One-parameter Fit Research Articles

Detecting stellar activity cycles in p-mode travel times

Context. The 11 yr solar cycle is known to affect the global modes of solar acoustic oscillations. In particular, p mode frequencies increase with solar activity. Aims. We propose a new method to detect the solar cycle from the p-mode autocorrelation function, and we validate this method using VIRGO/SPM photometric time series from solar cycles 23 and 24. Methods. The p-mode autocorrelation function shows multiple wavepackets separated by time lags of ∼123 min. Using a one-parameter fitting method (from local helioseismology), we measure the seismic travel times from each wavepacket up to skip number 40. Results. We find that the travel-time variations due to the solar cycle strongly depend on the skip number, with the strongest signature in odd skips from 17 to 31. Taking the noise covariance into account, the travel-time perturbations can be averaged over all skip numbers to enhance the signal-to-noise ratio. Conclusions. This method is robust to noise, simpler to implement than peak bagging in the frequency domain, and is promising for asteroseismology. We estimate that the activity cycle of a Sun-like star should be detectable with this new method in Kepler-like observations down to a visual magnitude of mK ∼ 11. However, for fainter stars, activity cycles are easier to detect in the photometric variability on rotational timescales.

Indirect constraints on top quark operators from a global SMEFT analysis

We perform a model-independent analysis of top-philic New Physics scenarios, under the assumption that only effective operators involving top quarks are generated at tree level. Within the SMEFT framework, we derive indirect constraints on Wilson Coefficients by combining a large set of low-energy observables: B-meson and kaon decays, meson mixing observables, precision electroweak and Higgs measurements, anomalous magnetic moments, lepton flavour violating processes, lepton flavour universality tests, and measurements of the Cabibbo angle. We consider the renormalization group evolution of the operators and use the one-loop matching of the SMEFT onto the LEFT. The global analysis is then used to perform one-parameter, two-parameter, and global fits, as well as applications to explicit ultraviolet models. We find that the inclusion of measurements from different physics sectors reveals a strong interplay and complementarity among the observables. The resulting constraints are also compared to direct bounds provided by top quark productions at the LHC.

Degree distributions in AB random geometric graphs

In this paper, we provide degree distributions for AB random geometric graphs, in which points of type A connect to the closest k points of type B. The motivating example to derive such degree distributions is in 5G wireless networks with multi-connectivity, where users connect to their closest k base stations. In this setting, it is important to know how many users a particular base station serves, which gives the degree of that base station. To obtain these degree distributions, we investigate the distribution of area sizes of the kth order Voronoi cells of B-points. Assuming that the A-points are Poisson distributed, we investigate the amount of users connected to a certain B-point, which is equal to the degree of this point. In the simple case where the B-points are placed in an hexagonal grid, we show that all kth order Voronoi areas are equal and thus all degrees follow a Poisson distribution. However, this observation does not hold for Poisson distributed B-points, for which we show that the degree distribution follows a compound Poisson–Erlang distribution in the 1-dimensional case. We then approximate the degree distribution in the 2-dimensional case with a compound Poisson-Gamma degree distribution and show that this one-parameter fit performs well for different values of k. Moreover, we show that for increasing k, these degree distributions become more concentrated around the mean. This means that k-connected AB random graphs balance the loads of B-type nodes more evenly as k increases. Finally, we provide a case study on real data of base stations. We show that with little shadowing in the distances between users and base stations, the Poisson distribution does not capture the degree distribution of these data, especially for k>1. However, under strong shadowing, our degree approximations perform quite good even for these non-Poissonian location data.

