Cauchy Distribution Research Articles

Variability of Blue Supergiants in the LMC with TESS

The blue supergiant (BSG) problem, namely, the overabundance of BSGs inconsistent with classical stellar evolution theory, remains an open question in stellar astrophysics. Several theoretical explanations have been proposed, which may be tested by their predictions for the characteristic time variability. In this work, we analyze the light curves of a sample of 20 BSGs obtained from the Transiting Exoplanet Survey Satellite (TESS) mission. We report a characteristic signal in the low-frequency (f ≲ 2 day−1) range for all our targets. The amplitude spectrum has a peak frequency of ∼0.2 day−1, and we are able to fit it by a modified Lorentzian profile. The signal itself shows strong stochasticity across different TESS sectors, suggesting its driving mechanism happens on short (≲months) timescales. Our signals resemble those obtained for a limited sample of hotter OB stars and yellow supergiants, suggesting their possible common origins. We discuss three possible physical explanations: stellar winds launched by rotation, convection motions that reach the stellar surface, and waves from the deep stellar interior. The peak frequency of the signal favors processes related to the convective zone caused by the iron opacity peak, and the shape of the spectra might be explained by the propagation of high-order, damped gravity waves excited from that zone. We discuss the uncertainties and limitations of all these scenarios.

Unveiling defect-related Raman modes of topological phononic β−MoB2 single crystal via angle-resolved polarized Raman spectra

As a rare topological phonon material, β−MoB2 exhibits superconductivity (SC) and undergoes structural transitions when subjected to pressure or doping. This unique property makes it an intriguing platform for investigating the interplay of diverse quantum order. However, the current understanding of phonons in this material remains limited. Therefore, in this study, we employ a combination of Raman scattering and first-principle calculations to investigate the phonon properties of β−MoB2. Several noteworthy observations were made during the study. (1) We identified five Raman-active modes (3A1g+2Eg) and two abnormal modes in β−MoB2. The authenticity of the five Raman-active modes was further confirmed through angle-resolved polarized Raman spectra (ARPRS) measurements and theoretical calculations. (2) We found that all Raman spectra obtained at various temperatures exhibited symmetric Lorentzian profiles. This finding implies a weak electron-phonon coupling (EPC) strength in β−MoB2. We calculated the EPC strength λ of bulk β−MoB2 to be 0.37, which is significantly lower than 1.71 of superconducting α−MoB2. (3) Based on ARPRS measurements and the phonon dispersion, we attributed the origin of the two abnormal modes to structural distortions with regard to B atom layers of β−MoB2. This research provides a foundation for exploring the relationship between defect structures and various intriguing physical phenomena observed in β−MoB2. Published by the American Physical Society 2024

Transform coefficient distribution modeling based frame-level adaptive rate control for VVC

Rate control is a key issue in the research of video coding optimization. In this work, we propose a statistical modeling based frame-level distortion estimation model and a distortion dependency based rate control optimization algorithm for Versatile Video Coding (VVC). VVC has incorporated into more advanced coding tools, resulting in the distribution of transform coefficient more sharper. In response to this phenomenon, the TCD of VVC is modeled by the probability density function (PDF) of Cauchy distribution and generalized Gaussian distribution (GGD) individually. Then, a sliding window-based frame-level distortion model is proposed, which is used for derivation of inter-frame distortion dependency factor. According to the derived distortion dependency factor, a frame-level rate control optimization algorithm is presented to update the coding parameters in practical coding process. Experiments have shown that the proposed method could effectively improve rate–distortion performance, achieving an average rate distortion performance improvement of 0.72% in sequences blow 4K resolution, and 1.47% in 4K sequences in low delay P frame (LDP) configuration.

VT‐NMR Analysis of Rotation‐Inversion of N‐(4‐hydroxybutyl)‐N‐(2,2,2‐trifluoroethyl) tert‐butyl Carbamate: Utilizing the −CH2CF3 Appendage as a Reporter on E/Z‐Isomerization

AbstractThe rotational barrier about the CN carbamate bond of N‐(4‐hydroxybutyl)‐N‐(2,2,2‐trifluoroethyl) tert‐butyl carbamate 1 was determined by variable temperature (VT) 13C and 19F NMR spectroscopy. The −CH2CF3 appendage reports on rotational isomerism and allows for the observation of separate signals for the E‐ and Z‐ensembles at low temperature. The activation barrier for E/Z‐isomerization was quantified using Eyring‐Polanyi theory which requires the measurements of the maximum difference in Larmor frequency Δνmax and the convergence temperature Tc. Both Δνmax and Tc were interpolated by analyzing sigmoidal functions fitted to data describing signal separation and the quality of the superposition of the E‐ and Z‐signals, respectively. Methods for generating the quality‐of‐fit parameters for Lorentzian line shape analysis are discussed. Our best experimental value for the rotational barrier ΔGc≠(1)=15.65±0.13 kcal/mol is compared to results of a higher level ab initio study of the model N‐ethyl‐N‐(2,2,2‐trifluoroethyl) methyl carbamate.

