We address the problem of non-parametric density estimation under the additional constraint that only privatised data are allowed to be published and available for inference. For this purpose, we adopt a recent generalisation of classical minimax theory to the framework of local α-differential privacy and provide a lower bound on the rate of convergence over Besov spaces B s pq under mean integrated L r -risk. This lower bound is deteriorated compared to the standard setup without privacy, and reveals a twofold elbow effect. In order to fulfil the privacy requirement, we suggest adding suitably scaled Laplace noise to empirical wavelet coefficients. Upper bounds within (at most) a logarithmic factor are derived under the assumption that α stays bounded as n increases: A linear but non-adaptive wavelet estimator is shown to attain the lower bound whenever p ≥ r but provides a slower rate of convergence otherwise. An adaptive non-linear wavelet estimator with appropriately chosen smoothing parameters and thresholding is shown to attain the lower bound within a logarithmic factor for all cases.Date: March 6, 2019. 2010 Mathematics Subject Classification. 62G07 (primary), and 62G20 (secondary).
Scanning tunnelling microscopy (STM) and X-ray photoelectron spectroscopy (XPS, AES) were used to study MOCVD of Cu-clusters on the mixed terminated ZnO(1010) surface in comparison to MBE Cu-deposition. Both deposition methods result in the same Cu cluster morphology. After annealing to 670 K the amount of Cu visible above the oxide surface is found to decrease substantially, indicating a substantial diffusion of Cu atoms inside the ZnO-bulk. The spectroscopic data do not show any evidence for changes in the Cu oxidation state during thermal treatment up to 770 K.
The central focus of this paper is an analysis of the weaknesses of the current structural options that aim to allow older employees to continue working. The point of departure of the analysis is a reappraisal of the questions arising from the employment of older people in the internal and external labour market in Germany. In the course of the investigation it shall become clear that competencies, or rather, the lifelong development of competencies, constitute the key problem in laying the foundations for the further employment of older workers. There is however insufficient data in this field of research, since other than formal qualifications scarcely any information about employees' skills is available. Particularly in the case of those over the age of 45, one simply``fumbles about in the dark''. When comparing the various structural options (e.g. part-time work for older people, teamwork, HR planning for the future, etc.) competency development assumes a decisive role. Yet management of competency development in the technocratic sense proves unsuited to meet the requirements for the further employment of older employees. The organisation of competency development should rather be conceptualised as originating from the particular self-regulating processes and mechanisms in question and should simultaneously be integrated into the company's human resource and organisational development.
With the goal of improving data based materials design, it is shown that by a sequential design of experiment scheme the process of generating and learning from the data can be combined to discover the relevant sections of the parameter space. The application is the energy of grain boundaries as a function of their geometric degrees of freedom, calculated from a simple model, or via atomistic simulations. The challenge is to predict the deep cusps of the energy, which are located at irregular intervals of the geometric parameters. Existing sampling approaches either use large sets of datapoints or a priori knowledge of the cusps' positions. By contrast, the authors' technique can find unknown cusps automatically with a minimal amount of datapoints. Key point is a Kriging interpolator with Matérn kernel to estimate the energy function. Using the jackknife variance, the next point in the sequential design is a compromise between sampling the region of largest fluctuations and avoiding a clustering of datapoints. In this way, the cusps of the energy can be found within only a few iterations, and refined as desired. This approach will be advantageous for any application with strong, localized fluctuations in the values of the unknown function.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.