Territorial behaviour of buzzards versus random matrix spacing distributions

A deeper understanding of the processes underlying the distribution of animals in space is crucial for both basic and applied ecology. The Common buzzard (Buteo buteo) is a highly aggressive, territorial bird of prey that interacts strongly with its intra- and interspecific competitors. We propose and use random matrix theory to quantify the strength and range of repulsion as a function of the buzzard population density, thus providing a novel approach to model density dependence. As an indicator of territorial behaviour, we perform a large-scale analysis of the distribution of buzzard nests in an area of 300 square kilometres around the Teutoburger Wald, Germany, as gathered over a period of 20 years. The nearest and next-to-nearest neighbour spacing distribution between nests is compared to the two-dimensional Poisson distribution, originating from uncorrelated random variables, to the complex eigenvalues of random matrices, which are strongly correlated, and to a two-dimensional Coulomb gas interpolating between these two. A one-parameter fit to a time-moving average reveals a significant increase of repulsion between neighbouring nests, as a function of the observed increase in absolute population density over the monitored period of time, thereby proving an unexpected yet simple model for density-dependent spacing of predator territories. A similar effect is obtained for next-to-nearest neighbours, albeit with weaker repulsion, indicating a short-range interaction. Our results show that random matrix theory might be useful in the context of population ecology.

Skyrme forces and isotopic dependence of evaporation residue cross-section in the decay of 252,254−256No∗ formed in 204,206,207,208Pb+48Ca reactions

The fusion evaporation residue (ER) cross-sections [Formula: see text] for the decay of compound nucleus (CN) [Formula: see text]No[Formula: see text] via 1[Formula: see text]–4[Formula: see text] decay channels, synthesized in [Formula: see text]Pb[Formula: see text][Formula: see text][Formula: see text][Formula: see text]Ca reaction, are studied, including deformations [Formula: see text] for cold-optimum orientations [Formula: see text] at various [Formula: see text]Ca excitation energies of [Formula: see text] to 45[Formula: see text]MeV. For the nuclear interaction potentials, we use the Skyrme energy density functional (SEDF)-based on semi-classical extended Thomas Fermi (ETF) approach under frozen density approximation on our earlier study of fusion ER cross-section for the decay of [Formula: see text]No[Formula: see text], via 1[Formula: see text]–4[Formula: see text] decay channels synthesized in [Formula: see text]Pb[Formula: see text][Formula: see text][Formula: see text][Formula: see text]Ca reaction based on the Dynamical cluster-decay model (DCM) using the pocket formula for nuclear proximity potential in which the above reaction was investigated by using hot-optimum orientations. In this work the above reaction has been investigated in two parts, in the first part, [Formula: see text][Formula: see text]MeV is used for cold elongated configurations and in the second part, [Formula: see text][Formula: see text]MeV is used for hot compact configurations. The Skyrme forces used here are the old SIII, and new GSkI and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in frozen density approximation. Interestingly, independent of the Skyrme force used, the DCM gives an excellent fit within one-parameter fitting of [Formula: see text] to the measured data on fusion ER for cold fusion. Of all the three Pb-isotopes and three [Formula: see text] considered, at each [Formula: see text], the [Formula: see text] is largest for compound system with mass numbers 256 and 254, and smallest for 252, which means that the neutrons emission occur earliest for 256, then 255 followed by 254 and finally for 252, in complete agreement with experimental data. The possible fusion–fission (ff) and quasi-fission (qf) mass-regions of fragments on DCM are also predicted. The DCM with Skyrme forces is further used to look for all the possible target-projectile ([Formula: see text]-[Formula: see text]) combinations forming the “cold” CN [Formula: see text]No[Formula: see text] at the CN excitation energy of [Formula: see text] for “optimum cold” configurations. The fusion ER cross-sections, for the proposed new reactions in synthesizing the CN [Formula: see text]No[Formula: see text], are also estimated for the future experiments.