Raman spectroscopy study on the vibration and structural changes of graphene oxide: effect of laser power and time

Graphene oxide and its nanocomposites play a crucial role in various applications. Laser irradiation is a low-cost technique to tune the graphene oxide material, and a detailed study of the vibrational modes and structural changes during the laser–graphene oxide interaction is required. The evolution of defect modes and reduction process in graphene oxide at varying laser power and different exposure time duration, respectively, via Raman spectroscopy, is of interest in the present study. Graphene oxide (GO) is synthesized via Improved Hummer's method and characterized by X-Ray Diffraction (XRD), Thermogravimetric analysis (TGA), Field Emission Scanning Electron Microscopy (FESEM), Energy Dispersive X-ray analysis (EDX), UV-Vis-NIR and Raman spectroscopy. The first-order Raman spectrum of GO consists of broad D and G peaks around 1350 and 1584 cm-1, respectively, and the broad second-order band around 2700 cm-1 . Using the Lorentzian function, the first-order band is deconvoluted into five modes and the secondorder into four modes. The peak positions and FWHM of these modes undergo indicative changes. The variations in the intensity ratios of the defect modes and the (𝐷𝐷𝑖𝑖𝑖𝑖𝑖𝑖 ′ – 𝐺𝐺𝑎𝑎𝑎𝑎𝑎𝑎) with laser power at different exposure time durations indicates the predominance of edge defects and reduction of graphene oxide, respectively. These results broaden the understanding of the effect of laser power over different time durations on the graphene oxide features. Our study provides quantitative information on the laser-GO interaction.

Nanocrystalline Iron Oxides with Various Average Crystallite Size Investigated Using Magnetic Resonance Method

A series of nanocrystalline iron oxide samples (M1–M5) which differ from each other in average crystallite size (from 26 to 37 nm) was studied. The raw material was nanocrystalline iron with an average crystallite size equal to 21 nm promoted with hardly reducible oxides: Al2O3, CaO, K2O (in total, max. 10 wt%). Nanocrystalline iron was subjected to oxidation with water vapor to achieve different oxidation degrees (α = 0.16–1.00). Metallic iron remaining in the samples after the oxidizing step was removed by etching. Magnetic resonance spectra of all samples were obtained at room temperature. All resonance lines were asymmetric and intense. These spectra were fitted by Lorentzian and Gaussian functions. All spectral parameters depend on the preparation method of the nanoparticles. We suppose that the Lorentz fit gives us a spectrum from larger agglomerated sizes whereas the Gaussian fit comes from much smaller magnetic centers. For the nanocrystalline samples with the largest size of iron oxide nanocrystallites, the highest value of total integrated intensity was obtained, indicating that at smaller sizes, they are more mobile in reorientation processes resulting in more settings of anti-parallel magnetic moments. The magnetic anisotropy should also increase with the increase in size of nanocrystallites.

Radiative transfer of excitation: Lévy flights and self-similarity

The Green function of the Biberman–Holstein integral equation, both nonstationary (instantaneous point flash) and stationary (stationary point source) is studied. The point flash produces a self-similar spherical wave of excitation in homogenous gas medium. The transfer of excitation is due to the Lévy flights of resonance line photons. The properties of the wave – its shape, time evolution and propagation – are found for arbitrary line profile. The cases of Doppler, Lorentz and Voigt profiles are considered in some detail. For the Doppler broadened line, the structure of the self-similar wave is given by a rational function. The properties of the Green function of stationary Biberman–Holstein equation are reviewed. Some unexpected parallels with non-stationary case are found. The spherically-symmetric version of the longest flight approximation is discussed and the condition of its validity is formulated.

