Information content of the low-energy electric dipole strength: Correlation analysis
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Reinhard, P. -G.↗
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Geodesic-based relaxation for deep canonical correlation analysis
Deep canonical correlation analysis (DCCA) is often applied to paired data samples from diverse sources to extract meaningful common information. However, when the data sources are heterogeneous, some of the useful information may be complementary but not exactly common. In spite of this fact, existing techniques learn maximally correlated representations from multiple views and are formulated so that they aim to yield identical latent subspaces for each view. This approach is sub-optimal in estimating the true signal subspaces for heterogeneous data sources. We propose a residual relaxation for deep canonical correlation analysis (RDCCA) based on a subspace distance metric, which generalizes the existing problem formulation and extracts representations that are better estimates of the actual, non-identical subspaces. We demonstrate that when using such a relaxation, the learned representations are closer to the true ones and that RDCCA outperforms CCA and DCCA in scenarios with heterogeneous data.
Kuschel, Maurice↗
Data mining graphene: Correlative analysis of structure and electronic degrees of freedom in graphenic monolayers with defects
The link between changes in the material crystal structure and its mechanical, electronic, magnetic, and optical functionalities known as the structure-property relationship is the cornerstone of the contemporary materials science research. The recent advances in scanning transmission electron and scanning probe microscopies (STEM and SPM) have opened an unprecedented path towards examining the materials structure property relationships on the single-impurity and atomic-configuration levels. Lacking, however, are the statistics-based approaches for cross-correlation of structure and property variables obtained in different information channels of the STEM and SPM experiments. Here we have designed an approach based on a combination of sliding window Fast Fourier Transform, Pearson correlation matrix, linear and kernel canonical correlation, to study a relationship between lattice distortions and electron scattering from the SPM data on graphene with defects. Our analysis revealed that the strength of coupling to strain is altered between different scattering channels which can explain coexistence of several quasiparticle interference patterns in the nanoscale regions of interest. In addition, the application of the kernel functions allowed us extracting a non-linear component of the relationship between the lattice strain and scattering intensity in graphene. Lastly, the outlined approach can be further utilized to analyzing correlations in various multi-modal imaging techniques where the information of interest is spatially distributed and has usually a complex multidimensional nature.
36 MATERIALS SCIENCE↗
TRANSIT TIMING OBSERVATIONS FROM KEPLER. II. CONFIRMATION OF TWO MULTIPLANET SYSTEMS VIA A NON-PARAMETRIC CORRELATION ANALYSIS
We present a new method for confirming transiting planets based on the combination of transit timing variations (TTVs) and dynamical stability. Correlated TTVs provide evidence that the pair of bodies is in the same physical system. Orbital stability provides upper limits for the masses of the transiting companions that are in the planetary regime. This paper describes a non-parametric technique for quantifying the statistical significance of TTVs based on the correlation of two TTV data sets. We apply this method to an analysis of the TTVs of two stars with multiple transiting planet candidates identified by Kepler. We confirm four transiting planets in two multiple-planet systems based on their TTVs and the constraints imposed by dynamical stability. An additional three candidates in these same systems are not confirmed as planets, but are likely to be validated as real planets once further observations and analyses are possible. If all were confirmed, these systems would be near 4:6:9 and 2:4:6:9 period commensurabilities. Our results demonstrate that TTVs provide a powerful tool for confirming transiting planets, including low-mass planets and planets around faint stars for which Doppler follow-up is not practical with existing facilities. Continued Kepler observations will dramatically improve the constraints on the planet masses and orbits and provide sensitivity for detecting additional non-transiting planets. If Kepler observations were extended to eight years, then a similar analysis could likely confirm systems with multiple closely spaced, small transiting planets in or near the habitable zone of solar-type stars.
79 ASTRONOMY AND ASTROPHYSICS↗
Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients
Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.
