Spectral Function Research Articles

Prediction of the Infrared Absorbance Intensities and Frequencies of Hydrocarbons: A Message Passing Neural Network Approach.

Accurately and efficiently predicting the infrared (IR) spectra of a molecule can provide insights into the structure-properties relationships of molecular species, which has led to a proliferation of machine learning tools designed for this purpose. However, earlier studies have focused primarily on obtaining normalized IR spectra, which limits their potential for a comprehensive analysis of molecular behavior in the IR range. For instance, to fully understand and predict the optical properties, such as the transparency characteristics, it is necessary to predict the molar absorptivity IR spectra instead. Here, we propose a graph-based communicative message passing neural network algorithm that can predict both the peak positions and absolute intensities corresponding to density functional theory calculated molar absorptivities in the IR domain. By modifying existing spectral loss functions, we show that our method is able to predict with DFT-accuracy level the IR molar absorptivities of a series of hydrocarbons containing up to ten carbon atoms and apply the model to a set of larger molecules. We also compare the predicted spectra with those generated by the direct message passing neural network. The results suggest that both algorithms demonstrate similar predictive capabilities for hydrocarbons, indicating that either model could be effectively used in future research on spectral prediction for such systems.

Some Improvements of the Bootstrap over the Delta Method Probability Errors for Whittle Estimators

The purpose of this paper is to compare the coverage probability errors of the parametric bootstrap with that of the delta method for the covariance parameters of a regression model with auto-regressive fractionally integrated moving average (ARFIMA) errors. We consider the coverage probability errors of both confidence intervals (CIs) and tests based on the the plug-in Whittle maximum likelihood (PWML) estimators. We first show that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of the two-sided delta method and parametric bootstrap confidence intervals on the plug-in Whittle likelihood estimator or the covariance parameter are shown to be $O(n^{-1})$ and $o(n^{-3/2}\ln{n})$, respectively, where n is the sample size. Next, we show that those of the one-sided parametric bootstrap confidence intervals are shown to be $O(n^{-1/2})$ and $o(n^{-1}\ln{n})$, respectively. These results show that for both one-sided and two-sided confidence intervals and tests, the bootstrap provides a significant improvement over that of the delta method.

Riemann–Hilbert problem and soliton solutions with their asymptotic analysis for the focusing nonlocal Hirota equation with step-like initial data

The Riemann–Hilbert (RH) problem is developed to study the Cauchy problem of focusing space symmetric nonlocal Hirota (fsNH) equation with step-like initial data. Firstly, we analyze the characteristics of the Jost solutions and spectral functions, including analyticity, symmetry, and asymptotics as k→∞ and k→0. Then, we discuss three cases of zero point distributions of the spectral functions, and derive the expressions of spectral functions by constructing the special analytic functions and establishing the scalar RH problem. Furthermore, the constraint relations among the zeros of the spectral functions are analyzed. Next, the corresponding RH problem equipped with residual and singularity conditions is successfully derived. These singularity conditions are then transformed into a general residue condition, which reduces the problem of solving the RH problem with reflection-less potential to solving a system of algebraic equations. Ultimately, the corresponding soliton solutions of the fsNH equation and their asymptotics are derived from the solution of the RH problem.

Method for reconstructing the self-energy from the spectral function

Method for reconstructing the self-energy from the spectral function

Enhanced multi-layer Ramanujan decomposition: an effective rolling bearing condition monitoring method

ABSTRACT Due to the influence of strong noise, it is difficult to extract and identify the fault features of rolling bearing when it is slightly damaged, which greatly increases the risk of fault miss detection. In this paper, the enhanced multi-layer Ramanujan decomposition (EMRD) method is proposed. On the one hand, EMRD method adopts accurate spectrum segmentation technology (ASST) to realise adaptive frequency band division. ASST firstly minimises the frequency erosion caused by noise through prior-unknown blind deconvolution method based on SOSO (SOSO-PUBD), then obtains relatively pure frequency distribution through power spectral density function, and finally realises frequency band segmentation by minimum segmentation method. On the other hand, EMRD method obtains the optimal number of decomposition modes in the form of multi-layer decomposition, and selects the optimal mode by Ramanujan spectrum signal-to-noise ratio index. The comparative experimental results show that EMRD method has excellent accuracy of frequency band segmentation and meets the requirements of rolling bearing fault diagnosis.