An Enhanced IHHO-LSTM Model for Predicting Online Public Opinion Trends in Public Health Emergencies

Social networks accelerate information communication in public health emergencies. Some negative information may cause an outbreak of public opinion crisis. Accurately predicting online public opinion trends can help the relevant departments take timely and effective measures to cope with risks. Therefore, this research proposes a prediction model incorporating the swarm intelligence optimization algorithm and the deep learning method. In this model, we improve the Harris Hawks Optimization (HHO) algorithm by introducing the Cauchy distribution function, the stochastic contraction exponential function, and the adaptive inertia weight. Then we utilize the improved HHO (IHHO) algorithm to optimize the hyperparameters of the deep learning method LSTM, including the learning rate and the number of neurons in the hidden layer. Finally, we construct the IHHO-LSTM model to make predictions in three public health emergencies. The experiments verify that the proposed model outperforms other single and hybrid models. The MAPE values reduce by 78.34%, 54.46%, and 46.42% relative to the average values of the three single models. Compared with the mean values of the two hybrid models, the MAPE values decrease by 47.69%, 18.45%, and 5.78%. The IHHO-LSTM model can be applied to public opinion early warning and reversal identification, providing a reference in public opinion management.

An adaptative differential evolution with enhanced diversity and restart mechanism

Differential Evolution (DE) stands out as an exceptional intelligent evolutionary algorithm, acclaimed for its simplicity in implementation and the ability to optimize without necessitating differentiable conditions. However, a significant pitfall of DE lies in its susceptibility to getting trapped in local minima, leading to algorithmic stagnation and substantial performance impairments. To counteract the shortcoming, the Adaptative Differential Evolution with Diversity Maintenance and Restart Mechanism (ADE-DMRM) is proposed. This approach integrates three primary innovations. Firstly, the algorithm controls the number of generations that individuals stay in the external archive based on the successful evolution rate, thereby optimizing the mutation strategy to effectively maintain population diversity. Secondly, ADE-DMRM proposes a novel restart mechanism in which the current stagnant individuals are identified by combining a stagnation tracker and a diversity assessment indicator and then regenerated using a dimension-learning-based approach. Thirdly, wavelet basis functions and Cauchy distributions are employed for scaling factor implementation across different stages, while the dimension change information of successfully evolved individuals is harnessed to refine the adaptive parameter control scheme. Finally, comprehensive experiments were undertaken on the CEC2013, CEC2014, and CEC2017 test sets, assessing accuracy, convergence speed, the efficacy of each module, and time complexity. The results confirm that ADE-DMRM is an efficient single-objective optimization algorithm that outperforms current advanced variants.

Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions

A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models.

Diffuse interstellar bands in Gaia DR3 RVS spectra

Diffuse interstellar bands (DIBs) are weak and broad interstellar absorption features in astronomical spectra that originate from unknown molecules. To measure DIBs in spectra of late-type stars more accurately and more efficiently, we developed a random forest model to isolate the DIB features from the stellar components. We applied this method to 780 thousand spectra collected by the Gaia Radial Velocity Spectrometer (RVS) that were published in the third data release (DR3). After subtracting the stellar components, we modeled the DIB at 8621 Å (λ8621) with a Gaussian function and the DIB around 8648 Å (λ8648) with a Lorentzian function. After quality control, we selected 7619 reliable measurements for DIB λ8621. The equivalent width (EW) of DIB λ8621 presented a moderate linear correlation with dust reddening, which was consistent with our previous measurements in Gaia DR3 and the newly focused product release. The rest-frame wavelength of DIB λ8621 was updated as λ0 = 8623.141 ± 0.030 Å in vacuum, corresponding to 8620.766 Å in air, which was determined by 77 DIB measurements toward the Galactic anticenter. The mean uncertainty of the fit central wave-length of these 77 measurements is 0.256 Å. With the peak-finding method and a coarse analysis, DIB λ8621 was found to correlate better with the neutral hydrogen than with the molecular hydrogen (represented by 12CO J = (1−0) emission). We also obtained 179 reliable measurements of DIB λ8648 in the RVS spectra of individual stars for the first time, further confirming this very broad DIB feature. Its EW and central wavelength presented a linear relation with those of DIB λ8621. A rough estimation of λ0 for DIB λ8648 was 8646.31 Å in vacuum, corresponding to 8643.93 Å in air, assuming that the carriers of λ8621 and λ8648 are comoving. Finally, we confirmed the impact of stellar residuals on the DIB measurements in Gaia DR3, which led to a distortion of the DIB profile and a shift of the center (≲0.5 Å), but the EW was consistent with our new measurements. With our measurements and analyses, we propose that the approach based on machine learning can be widely applied to measure DIBs in numerous spectra from spectroscopic surveys.