97 MATHEMATICS AND COMPUTING↗
Morphology Development in Model Polyethylene via Two-Dimensional Correlation Analysis
Two-dimensional (2D) correlation analysis is applied to synchrotron X-ray scattering data to characterize morphological regimes during nonisothermal crystallization of a model ethylene copolymer (hydrogenated polybutadiene, HPBD). The 2D correlation patterns highlight relationships among multiple characteristics of structure evolution, particularly the extent to which separate features change simultaneously versus sequentially. By visualizing these relationships during cooling, evidence is obtained for two separate physical processes occurring in what is known as 'irreversible crystallization' in random ethylene copolymers. Initial growth of primarily lamellae into unconstrained melt ('primary-irreversible crystallization') is distinguished from subsequent secondary lamellae formation in the constrained, noncrystalline regions between the primary lamellae ('secondary-irreversible crystallization'). At successively lower temperatures ('reversible crystallization'), growth of the crystalline reflections is found to occur simultaneously with the change in shape of the amorphous halo, which is inconsistent with the formation of an additional phase. Rather, the synchronous character supports the view that growth of frustrated crystals distorts the adjacent noncrystalline material. Furthermore, heterocorrelation analysis of small-angle and wide-angle X-ray scattering data from the reversible crystallization regime reveals that the size of new crystals is consistent with fringed-micellar structures (9 nm). Thus, 2D correlation analysis provides new insights into morphology development in polymeric systems.
36 MATERIALS SCIENCE↗
On the equivalence of the RTI and SVM approaches to time correlated analysis
Recently two papers on how to perform passive neutron auto-correlation analysis on time gated histograms formed from pulse train data, generically called time correlation analysis (TCA), have appeared in this journal [1,2]. For those of us working in international nuclear safeguards these treatments are of particular interest because passive neutron multiplicity counting is a widely deployed technique for the quantification of plutonium. The purpose of this letter is to show that the skewness-variance-mean (SVM) approach developed in [1] is equivalent in terms of assay capability to the random trigger interval (RTI) analysis laid out in [2]. Mathematically we could also use other numerical ways to extract the time correlated information from the histogram data including for example what we might call the mean, mean square, and mean cube approach. The important feature however, from the perspective of real world applications, is that the correlated information extracted is the same, and subsequently gets interpreted in the same way based on the same underlying physics model.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Scanning Transmission Electron Microscopy–Atom Probe Tomography Correlative Analysis for the Characterization of Solute-defect Interactions
Atom probe tomography (APT) and (scanning) transmission electron microscopy ((S)TEM) are complementary techniques that provide spatially resolved chemical and structural information at the atomic scale. Here, in this study, we employ two different STEM/APT correlative analysis methods to investigate Cr segregation at dislocation loops in ultra-high purity Fe–Cr alloys. APT needles for the correlative analysis were extracted either from bulk material or from thinned TEM lamellae. STEM analysis was used to determine the Burgers vectors of ion-irradiation-induced dislocation loops, while APT reconstruction of the same region revealed the Cr segregation to these loops. We extended the g•b = 0 invisibility criterion of dislocation loops from TEM mode in a lamella to STEM mode in a needle-shaped specimen. STEM and APT analysis on the same needle provide straightforward correlative analysis, although it is limited by a small observation volume. In contrast, iterative STEM analysis of TEM lamellae, followed by the selective extraction of specific regions of interest for APT analysis, expands the observation area by up to 100 times but requires additional time-consuming steps for APT needle extraction from the lamellae.