Stochastic homology of Gaussian vs. non-Gaussian random fields: graphs towards Betti numbers and persistence diagrams

The topology and geometry of random fields—in terms of the Euler characteristic and the Minkowski functionals—has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial non-Gaussianities would form a valuable clue on the physics of the early Universe. The virtue of both the Euler characteristic and the Minkowski functionals in general, lies in the fact that there exist closed form expressions for their expectation values for Gaussian random fields. However, the Euler characteristic and Minkowski functionals are summarizing characteristics of topology and geometry. Considerably more topological information is contained in the homology of the random field, as it completely describes the creation, merging and disappearance of topological features in superlevel set filtrations. In the present study we extend the topological analysis of the superlevel set filtrations of two-dimensional Gaussian random fields by analysing the statistical properties of the Betti numbers—counting the number of connected components and loops—and the persistence diagrams—describing the creation and mergers of homological features. Using the link between homology and the critical points of a function—as illustrated by the Morse-Smale complex—we derive a one-parameter fitting formula for the expectation value of the Betti numbers and forward this formalism to the persistence diagrams. We, moreover, numerically demonstrate the sensitivity of the Betti numbers and persistence diagrams to the presence of non-Gaussianities.

The self-similarity of weak lensing peaks

ABSTRACT We study the statistics of weak lensing convergence peaks, such as their abundance and two-point correlation function (2PCF), for a wide range of cosmological parameters Ωm and σ8 within the standard ΛCDM paradigm, focusing on intermediate-height peaks with signal-to-noise ratio (SNR) of 1.5–3.5. We find that the cosmology dependence of the peak abundance can be described by a one-parameter fitting formula that is accurate to within $\sim 3{{\ \rm per\ cent}}$. The peak 2PCFs are shown to feature a self-similar behaviour: if the peak separation is rescaled by the mean interpeak distance, catalogues with different minimum peak SNR values have identical clustering, which suggests that the peak abundance and clustering are closely interconnected. A simple fitting model for the rescaled 2PCF is given, which together with the peak abundance model above can predict peak 2PCFs with an accuracy better than $\sim 5{{\ \rm per\ cent}}$. The abundance and 2PCFs for intermediate peaks have very different dependencies on Ωm and σ8, implying that their combination can be used to break the degeneracy between these two parameters.

Hot star extension to theHubbleSpace Telescope stellar spectral library

Context.Libraries of stellar spectra find many uses in astrophysics, from photometric calibration to stellar population synthesis.Aims.We present low resolution spectra of 40 stars from 0.2μm (ultraviolet) to 1.0μm (near infrared) with excellent fluxing. The stars include normal O-type stars, helium-burning stars, and post-asymptotic giant branch (PAGB) stars.Methods.Spectra were obtained with the Space Telescope Imaging Spectrograph (STIS) installed in theHubbleSpace Telescope (HST) using three low resolution gratings, G230LB, G430L, and G750L. Cosmic ray hits and fringing in the red were corrected. A correction for scattered light was applied, significant only for our coolest stars. Cross-correlation was used to bring the spectra to a common, final, zero velocity wavelength scale. Finally, synthetic stellar spectra were used to estimate line of sight dust extinction to each star, and a five-parameter dust extinction model was fit, or a one-parameter fit in the case of low extinction.Results.These spectra dovetail with the similar Next Generation Stellar Library (NGSL) spectra, extending the NGSL’s coverage of stellar parameters, and extending to helium burning stars and stars that do not fuse.Conclusions.The fitted dust extinction model showed considerable variation from star to star, indicating variations in dust properties for different lines of sight. Interstellar absorption lines are present in most stars, notably MgII.

Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions

Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time-scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. In the regime $T>1$ MeV, Kramers' theory should be replaced by a new theory based on the Ornstein-Uhlenbeck first-passage time method that is proposed here. The theory is applied to fission time data from fusion-fission experiments on $^{16}$O+$^{208}$Pb $\rightarrow$ $^{224}$Th. The proposed model provides an internally consistent one-parameter fitting of fission data with a constant nuclear friction as the fitting parameter, whereas Kramers' fitting requires a value of friction which falls out of the allowed range. The theory provides also an analytical formula that in future work can be easily implemented in numerical codes such as CASCADE or JOANNE4.