Modeling Water Clusters: Spectral Analyses, Gaussian Distribution, and Linear Function during Time

Our experimental and theoretical studies have consistently revealed the presence of water clusters in various environments, particularly under hydrophobic conditions, where slower hydrogen ion interactions prevail. Crucial methods like Nuclear Magnetic Resonance (NMR) and Fourier Transform Infrared (FTIR) method have played a pivotal role in our understanding of these clusters, unveiling their potential medical applications. The stability and behavior of these clusters can be influenced by factors such as metal ions’ presence, leading to stable clusters’ formation. This potential for medical applications should inspire hope and further research. Moreover, our research has revealed that water clusters exhibit characteristics of dissipative structures, demonstrating the self-organization under physical, chemical, or thermal changes akin to Rayleigh–Benard convection cells. This dynamic and significant behavior supports the notion that water’s role transcends simple chemistry, potentially influencing biological processes at a fundamental level. The interaction of water clusters with their environment and the ability to maintain non-equilibrium states through the energy exchanges further underscores their complexity and significance in both natural and technological contexts. Water filtration is a process for improving water quality. The effect is re-structuring hydrogen bonds and structuring water clusters, most of which are hexagonal. In our research, we applied filtered water using patented EVOdrop Swiss technology.

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach.

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.

The Spectral Gamma Function of gas absorption coefficient and its application to analysis and enhancement of the correlated spectral modeling of radiative transfer in non-uniform gaseous media

A novel Spectral Gamma Function is introduced to address the limitations associated with the “correlated” spectrum assumption in radiative transfer modeling in non-uniform gaseous media. The Spectral Gamma Function combines high-resolution gas absorption spectra with their distribution functions, capturing the “correlated” properties of absorption spectra at different thermodynamic states. This concept is applicable both to narrow bands and the full spectrum, enabling the construction of truly “correlated” models and the calculation of statistical relationships between absorption spectra. The paper presents the definition and properties of the Spectral Gamma Function. The Function 1) allows the construction of sets of truly “correlated” high-resolution spectra from which the “distance” to a real set of gas spectra can be characterized; 2) provides a simple way to evaluate Spearman's rank correlation between spectra in distinct states yielding useful information about the statistical relationship between these spectra; and 3) allows for the approximation of a real set of Line-by-Line (LBL) data as a non-linear combination of “correlated” models called MetaLBL modeling. Additionally, the function may be used to demonstrate the optimality of the Rank Correlated Spectral Line Weighted-sum-of-gray-gases (RC-SLW) Model in the space of “correlated” models, thus demonstrating that the RC-SLW Model represents the limit of accuracy in the family of correlated models. This work represents the first proposal of such a development extending modeling approaches beyond those inherent in the assumption of correlated spectra in the field of gas radiation modeling, offering promising insights for practical applications. Moreover, the MetaLBL modeling strategy is applied in a test case from atmospheric sciences for which models with a user-specified accuracy are constructed.

Polarized spectral bidirectional reflectance distribution function in visible band based on Cauchy’s empirical dispersion equation

The polarized bidirectional reflectance distribution function (pBRDF) can describe the changes between the Stokes vectors of incident and reflected light. The existing model can only describe the spatial distribution of the target’s polarization characteristics at a single wavelength, so further research is needed for the description of the target’s polarized spectral characteristics. In this paper, a modified three-component polarized spectral bidirectional reflectance distribution function (pSBRDF) is proposed, which combines Fresnel equation in the specular reflection component with Cauchy’s empirical dispersion equation, by introducing the wavelength variable and dispersion constants that do not change with wavelength. The degree of the linear polarization (DoLP) of two types of coated fabric samples was measured at three incident angles and 400 to 760 nm wavelength. The error of the model in describing the spectral and the spatial distribution of DoLP are controlled within 0.00743 and 0.0757 respectively, which proves the accuracy of the model. This research provides the model basis for analysis of the target’s polarization characteristics and the theoretical basis for the application of polarization detection.