47 OTHER INSTRUMENTATION↗
Linearized spectrum correlation analysis for line emission measurements
A new spectral analysis method, Linearized Spectrum Correlation Analysis (LSCA), for charge exchange and passive ion Doppler spectroscopy is introduced to provide a means of measuring fast spectral line shape changes associated with ion-scale micro-instabilities. This analysis method is designed to resolve the fluctuations in the emission line shape from a stationary ion-scale wave. The method linearizes the fluctuations around a time-averaged line shape (e.g., Gaussian) and subdivides the spectral output channels into two sets to reduce contributions from uncorrelated fluctuations without averaging over the fast time dynamics. In principle, small fluctuations in the parameters used for a line shape model can be measured by evaluating the cross spectrum between different channel groupings to isolate a particular fluctuating quantity. High-frequency ion velocity measurements (100–200 kHz) were made by using this method. We also conducted simulations to compare LSCA with a moment analysis technique under a low photon count condition. Both experimental and synthetic measurements demonstrate the effectiveness of LSCA.
47 OTHER INSTRUMENTATION↗
Using quantum noise correlation analysis to measure ion temperature
Quantum noise correlation analysis was tested at the proof-of-concept level as a technique to measure ion temperature in a plasma. If eventually successful, this technique could enable a compact, inexpensive, and robust ion temperature diagnostic suitable for a burning plasma environment. Ion temperature is a key parameter determining the fusion performance of a burning plasma, as the fusion cross-section has a strong dependence on ion temperature. This ion temperature diagnostic would require only a small optical view of the plasma through a port to passively record impurity line emission. The instrumentation would be remote from the reactor behind the neutron and bio-shielding. The technique relies solely on quantum correlations of the photons emitted by a plasma impurity to measure ion temperature; there is no grating dispersion of an emission line-width or pulse-height analysis of photon energy. This measurement innovation was tested with instrumentation consisting of two single-photon detectors with high timing resolution, a time-tagging unit, and simple light collection optics. This instrumentation measures the second-order correlation between the light intensity falling on the two detectors. The next steps beyond the proof-of-concept level will be development of diagnostic designs for application of this technique to high-temperature and burning plasmas. Arrays of single-photon avalanche detectors to multiplex measurements of photon correlation will be required to reduce signal integration time to an acceptable duration.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Identifying RNA contacts from SHAPE-MaP by partial correlation analysis
In a recent paper Siegfried et al. published a new sequence-based structural RNA assay that utilizes mutational profiling to detect base pairing (MaP). Output from MaP provides information about both pairing (via reactivities) and contact (via correlations). Reactivities can be coupled to partition function folding models for structural inference, while correlations can reveal pairs of sites that may be in structural proximity. The possibility for inference of 3D contacts via MaP suggests a novel approach to structural prediction for RNA analogous to covariance structural prediction for proteins. We explore this approach and show that partial correlation analysis outperforms na\"ive correlation analysis. Our results should be applicable to a wide range of high-throughput sequencing based RNA structural assays that are under development.
Tambe, Akshay↗
General order parameter based correlation analysis of protein backbone motions between experimental NMR relaxation measurements and molecular dynamics simulations
Internal backbone dynamic motions are essential for different protein functions and occur on a wide range of time scales, from femtoseconds to seconds. Molecular dynamic (MD) simulations and nuclear magnetic resonance (NMR) spin relaxation measurements are valuable tools to gain access to fast (nanosecond) internal motions. However, there exist few reports on correlation analysis between MD and NMR relaxation data. Here, backbone relaxation measurements of {sup 15}N-labeled SH3 (Src homology 3) domain proteins in aqueous buffer were used to generate general order parameters (S{sup 2}) using a model-free approach. Simultaneously, 80 ns MD simulations of SH3 domain proteins in a defined hydrated box at neutral pH were conducted and the general order parameters (S{sup 2}) were derived from the MD trajectory. Correlation analysis using the Gromos force field indicated that S{sup 2} values from NMR relaxation measurements and MD simulations were significantly different. MD simulations were performed on models with different charge states for three histidine residues, and with different water models, which were SPC (simple point charge) water model and SPC/E (extended simple point charge) water model. S{sup 2} parameters from MD simulations with charges for all three histidines and with the SPC/E water model correlated well with S{sup 2} calculated from the experimental NMR relaxation measurements, in a site-specific manner. - Highlights: • Correlation analysis between NMR relaxation measurements and MD simulations. • General order parameter (S{sup 2}) as common reference between the two methods. • Different protein dynamics with different Histidine charge states in neutral pH. • Different protein dynamics with different water models.
