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When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
Electronic correlation energies from the random-phase approximation converge slowly with respect to the plane wave basis set size. We study the conditions, under which a short-range local density functional can be used to account for the…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Spectro-microscopy is an experimental technique which can be used to observe spatial variations in chemical state and changes in chemical state over time or under experimental conditions. As a result it has broad applications across areas…
We provide a general approach for the analysis of optical state evolution under conditional measurement schemes, and identify the necessary and sufficient conditions for such schemes to simulate unitary evolution on the freely propagating…
With the establishment of global biological monitor network and development of remote sensing technology, data won't be a limitation, but the variance brought by spatial heterogeneous and fractal will influence correlation coefficient…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We derive analytic formulas to reconstruct particle-averaged quantities from experimental results that suffer from the efficiency loss of particle measurements. These formulas are derived under the assumption that the probabilities of…
Accurate model stellar fluxes are key for the analysis of observations of individual stars or stellar populations. Model spectra differ from real stellar spectra due to limitations of the input physical data and adopted simplifications, but…
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…
With the help of some remarkable examples, it is shown that conditional measurements performed on two-level atoms just after they have interacted with a resonant cavity field mode are able to recover the coherence of number-state…
A new method of accessing information on the symmetry free energy from yields of fragments produced in Fermi-energy heavy-ion collisions is proposed. Furthermore, by means of quantum fluctuation analysis techniques, correlations between…
Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
Novel optical phenomena, including electromagnetically induced transparency, slow light, superluminal light propagation, have recently been demonstrated in diverse physical implementations. These phenomena are challenging to realize in…
Crucial progress in our understanding of star formation and feedback will depend on the ability to obtain spatially resolved spectroscopic observations of \ion{H}{ii} regions, from which reliable instantaneous measurements of their physical…
Consideration is given to the methods of gaining experimental data on the substances which constitute a part of multicomponent samples to be measured. The methods are applicable to the samples comprising an arbitrary number of components;…
A new experimental technique for investigating characteristics of plasma generated with plasmotrons in electrophysical installations was proposed. The technique involves a simultaneous registration of both radiation spectra and images of…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral…