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Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…
In this paper, we present a novel approach to the estimation of strongly varying backgrounds in astronomical images by means of small objects removal and subsequent missing pixels interpolation. The method is based on the analysis of a…
This chapter reviews the fundamental optical properties and applications of pho-tonic molecules (PMs) - photonic structures formed by electromagnetic coupling of two or more optical microcavities (photonic atoms). Controllable interaction…
Temporal-spectral modes of light provide a fundamental window into the nature of atomic and molecular systems and offer robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the…
All stars exhibit universal central behavior in terms of new homology variables (u,w). In terms of these variables, we obtain simple analytic fits to numerical standard solar models for the core and radiative zones of the ZAMS and present…
Spatial modes are a promising candidate for encoding information for classical and quantum optical communication due to their potential high information capacity. Unfortunately, compensation of the wavefront upon propagation through the…
Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix…
We introduce a novel strategy for cosmological Boltzmann codes leading to an increase in speed by a factor of \sim 30 for small scale Fourier modes. We (re-)investigate the tight coupling approximation and obtain analytic formulae reaching…
In global seismology Earth's properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth's…
Inversion codes allow reconstructing a model atmosphere from observations. With the inclusion of optically thick lines that form in the solar chromosphere, such modelling is computationally very expensive because a non-LTE evaluation of the…
The methods for determination of the characteristics of the extrema are discussed with an application to irregularly spaced data, which are characteristic for photometrical observations of variable stars. We introduce new special functions,…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
Photonic technologies offer promising solutions to the power consumption, bandwidth constraints and latency limits of electronic hardware used in high-performance computing and artificial intelligence. Recently, many studies have proposed…
Millisecond pulsar (MSP) binaries are unique laboratories for studying matter and radiation under extreme conditions that are unattainable on Earth. Recent detections of optical millisecond pulsations from three systems in distinct…
Gravitational lensing is the deflection of light rays due to the gravity of intervening masses. This phenomenon is observed in a variety of scales and configurations, involving any non-uniform mass such as planets, stars, galaxies, clusters…
The Helioseismic and Magnetic Imager (HMI) has just started producing data that will help determine what the sources and mechanisms of variability in the Sun's interior are. The instrument measures the Doppler shift and the polarization of…
We propose a technique to train semantic part-based models of object classes from Google Images. Our models encompass the appearance of parts and their spatial arrangement on the object, specific to each viewpoint. We learn these rich…
The answers to many unsolved problems lie in the intractable chemical space of molecules and materials. Machine learning techniques are rapidly growing in popularity as a way to compress and explore chemical space efficiently. One of the…
The influence of a magnetic field on the broadening of spectral lines and transition arrays in complex spectra is investigated. The anomalous absorption or emission Zeeman pattern is a superposition of many profiles with different relative…