60 APPLIED LIFE SCIENCES↗
Validation of a Global Geospace Model With a Systems Science Approach Based on Canonical Correlation Analysis
A systems science approach based on canonical correlation analysis (CCA) is applied as a new, behavioral way to validate global geospace models. The biggest novelty of the technique is that it validates models at a system level, whereby a side‐by‐side comparison is performed of CCA applied to a 30‐day observational and the corresponding simulation data sets comprising quiet, moderate and active times. The simulation used the Multiscale Atmosphere‐Geospace Environment (MAGE) model. It is shown that (a) CCA must be combined with sensitivity analysis to be effective, (b) the MAGE model generally reproduces the observed behavior (more so for quieter time intervals), quantified by the intercorrelations between different variables and (c) the technique identifies the SuperMAG SML index as a quantity for which refinements of the model are needed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Ultrafast structural dynamics of photo-reactions observed by time-resolved x-ray cross-correlation analysis
We applied angular X-ray Cross-Correlation analysis (XCCA) to scattering images from a femtosecond resolution X-ray free-electron laser pump-probe experiment with solvated PtPOP {[Pt2(P2O5H2)4]4–} metal complex molecules. The molecules were pumped with linear polarized laser pulses creating an excited state population with a preferred orientational (alignment) direction. Two time scales of 1.9 ± 1.5 ps and 46 ± 10 ps were revealed by angular XCCA associated with structural changes and rotational dephasing of the solvent molecules, respectively. These results illustrate the potential of XCCA to reveal hidden structural information in the analysis of time-resolved x-ray scattering data from molecules in solution.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Insight into ideal shear strength of Ni-based dilute alloys using first-principles calculations and correlational analysis
Here the present work examines the effect of alloying elements (denoted X) on the ideal shear strength for 26 dilute Ni-based alloys, Ni11X, as determined by first-principles calculations of pure alias shear deformations. The variations in ideal shear strength are quantitatively explored with correlational analysis techniques, showing the importance of atomic properties such as size and electronegativity. The shear moduli of the alloys are affirmed to show a strong linear relationship with their ideal shear strengths, while the shear moduli of the individual alloying elements were not indicative of alloy shear strength. Through combination with available ideal shear strength data on Mg alloys, a potential application of the Ni alloy data is demonstrated in the search for a set of atomic features suitable for machine learning applications to mechanical properties. As another illustration, the calculated Ni ideal shear strengths play a key role in a predictive multiscale framework for deformation behavior of single crystal alloys at large strains, as shown by simulated stress–strain curves.
36 MATERIALS SCIENCE↗
Angular X-ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials
Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.
36 MATERIALS SCIENCE↗
Two-dimensional correlation analysis for x-ray photoelectron spectroscopy
Abstract X-ray photoelectron spectroscopy (XPS) measures the binding energy of core-level electrons, which are well-localised to specific atomic sites in a molecular system, providing valuable information on the local chemical environment. The technique relies on measuring the photoelectron spectrum upon x-ray photoionisation, and the resolution is often limited by the bandwidth of the ionising x-ray pulse. This is particularly problematic for time-resolved XPS, where the desired time resolution enforces a fundamental lower limit on the bandwidth of the x-ray source. In this work, we report a novel correlation analysis which exploits the correlation between the x-ray and photoelectron spectra to improve the resolution of XPS measurements. We show that with this correlation-based spectral-domain ghost imaging method we can achieve sub-bandwidth resolution in XPS measurements. This analysis method enables XPS for sources with large bandwidth or spectral jitter, previously considered unfeasible for XPS measurements.
47 OTHER INSTRUMENTATION↗