Nevanlinna analytic continuation for Migdal–Eliashberg theory

In this work, we present a method to reconstruct real-frequency properties from analytically continued causal Green’s functions within the framework of Migdal–Eliashberg (ME) theory for superconductivity. ME theory involves solving a set of coupled equations self-consistently in imaginary frequency space, but to obtain experimentally measurable properties like the spectral function and quasiparticle density of states, it is necessary to perform an analytic continuation to real frequency space. Traditionally, the ME Green’s function is decomposed into three fundamental complex functions, which are analytically continued independently. However, these functions do not possess the causal properties of Green’s functions, complicating or even preventing the application of standard methods such as Maximum Entropy. Our approach overcomes these challenges, enabling the use of various analytic continuation techniques that were previously impractical. We demonstrate the effectiveness of this method by combining it with Nevanlinna analytic continuation to achieve accurate real-frequency results for ME theory, which are directly comparable to experimental data, with applications highlighted for the superconductors MgB2 and LaBeH8.

Spectral functions of lattice fermions on the honeycomb lattice with Hubbard and long-range Coulomb interactions

Spectral functions of lattice fermions on the honeycomb lattice with Hubbard and long-range Coulomb interactions

Holistic and in situ calibration method for a spectral-temporally modulated Mueller spectropolarimeter

The spectral-temporally modulated Mueller spectropolarimeter (STMSP) offers advantages of broader band limitation, better resolution, and faster detection speed. However, the current STMSP calibration method separates the polarization state generator and analyzer, necessitating subsequent recombination, which is inefficient and unstable. In this paper, a holistic and in situ calibration method for STMSP is proposed. It only requires insertion of a polarizer as a reference sample, eliminating the need for separate calibration and recombination. The STMSP is calibrated in situ as a whole, addressing the misalignment error of the spectral modulation module, the total polarimetric errors of the temporal modulation module, and the spectral modulation transfer function of the spectrometer. Experimental results demonstrate high accuracy, with a root mean square error (RMSE) of 0.0004, which is an order of magnitude lower than that of the dual-rotating retarder spectropolarimeter (DRRSP) after eigenvalue calibration. This demonstrates its potential for enabling faster and more accurate acquisition of the Mueller spectra.

Dynamic reliability assessment for high CFRDs incorporating ground motion and material parameter variability via GPDEM

The randomness of earthquake and material parameters significantly impacts the seismic response and dynamic reliability of geotechnical engineering structures. In this study, a dynamic reliability analysis method for high concrete face rockfill dams (CFRDs) under the influence of random factors is proposed by combining random sample generation methods with the generalized probability density evolution method (GPDEM). Firstly, the spectral representation-random function method is employed to achieve dimensionality reduction expression for intensity-frequency non-stationary ground motion. Sensitivity analysis is then used to identify the random variables of the rockfill constitutive model, and the improved generalized F-discrepancy (GF-discrepancy) method is utilized to generate random material parameters. Then, the random samples of earthquake and material parameter are introduced into the finite element calculation of CFRD, conducting a series of dynamic finite element calculations. Finally, GPDEM is used to derive probability information and dynamic reliability from the deterministic time history responses. The results indicate that random factors contribute to the variability of seismic response and dynamic reliability. Stochastic ground motion significantly affects extreme values, while variability in material parameters has a more pronounced influence on the overall process of seismic response. These findings provide valuable references for the seismic design of CFRDs.

