 42 were malignant. Among persons with nodules, the rates of cancer in the two data sets were 5.5% and 3.7%, respectively. Predictors of cancer in the model included older age, female sex, family history of lung cancer, emphysema, larger nodule size, location of the nodule in the upper lobe, part-solid nodule type, lower nodule count, and spiculation. Our final parsimonious and full models showed excellent discrimination and calibration, with areas under the receiver-operating-characteristic curve of more than 0.90, even for nodules that were 10 mm or smaller in the validation set. CONCLUSIONS Predictive tools based on patient and nodule characteristics can be used to accurately estimate the probability that lung nodules detected on baseline screening low-dose CT scans are malignant. (Funded by the Terry Fox Research Institute and others; ClinicalTrials.gov number, NCT00751660.)