Reply to "Comment on `Inference with minimal Gibbs free energy in information field theory'" by Iatsenko, Stefanovska and McClintock

We endorse the comment on our recent paper [En{\ss}lin and Weig, Phys. Rev. E 82, 051112 (2010)] by Iatsenko, Stefanovska and McClintock [Phys. Rev. E 85 033101 (2012)] and we try to clarify the origin of the apparent controversy on two issues. The aim of the minimal Gibbs free energy approach to provide a signal estimate is not affected by their Comment. However, if one wants to extend the method to also infer the a posteriori signal uncertainty any tempering of the posterior has to be undone at the end of the calculations, as they correctly point out. Furthermore, a distinction is made here between maximum entropy, the maximum entropy principle, and the so-called maximum entropy method in imaging, hopefully clarifying further the second issue of their Comment paper.Comment: 1 page, no figures, Reply to Comment pape

Inference with minimal Gibbs free energy in information field theory

Non-linear and non-Gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the Gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from Poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a Gaussian signal with unknown spectrum and (iii) inference of a Poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how Gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-Gaussian posterior.Comment: 14 page

Damping of metallized bilayer nanomechanical resonators at room temperature

We investigate the influence of gold thin-films subsequently deposited on a set of initially bare, doubly clamped, high-stress silicon nitride string resonators at room temperature. Analytical expressions for resonance frequency, quality factor and damping for both in- and out-of-plane flexural modes of the bilayer system are derived, which allows for the determination of effective elastic parameters of the composite structure from our experimental data. We find the inverse quality factor to scale linearly with the gold film thickness, indicating that the overall damping is governed by losses in the metal. Correspondingly, the mechanical linewidth increases by more than one order of magnitude compared to the bare silicon nitride string resonator. Furthermore, we extract mechanical quality factors of the gold film for both flexural modes and show that they can be enhanced by complete deposition of the metal in a single step, suggesting that surface and interface losses play a vital role in metal thin-films

Motility and Relational Mobility of the Baka in North-Eastern Gabon

This thesis offers a first scientific portrait of the Baka in North-Eastern Gabon, a group of post-foragers living along the River Ivindo, and the way they practice and conceptualise mobility. The inquiry encompasses the long-term historical and the daily or short-term current mobility of this group, elicited through life histories and participant observation. The central premise of this work is that mobility is relational. Relational refers to interaction of movement and fixity, of position and outcome, and to the understanding of mobility as socially produced. The second concept employed is that of motility, the capacity or potential to be mobile. As motility analyses what comes before observable movement, of potential and actualised outcome as mobility or immobility, it takes up the idea of mobility as relational. The Baka living on the Ivindo migrated from Cameroon and Congo into Gabon over the last approximately 60 years. In contrast to established approaches to forest forager mobility, which focus mainly on resource mobility during an annual cycle, this study considers the long-term and larger geographical perspective and shows that the quality of personal relations between Baka and their neighbours is decisive in mobility considerations. Previously these relations were characterised as a structural opposition between two ethnic groups. This analysis demonstrates the heterogeneity of people and their interactions, in the past and the present, to argue, firstly, that relations are more appropriately conceptualised as multilateral, and, secondly, that an inquiry remains incomplete without considering affections and emotions. A principal mobility factor for the Baka is the search for a good life, meaning economic improvement and freedom from violence. This search coincides with a diversification of Baka livelihoods to include subsistence practices as well as working in the gold sites of Gabon. Employing motility shows the aspirations and limitations of Baka personal and group mobility in gold work. Motility is also understood as ‘mobility capital’ and thereby helps document social change, and how gold work is undertaken with reference to Baka egalitarian social organisation to be successful. By including group and individual as well as different temporalities in the analysis, and detailing the impact of social values on mobilities, motility gives depth to the analysis of mobility

Strong 4-mode coupling of nanomechanical string resonators

We investigate mechanical mode coupling between the four fundamental flexural modes of two doubly-clamped, high-Q silicon-nitride nanomechanical string resonators. Strong mechanical coupling between the strings is induced by the strain mediated via a shared clamping point, engineered to increase the exchange of oscillatory energy. One of the resonators is controlled dielectrically, which results in strong coupling between its out-of-plane and in-plane flexural modes. We show both, inter-string out-of-plane-in-plane and 3-mode resonance of the four coupled fundamental vibrational modes of a resonator pair, giving rise to a simple and a multimode avoided crossing, respectively.Comment: 5 pages, 4 figure

Finite time St\"uckelberg interferometry with nanomechanical modes

St\"uckelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we experimentally investigate finite time effects in St\"uckelberg interference and provide an exact analytical solution of the St\"uckelberg problem. Approximating this solution in distinct limits reveals uncharted parameter regimes of St\"uckelberg interferometry. Experimentally, we study these regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. The dielectric control and microwave cavity enhanced universal transduction of the nanoelectromechanical system allows for the experimental access to all theoretically predicted St\"uckelberg parameter regimes. We exploit our experimental and theoretical findings by studying the onset of St\"uckelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented theory is not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit

Exploiting the nonlinear impact dynamics of a single-electron shuttle for highly regular current transport

The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal.Comment: 5 pages, 4 figure

Size-independent Young's modulus of inverted conical GaAs nanowire resonators

We explore mechanical properties of top down fabricated, singly clamped inverted conical GaAs nanowires. Combining nanowire lengths of 2-9 $\mu$m with foot diameters of 36-935 nm yields fundamental flexural eigenmodes spanning two orders of magnitude from 200 kHz to 42 MHz. We extract a size-independent value of Young's modulus of (45$\pm$3) GPa. With foot diameters down to a few tens of nanometers, the investigated nanowires are promising candidates for ultra-flexible and ultra-sensitive nanomechanical devices