How to quantify energy landscapes of solids

We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii) descriptor of structure called fingerprint function, which can be represented as a one-dimensional function or a vector in abstract multidimensional space, (iii) definition of a ''distance'' between two structures enabling quantification of energy landscapes, (iv) definition of a degree of order of a structure, and (v) definitions of the quasi-entropy quantifying structural diversity. Our approach can be used for rationalizing large databases of crystal structures and for tuning computational algorithms for structure prediction. It enables quantitative and intuitive representations of energy landscapes and reappraisal of some of the traditional chemical notions and rules. Our analysis confirms the expectations that low-energy minima are clustered in compact regions of configuration space ("funnels") and that chemical systems tend to have very few funnels, sometimes only one. This analysis can be applied to the physical properties of solids, opening new ways of discovering structure-property relations. We quantitatively demonstrate that crystals tend to adopt one of the few simplest structures consistent with their chemistry, providing a thermodynamic justification of Pauling's fifth rule.Comment: Published in J. Chem. Phys. 130, 104504 (2009

Predicting the Benefits and Harms of Breast Cancer Screening: Current debates and future directions

Breast cancer is the most common cancer among women in Western countries. Presently, women in the Netherlands have a 1 : 7 chance of developing breast cancer during their lifetime. This means that in 2008, almost 15,000 women were newly diagnosed with the disease. The incidence of breast cancer in the Netherlands is among the highest in Europe.In 2006, for instance, the age-standardized incidence rate was 128 per 100,000 woman-years. As a comparison, the average in Europe was 94.3 per 100,000 woman-years. Although the probability of cure has improved over the last decennia, for a third of all women with breast cancer, the disease will be fatal. This makes breast cancer the most common cause of cancer death in women in Europe. The age-standardized mortality rate in the Netherlands in 2006 was 29.8 per 100,000 woman-years, versus 26.0 per 100,000 woman-years in Europe. Breast cancer develops as a single malignant cell with uncontrolled cell growth to a tumour of several millimeters or centimeters in diameter. At some point in time, the tumour may reach a size at which it becomes symptomatic. The larger the size, the less likely it is that the tumour can be cured. It is therefore thought that by diagnosing cancer at an earlier phase, for instance by screening, the probability of survival can be increased. Several methods for early detection of breast cancer exist: breast self examination, examination by a clinician or a nurse (‘clinical breast examination’), MRI or ultrasonography. Mammography, which involves one or more X-ray images of the breasts, is considered the best tool for examining postmenopausal women with an average risk for the disease, because it can reach a high sensitivity (>70%) and specificity (>95%) when it is applied on a large scale. At the same time, costs are moderate: 50 euro per screening examination in the Netherlands.The effects of breast cancer screening using mammography were therefore studied in several randomized controlled trials (RCTs), with various screening ages and intervals. Screening women aged 50 and older resulted in statistically significant reductions in breast cancer mortality, of between 25%–30% in those women that were randomized in the screening arms of the trials. Soon after the first positive trial outcomes, two pilot projects with large-scale mammography screening were started in the Netherlands, which also showed substantial reductions in breast cancer mortality in screened women. A cost-effectiveness analysis showed a favourable balance between screening costs and potential life years gained.15 Based on these findings, mammography screening was implemented in the Netherlands and other western countries