HyperDehazing: A hyperspectral image dehazing benchmark dataset and a deep learning model for haze removal

Haze contamination severely degrades the quality and accuracy of optical remote sensing (RS) images, including hyperspectral images (HSIs). Currently, there are no paired benchmark datasets containing hazy and haze-free scenes in HSI dehazing, and few studies have analyzed the distributional properties of haze in the spatial and spectral domains. In this paper, we developed a new hazy synthesis strategy and constructed the first hyperspectral dehazing benchmark dataset (HyperDehazing), which contains 2000 pairs synthetic HSIs covering 100 scenes and another 70 real hazy HSIs. By analyzing the distribution characteristics of haze, we further proposed a deep learning model called HyperDehazeNet for haze removal from HSIs. Haze-insensitive longwave information injection, novel attention mechanisms, spectral loss function, and residual learning are used to improve dehazing and scene reconstruction capability. Comprehensive experimental results demonstrate that the HyperDehazing dataset effectively represents complex haze in real scenes with synthetic authenticity and scene diversity, establishing itself as a new benchmark for training and assessment of HSI dehazing methods. Experimental results on the HyperDehazing dataset demonstrate that our proposed HyperDehazeNet effectively removes complex haze from HSIs, with outstanding spectral reconstruction and feature differentiation capabilities. Furthermore, additional experiments conducted on real HSIs as well as the widely used Landsat-8 and Sentinel-2 datasets showcase the exceptional dehazing performance and robust generalization capabilities of HyperDehazeNet. Our method surpasses other state-of-the-art methods with high computational efficiency and a low number of parameters.

A 40-Year Time Series of Land Surface Emissivity Derived from AVHRR Sensors: A Fennoscandian Perspective

Accurate land surface temperature (LST) retrieval depends on precise knowledge of the land surface emissivity (LSE). Neglecting or inaccurately estimating the emissivity introduces substantial errors and uncertainty in LST measurements. The emissivity, which varies across different surfaces and land uses, reflects material composition and surface roughness. Satellite data offer a robust means to determine LSE at large scales. This study utilises the Normalised Difference Vegetation Index Threshold Method (NDVITHM) to produce a novel emissivity dataset spanning the last 40 years, specifically tailored for the Fennoscandian region, including Norway, Sweden, and Finland. Leveraging the long and continuous data series from the Advanced Very High Resolution Radiometer (AVHRR) sensors aboard the NOAA and MetOp satellites, an emissivity dataset is generated for 1981–2022. This dataset incorporates snow-cover information, enabling the creation of annual emissivity time series that account for winter conditions. LSE time series were extracted for six 15 × 15 km study sites and compared against the Moderate Resolution Imaging Spectroradiometer (MODIS) MOD11A2 LSE product. The intercomparison reveals that, while both datasets generally align, significant seasonal differences exist. These disparities are attributable to differences in spectral response functions and temporal resolutions, as well as the method considering fixed values employed to calculate the emissivity. This study presents, for the first time, a 40-year time series of the emissivity for AVHRR channels 4 and 5 in Fennoscandia, highlighting the seasonal variability, land-cover influences, and wavelength-dependent emissivity differences. This dataset provides a valuable resource for future research on long-term land surface temperature and emissivity (LST&E) trends, as well as land-cover changes in the region, particularly with the use of Sentinel-3 data and upcoming missions such as EUMETSAT’s MetOp Second Generation, scheduled for launch in 2025.

Spectral weighting functions for localization of complex sound. III. The effect of sensorineural hearing lossa).

Spectral weighting functions for sound localization were measured in participants with bilateral mild sloping to moderately severe, high-frequency sensorineural hearing loss (SNHL) and compared to normal hearing (NH) participants with and without simulated SNHL. Each participant group localized three types of complex tones, comprised of seven frequency components spatially jittered and presented from the horizontal frontal field. A threshold-elevating noise masker was implemented in the free field to simulate SNHL for participants with NH. On average, participants with SNHL and NH (in quiet and simulated SNHL) placed the greatest perceptual weight on components within the interaural time difference "dominance region," found previously to peak around 800 Hz [Folkerts and Stecker, J. Acoust. Soc. Am. 151, 3409-3425 (2022)]. In addition to the peak at 800 Hz, both participant groups (including NH participants in quiet) placed near equal weight on 400 Hz, resulting in a broadened "peak" in the dominance region, most likely due to the reduction of audibility to higher frequency components. However, individual weighting strategies were more variable across participants with SNHL than participants with NH. Localization performance was reduced for participants with SNHL but not for NH participants with simulated hearing loss when compared to NH participants in quiet.

