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In recurrence analysis, the tau-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations.
However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis.
We introduce a novel method to decompose the tau-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization.
We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series.
We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.
In near- surface geophysics, ground-based mapping surveys are routinely used in a variety of applications including those from archaeology, civil engineering, hydrology, and soil science. The resulting geophysical anomaly maps of, for example, magnetic or electrical parameters are usually interpreted to laterally delineate subsurface structures such as those related to the remains of past human activities, subsurface utilities and other installations, hydrological properties, or different soil types. To ease the interpretation of such data sets, we have developed a multiscale processing, analysis, and visualization strategy. Our approach relies on a discrete redundant wavelet transform (RWT) implemented using cubic-spline filters and the a trous algorithm, which allows to efficiently compute a multiscale decomposition of 2D data using a series of 1D convolutions. The basic idea of the approach is presented using a synthetic test image, whereas our archaeogeophysical case study from northeast Germany demonstrates its potential to analyze and process rather typical geophysical anomaly maps including magnetic and topographic data. Our vertical-gradient magnetic data show amplitude variations over several orders of magnitude, complex anomaly patterns at various spatial scales, and typical noise patterns, whereas our topographic data show a distinct hill structure superimposed by a microtopographic stripe pattern and random noise. Our results demonstrate that the RWT approach is capable to successfully separate these components and that selected wavelet planes can be scaled and combined so that the reconstructed images allow for a detailed, multiscale structural interpretation also using integrated visualizations of magnetic and topographic data. Because our analysis approach is straightforward to implement without laborious parameter testing and tuning, computationally efficient, and easily adaptable to other geophysical data sets, we believe that it can help to rapidly analyze and interpret different geophysical mapping data collected to address a variety of near-surface applications from engineering practice and research.
The review describes how morphological priming can be utilised to study the processing of morphologically complex words in bilinguals. The article starts with an overview of established experimental paradigms based on morphological priming, discusses a number of basic methodological pitfalls with regard to experimental design and materials, then reviews previous L2 morphological priming studies, and concludes with a brief discussion of recent developments in the field as well as possible future directions.
We studied FeCO3 using Fe K-edge X-ray absorption near-edge structure (XANES) spectroscopy at pressures up to 54 GPa and temperatures above 2000 K. First-principles calculations of Fe at the K-edge in FeCO3 were performed to support the interpretation of the XANES spectra. The variation of iron absorption edge features with pressure and temperature in FeCO3 matches well with recently reported observations on FeCO3 at extreme conditions, and provides new insight into the stability of Fe-carbonates in Earth's mantle. Here we show that at conditions of the mid-lower mantle, ~50 GPa and ~2200 K, FeCO3 melts and partially decomposes to high-pressure Fe3O4. Carbon (diamond) and oxygen are also inferred products of the reaction. We constrained the thermodynamic phase boundary between crystalline FeCO3 and melt to be at 51(1) GPa and ~1850 K. We observe that at 54(1) GPa, temperature-induced spin crossover of Fe2+ takes place from low to high spin such that at 1735(100) K, all iron in FeCO3 is in the high-spin state. A comparison between experiment and theory provides a more detailed understanding of FeCO3 decomposition observed in X-ray absorption spectra and helps to explain spectral changes due to pressure-induced spin crossover in FeCO3 at ambient temperature.
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained.