Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Reducing the development gaps between regions in Poland with the use of European Union funds

The paper evaluates the processes of regional income convergence in Poland. This new research approach involves an attempt to assess the process of convergence from the point of view of development gaps. Six key development gaps were considered in the region of Eastern Poland, which is a singular case, significantly different from other regions. A dynamic panel data model was applied to investigate the impact of EU funds on the progress made towards closing these development gaps. Among the analysed development gaps, only the structural gap was not reduced in the period 2004–2015. Studies have also revealed the different impact of structural funds on each category of development gaps (a positive impact on reducing the regional transport accessibility gap and the investment gap, but negative – on reducing the innovation gap). Research has suggested the need for a change in the structure of using EU funds in the period 2014–2020 to favour stronger support for entrepreneurship and the creation of new jobs. Greater stimulation of the economic structure of peripheral regions has been proposed as the prerequisite for the future reduction in the discrepancies between regions and for the intensification of convergence. First published online 2 April 201

Accuracy investigations of impulse response estimation obtained by conditional averaging

Przedstawiono wyniki wybranych badań teoretycznych i eksperymentalnych metody wyznaczania odpowiedzi impulsowej wykorzystującej warunkowe uśrednianie sygnałów. Omówiono wpływ progu inicjującego uśrednianie, pasma częstotliwości testowego szumu białego, skorelowania sygnałów i liczby uśrednionych realizacji na dokładność estymacji odpowiedzi impulsowej.Determination of the linear system impulse response is presented in the paper. The white noise of normal distribution N(0, δx) and the band limited to low frequencies has been applied as a test signal. The cross conditional averaging of the input and output signal has been performed. The paper describes a method for estimating the impulse response based on conditional averaging. The results of theoretical and practical investigations are given. The influence of the threshold xp, the frequency band of the test noise signal and the number of averaging M have been considered. The results of algorithm testing with theoretical and practical signals are shown. At the first stage of investigations impulse responses of two systems have been obtained. The parameters of those systems have been known. The signals x(t), y(t) and theirs characteristics for identification of first order instruments are presented in Figs. 3 and 4. The conditional averaging can also be used for identification of a time delay. The algorithms of conditional averaging have been elaborated and practically realized in the LabVIEW environment

Comparison of Magnetic and Mössbauer Results Obtained for Palaeozoic Rocks of Hornsund, Southern Spitsbergen, Arctic

This analysis was performed as a part of the palaeomagnetic project focused on the reconstruction of the palaeogeographic position of the Svalbard Archipelago and adjacent crustal units (European Arctic) in the Palaeozoic and Mesozoic. Three rock formations - Cambrian, Devonian and Carboniferous were sampled in the area of Hornsund, southern Spitsbergen. The main aim of the presented study is to identify ferromagnetic minerals (sensu lato) - the carriers of the natural remanent magnetisation in the investigated rocks. A wide range of magnetic methods were used: the Lowrie tests, unblocking temperatures determinations and the measurement of coercivity spectra as well as the Mössbauer studies. In Devonian and Carboniferous samples all applied methods indicate the domination of the hematite natural remanent magnetisation carrier. In Cambrian rocks magnetic measurements reveal a mixture of ferromagnetic (sensu lato) minerals with varying coercivities and unblocking temperatures. The Mössbauer data improve the identification, suggesting that in Cambrian rocks the carrier of the dominating natural remanent magnetisation component is maghemite

Regional Innovation and Research Policy Outlook: Policy Practices in Eight European Regions

This publication is part of a project called 'Practical Regional Research and Innovation policy in Action. The Efficient Tools for Regional Catching-up in New Member States'