Massive MIMO With Cauchy Noise: Channel Estimation, Achievable Rate and Data Decoding

Massive MIMO With Cauchy Noise: Channel Estimation, Achievable Rate and Data Decoding

New theoretical study of potassium perturbed by He and a comparison to laboratory spectra

The visible and near-infrared spectra of late L- and T-type dwarf stars are dominated in large part by the resonance lines of neutral Na and K. It is the collision broadening of these atomic lines by H2 and He in the stellar atmosphere that determines the continuum from below 0.5 µm to above 0.9 µm in the spectrum. Their line profiles can be detected as far as 3000 cm−1 from the line center in T dwarfs and consequently an accurate and detailed determination of the complete profile, including the extreme far wing, is required to model the contribution of these strong alkali resonance lines to brown dwarf spectra. We report on our new calculations of unified line profiles of K perturbed by He using ab initio potential data for the conditions prevailing in cool substellar brown dwarfs and hot dense planetary atmospheres with temperatures from Teff = 500 to 3000 K. For such objects with atmospheres of H2 and He, conventional laboratory absorption spectroscopy can be used to examine the line wings and test the line shape theories and molecular potentials. We find that an analytical Lorentzian profile is useful for a few cm−1 from the line center, but not in the line wings, where the radiative transfer is a consequence of the K–He radiative collisions that are sensitive to the interaction potentials. Tables of the K–He absorption coefficients of the resonance lines allow accurate model atmospheres and synthetic spectra. For this purpose, we present new opacities from comprehensive line shape theory incorporating accurate ab initio potentials. Use of these new tables for the modeling of emergent spectra will be an improvement over previous line shape approximations based on incomplete or inaccurate potentials. We also present Lorentzian impact parameters obtained in the semi-classical and quantum theory for the K 4s − 4p resonance line centered at 0.77 µm specifically for the line core regime.

A fuzzy track-to-track association algorithm with dynamic time warping for trajectory-level vehicle detection

Multi-source track-to-track association (TTTA), which identifies trajectories from multiple sensors or data sources of the same dynamic vehicle, is an important data fusion technique widely applied to vehicle detection in the fields of road, marine, and aviation transportation. However, issues such as time asynchrony, heterogeneous sampling intervals, and random sensing errors have posed considerable challenges to the accuracy and robustness of TTTA. Aiming to address these issues in an integrated manner, this paper proposes a TTTA algorithm that comprehensively calculates the similarity between trajectories using multiple trajectory features through dynamic time warping and Cauchy distribution degree of membership function. Multiple experimental datasets were generated by randomly sampling real AIS trajectory data into two trajectory data sources and adding random errors. The average association accuracy of all scenarios and error levels of the proposed method reached 97.33%, far higher than other benchmark methods. Experimental results demonstrated the advantage of the proposed algorithm in various TTTA scenarios, especially its robustness in intricate trajectory situations. The results also indicated that more features can maintain the stability of associations in the presence of larger random errors, and dynamic time warping can improve association accuracy in intricate scenarios. This study provides a practical solution for the problem of time asynchrony, heterogeneous sampling intervals, and random errors in multi-source trajectory data fusion, showcasing promising applications across diverse domains.

Non-commutative Wormhole geometries in presence of modified Chaplygin–Jacobi gas and Anton–Schmidt fluid

In this work, we have found Wormhole (WH) solutions in isotropic cosmology in the backdrop of general relativity while utilizing the “Modified Chaplygin–Jacobi Gas” and “Anton–Schmidt fluid” equations of state. As a starting point for our calculations, we have also considered two matter distributions, namely the Gaussian distribution and the Lorentzian distribution. All four energy conditions (i.e. strong, weak, null and dominant) are calculated, and their respective graphs are plotted as well. The shape function and redshift function associated with the wormhole structure are also derived and plotted graphically. After that, the embedding diagram of our wormhole models and proper radial distance are presented graphically. Finally, we have discussed the stability of the wormhole solutions obtained using the generalized Tolman–Oppenheimer–Volkov (TOV) equation and have examined the aspect of vanishing sound speed inside the wormhole throat to study the role of perturbations of the system.

