Bayesian on-line anticipation of critical transitions

The design of reliable indicators to anticipate critical transitions in complex systems is an important task in order to detect imminent regime shifts and to intervene at an early stage to either prevent them or mitigate their consequences. We present a data-driven method based on the estimation of a parameterized nonlinear stochastic differential equation that allows for a robust anticipation of critical transitions even in the presence of strong noise which is a characteristic of many real world systems. Since the parameter estimation is done by a Markov chain Monte Carlo approach, we have access to credibility bands allowing for a better interpretation of the reliability of the results. We also show that the method can yield meaningful results under correlated noise. By introducing a Bayesian linear segment fit it is possible to give an estimate for the time horizon in which the transition will probably occur based on the current state of information. This approach is also able to handle nonlinear time dependencies of the parameter that controls the transition. The method can be used as a tool for on-line analysis to detect changes in the resilience of the system and to provide information on the probability of the occurrence of critical transitions in future. Additionally, it can give valuable information about the possibility of noise induced transitions. The discussed methods are made easily accessible via a flexibly adaptable open source toolkit named 'antiCPy' which is implemented in the programming language Python

Superparamagnetism in small Fe clusters on Cu(111)

Fe clusters of 105±2 atoms/cluster were mass selectively deposited onto Cu(111) at cryogenic temperatures. XMCD was used to measure temperature and direction dependent magnetization curves. The clusters are superparamagnetic at the lowest temperature measured (10 K). Their magnetization curves are consistent with magnetic moments of ≈2.5μB per atom which are thus enhanced over the bulk values. Within experimental accuracy, the clusters do not present magnetocrystalline anisotropy in the temperature range of 10 K to 60 K

Photoelectron spectroscopy on Pt atoms and clusters deposited on C(0001)

An experimental photoelectron spectroscopy study is presented highlighting several aspects of importance for the study of deposited metal clusters and particles with photoemission. It is shown that the Fermi level is the correct energy reference for the core level binding energies. The choice of different deposition conditions, well within the range of soft landing, has a strong impact on the outcome of the spectroscopic experiments. Single adatoms as well as clusters deposited with some excess energy display relatively narrow core level spectra at much lower binding energies than previously reported, even when atomic mass selection is not performed. In contrast, single sized Pt19 clusters, deposited onto a thin Ar film before being exposed to the graphite surface show spectral broadening and shifts to higher binding energies. We discuss our results in terms of the cluster substrate interaction and the influence of deposition conditions on the metal adsorbate structure.