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This paper discusses the mathematical aspects of band fitting and introduces the mathematics of the Asymmetric Gaussian shape and its tangent space for the first time. First, we derive an equation for an Asymmetric Gaussian shape. We then…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient $C(\omega)$ and, in particular, its low frequency limit.…
The unique spectral behavior exhibited by a class of non-uniform Bragg periodic structures, namely chirped and apodized fiber Bragg gratings (FBGs) influenced by parity and time reversal ($\mathcal{PT}$) symmetry, is presented. The…
Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…
The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from…
In this paper we explore practicable ways for self-consistent calculations of spectral functions from analytically continued functional renormalization group (aFRG) flow equations. As a particularly straightforward one we propose to include…
Despite the benefits that directional coupler based parity-time symmetric systems may offer to the field of integrated optics, the realization of such couplers relies on rather strict design constraints on the waveguide parameters. Here, we…
Fano resonance exhibiting an asymmetric spectral line shape is a universal phenomenon observed in diverse physical systems. Here we experimentally establish a direct link between the spectral asymmetry parameter and a physically realizable…
We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…
Within the framework of density functional perturbation theory (DFPT), we implement and test a novel "metric wave" response-function approach. It consists in the reformulation of an acoustic phonon perturbation in the curvilinear frame that…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…
Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
We demonstrate that the present superaccurate measurements of transition processes between atomic states in hydrogen atom reached the limit of accuracy when transition frequency cannot be defined anymore in a unique way. This was predicted…
This paper proposes a novel and rapid calibration-free wavelength modulation spectroscopy algorithm based on even-order harmonics. The proposed algorithm, analytically deduced from Voigt line-shape function, only involves simple algebraic…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
Line defects and scattering amplitudes have proven to be fruitful objects of study in the context of holographic dualities. They serve as valuable theoretical laboratories for the development of non-perturbative methods and have provided…
In this paper we propose an ad-hoc construction of the Likelihood Function, in order to develop a data analysis procedure, to be applied in atomic and nuclear spectral analysis. The classical Likelihood Function was modified taking into…