Mid-infrared imaging spectroscopic measurements of C2H4 frost simulating the outer solar system environments

In the dense and cold atmosphere of Titan, the presence of C2H4 haze has been confirmed by the observations of spacecraft. In the present study, original cryogenic experimental equipment was developed to simulate the low-temperature solid formation of C2H4 in combination with in-situ infrared spectroscopic measurements. As a result, out-of-plane bending vibration ν7 of solid-phase C2H4 located at ~ 10.5 μm was successfully detected with high sensitivity, and two-dimensional spectrographs of C2H4 at low temperatures were obtained. The obtained spectra of C2H4 can be fitted to the double Lorentzian function with various heights, central wavelengths, and full widths at half the maximum (FWHM) of the two-component Lorentzian functions. They were classified into three types using the fitting parameters. However, their spectral shapes are different from the amorphous, metastable, and crystalline forms obtained by the previous laboratory experiment in terms of the distance of two peak wavelengths and FWHM. The results may link to understanding the spectral band properties of C2H4 condensation in the haze component of Titan.Graphical

Terahertz Time-Domain Spectroscopic (THz-TDS) Insights into Protein Deformation

In this study, we utilized terahertz time-domain spectroscopy (THz-TDS) to study the radiation-induced protein deformation. The absorption coefficient spectra obtained from THz-TDS measurements in the frequency range (0.06–2 THz) was fitted using the Lorentzian model. The absorption coefficient fitting data was used to identify the α-helix and β-structure relative contributions in the protein secondary structure of the kidney tissue of rats irradiated with 10-cGy and 2-Gy X-ray separately or in combination. Our data show that 2-Gy X-irradiation leads to an increase in the β-structure contribution associated with a decrease in the α-helix contribution as indicated by the fitting parameters extracted from fitting the absorption coefficient α(ω) spectra with the Lorentzian function. The results point out that there is a strong correlation between the strength of the hydrogen bonds located between or inside the polypeptide chains of the extended β-sheet and α-helix, respectively, and the absolute value of the absorption coefficient α(ω), the refractive index, and the dielectric constant. The lowest refractive index and dielectric constant are recorded in the 2-Gy-irradiated group followed by the 10-cGy–2 Gy-irradiated group while the least effect was recorded in the 10-cGy-irradiated group. These data provide evidence of the adaptive effect of the 10-cGy X-irradiation delivered 24 h prior to the 2-Gy x-irradiation.

Study of several probability distribution functions for the Klein–Kramers equation

In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.

Adaptation of the Scaling Factor Based on the Success Rate in Differential Evolution

Differential evolution is a popular heuristic black-box numerical optimization algorithm which is often used due to its simplicity and efficiency. Parameter adaptation is one of the main directions of study regarding the differential evolution algorithm. The main reason for this is that differential evolution is highly sensitive to the scaling factor and crossover rate parameters. In this study, a novel adaptation technique is proposed which uses the success rate to replace the popular success history-based adaptation for scaling factor tuning. In particular, the scaling factor is sampled with a Cauchy distribution, whose location parameter is set as an nth order root of the current success rate, i.e., the ratio of improved solutions to the current population size. The proposed technique is universal and can be applied to any differential evolution variant. Here it is tested with several state-of-the-art variants of differential evolution, and on two benchmark sets, CEC 2017 and CEC 2022. The performed experiments, which include modifications of algorithms developed by other authors, show that in many cases using the success rate to determine the scaling factor can be beneficial, especially with relatively small computational resource.

Directional distribution of the pseudo intensity vector in anisotropic late reverberation.

The pseudo intensity vector (PIV) is often used to analyze the directional properties of spatial room impulse responses. In the early part of the response, it is capable of estimating the directions of individual reflections. However, thus far, its behaviour in the late field is unclear. Specifically, it is unknown whether anisotropy, i.e., a direction-dependent energy distribution, is captured by the directional estimates. In this study, a closed-form expression of the directional distribution of the pressure-normalized pseudo intensity vector contingent on a general stochastical model of anisotropic fields was analytically derived. This paper shows that the probability density function of this PIV is a multivariate Cauchy distribution, which does indeed depend on the energy distribution of the field, yet the directional distribution has very limited degrees of freedom. The derived distribution is compared to the results of Monte Carlo simulations and fields captured with a microphone array in a real room. These results facilitate better understanding of the behaviour of parametric spatial room impulse response methods and may enable improved directional estimators for anisotropic fields.