This paper demonstrates the importance of the structural changeover in controlling the physical-chemical properties of hexacyanometalate-like materials (Prussian Blue). A meticulous in situ study of compositional variations using electroacoustic impedance techniques associated to electrogravimetric techniques in hexacyanoferrates containing K+ alkali metals reveals the existence of a nanostructural changeover coupled to a change of the magnetic properties of these electromagnetic materials. In the same way, the electroacoustic impedance techniques can be useful both in the understanding and in the in situ monitoring of the structural changeovers and the magnetic behavior of all kinds of materials.

Balancing access to antibiotics with control of antibiotic resistance is a global public health priority. Currently, antibiotic stewardship is informed by a 'use it and lose it' principle, in which population antibiotic use is linearly related to resistance rates. However, theoretical and mathematical models suggest use-resistance relationships are non-linear. One explanation is that resistance genes are commonly associated with 'fitness costs', impairing pathogen replication or transmissibility. Therefore, resistant genes and pathogens may only gain a survival advantage where antibiotic selection pressures exceed critical thresholds. These thresholds may provide quantitative targets for stewardship: optimising control of resistance while avoiding over-restriction of antibiotics. We evaluated the generalisability of a nonlinear time-series analysis approach for identifying thresholds using historical prescribing and microbiological data from five populations in Europe. We identified minimum thresholds in temporal relationships between use of selected antibiotics and rates of carbapenem-resistant Acinetobacter baumannii (in Hungary), extended spectrum β-lactamase producing Escherichia coli (Spain), cefepime-resistant Escherichia coli (Spain), gentamicin-resistant Pseudomonas aeruginosa (France), and methicillin-resistant Staphylococcus aureus (Northern Ireland) in different epidemiological phases. Using routinely generated data, our approach can identify context-specific quantitative targets for rationalising population antibiotic use and controlling resistance. Prospective intervention studies restricting antibiotic consumption are needed to validate Results Identifying non-linear temporal relationships: from experiment to applicationIn a Monte Carlo experiment we compared the ability of linear and non-linear time-series analysis (Multivariate Adaptive Regression Splines, MARS) to identify pre-defined relationships between simulated explanatory and outcome time-series (Supplementary Figure 1). Non-linear time-series analysis (NL-TSA) accurately identified both truly linear and nonlinear associations. However, linear time-series analysis provided biased estimations and overall poorer data-fit if relationships were non-linear. NL-TSA models applied to retrospective time-series data from five European study populations (examples 1-5), frequently identified minimum thresholds in antibiotic useresistance relationships, (figures 1-5 and Supplementary Table 1). 'Ceiling effects', in which further increases in explanatory variables did not affect resistance rates, were found at highlevels of use of some antibiotics and hand hygiene. Non-linearities in autoregression and population interaction terms further indicated the complexity of transmission dynamics within and between clinical populations. Example 1: Carbapenem-resistant Acinetobacter baumannii (Debrecen, Hungary) We examined ecological determinants of carbapenem-resistant A. baumannii (CRAb) in a tertiary hospital population in Debrecen, Hungary (figure 1). Betwee...