Solitons moving on background waves of the focusing nonlinear Schrödinger equation with step-like initial condition

This work concerns the long-time asymptotic behaviors of the focusing nonlinear Schrödinger equation with step-like initial condition in present of discrete spectrum. The exact step initial-value problem with non-vanishing boundary on one side has been solved, while the step-like initial-value problem with solitons emerging remains open. We study this problem and explore the solitons moving on background waves of the focusing nonlinear Schrödinger equation by classifying all possible locations of discrete spectrum associated with the spectral functions. It is shown that there are five kinds of zones for the discrete spectrum in complex plane, which are called dumbing zone, trapping zone, trapping/waking zone, transmitting/waking zone and transmitting zone, respectively. By means of Deift–Zhou nonlinear steepest-descent method for Riemann–Hilbert problems, the long-time asymptotics of the solution along with the locations of the solitons for each case are formulated. Numerical simulations match very well with the theoretical analysis.

Light scalar quarkonia from Laplace sum rule at NLO

We review our results on light scalar quarkonia (q¯q and four-quark states) from (inverse) QCD Laplace sum rules (LSR) and their ratios R within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) O(αs5). As the Operator Product Expansion (OPE) usually converges for D⩽6−8, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the D=6 dimension vaccum condensates. We request that the optimal results obey the constraint: Pole (Resonance) contribution to the spectral integral is larger than the QCD continuum one which excludes an on-shell mass around (500−600)MeV obtained for values of the QCD continuum threshold tc⩽(1∼1.5)GeV2. Our results for the different assignments of the scalar mesons are compiled in Tables 1 to 3.

Advancing CubeSats Capabilities: Ground-Based Calibration of Uvsq-Sat NG Satellite’s NIR Spectrometer and Determination of the Extraterrestrial Solar Spectrum

Uvsq-Sat NG is a French 6U CubeSat (10 × 20 × 30 cm) of the International Satellite Program in Research and Education (INSPIRE) designed primarily for observing greenhouse gases (GHG) such as CO2 and CH4, measuring the Earth’s radiation budget (ERB), and monitoring solar spectral irradiance (SSI) at the top-of-atmosphere (TOA). It epitomizes an advancement in CubeSat technology, showcasing its enhanced capabilities for comprehensive Earth observation. Scheduled for launch in 2025, the satellite carries a compact and miniaturized near-infrared (NIR) spectrometer capable of performing observations in both nadir and solar directions within the wavelength range of 1100 to 2000 nm, with a spectral resolution of 7 nm and a 0.15° field of view. This study outlines the preflight calibration process of the Uvsq-Sat NG NIR spectrometer (UNIS), with a focus on the spectral response function and the absolute calibration of the instrument. The absolute scale of the UNIS spectrometer was accurately calibrated with a quartz-halogen lamp featuring a coiled-coil tungsten filament, certified by the National Institute of Standards and Technology (NIST) as a standard of spectral irradiance. Furthermore, this study details the ground-based measurements of direct SSI through atmospheric NIR windows conducted with the UNIS spectrometer. The measurements were obtained at the Pommier site (45.54°N, 0.83°W) in Charentes–Maritimes (France) on 9 May 2024. The objective of these measurements was to verify the absolute calibration of the UNIS spectrometer conducted in the laboratory and to provide an extraterrestrial solar spectrum using the Langley-plot technique. By extrapolating the data to AirMass Zero (AM0), we obtained high-precision results that show excellent agreement with SOLAR-HRS and TSIS-1 HSRS solar spectra. At 1.6 μm, the SSI was determined to be 238.59 ± 3.39 mW.m−2.nm−1 (k = 2). These results demonstrate the accuracy and reliability of the UNIS spectrometer for both SSI observations and GHG measurements, providing a solid foundation for future orbital data collection and analysis.

Lattice QCD estimates of thermal photon production from the QGP

Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at T=470 MeV (∼1.5Tc), as well as in 2+1 flavor QCD at T=220 MeV (∼1.2Tpc) with mπ=320 MeV. In order to quantify the nonperturbative effects, the lattice correlator is compared with the corresponding NLO+LPMLO estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian process regression. We find that the resulting photon rates agree within errors. Published by the American Physical Society 2024