Quantitative Analysis of Intravoxel Incoherent Motion (IVIM) Diffusion MRI using Total Variation and Huber Penalty Function.

Quantitative analysis in intravoxel incoherent motion (IVIM) imaging commonly uses voxel-wise estimation of the bi-exponential model, which might not be reliable for clinical interpretation. Improving model fitting performance and qualitative and quantitative parametric estimation, two novel methodologies are proposed here. Five IVIM analyses methodologies: (a) Bi-exponential (BE) model, (b) Segmented BE method with two-parameter fitting (BEseg-2), (c) Segmented BE method with one-parameter fitting (BEseg-1), (d) BE with adaptive Total Variation penalty function (BE+TV) and (e) BE with adaptive Huber penalty function (BE+HPF) were evaluated. Relative root-mean-square error (RRMSE), relative bias (RB) and relative parameters (Drel,Drel∗,&frel) were calculated to estimate the accuracy of methods in simulations. Empirical datasets from 14 patients with bone tumor were analyzed using these methodologies. Coefficient of variation (CV) were estimated for each IVIM parameter in tumor volume to measure the precision of the estimation methods invivo. Both BE+TV and BE+HPF showed consistently lower RRMSE (~10-42%) and lower RB (-4 to 8%) at all noise levels, compared to BE, BEseg-2 and BEseg-1 (RRMSE: ~15-120% and RB: -20 to 62%). Estimated Drel,Drel∗&frel for both BE+TV and BE+HPF methods were ~1 (0.96-1.08), whereas BE, BEseg-2 and BEseg-1 showed sub-optimal parameter estimation (0.80-1.62). For clinical data BE+TV and BE+HPF showed 30-50% improved CV in estimating D, D*, and f than BE and improved CV in estimating D* (7-23%) and f (26-30%) than BEseg-2 and BEseg-1. Bi-exponential model with penalty function showed quantitatively and qualitatively improved IVIM parameter estimation for both simulated and clinical dataset of bone tumors, thus potentially making this approach suitable for clinical applications in future.

Probing the Higgs self coupling via single Higgs production at the LHC

We propose a method to determine the trilinear Higgs self coupling that is alternative to the direct measurement of Higgs pair production total cross sections and differential distributions. The method relies on the effects that electroweak loops featuring an anomalous trilinear coupling would imprint on single Higgs production at the LHC. We first calculate these contributions to all the phenomenologically relevant Higgs production ($gg{\rm F}$, VBF, $WH$, $ZH$, $t\bar tH$) and decay ($\gamma \gamma$, $WW^{*}/ZZ^{*}\to 4f$, $b\bar b$, $\tau \tau$) modes at the LHC and then estimate the sensitivity to the trilinear coupling via a one-parameter fit to the single Higgs measurements at the LHC 8 TeV. We find that the bounds on the self coupling are already competitive with those from Higgs pair production and will be further improved in the current and next LHC runs.

Modeling the Landau-gauge ghost propagator in 2, 3, and 4 spacetime dimensions

We present an analytic description of numerical results for the ghost propagator G(p^2) in minimal Landau gauge on the lattice. The data were produced in the SU(2) case using the largest lattice volumes to date, for d = 2, 3 and 4 space-time dimensions. Our proposed form for G(p^2) is derived from the one-loop relation between ghost and gluon propagators, considering a tree-level ghost-gluon vertex and our previously obtained gluon-propagator results \cite{Cucchieri:2011ig}. Although this one-loop expression is not a good description of the data, it leads to a one-parameter fit of our ghost-propagator data with a generally good value of \chi^2/dof, comparable to other fitting forms used in the literature. At the same time, we present a simple parametrization of the difference between the lattice data and the one-loop predictions.

Improvement of the crystal rotation method to measure the flexoelectric difference (e1–e3) in achiral materials using AC electric fields

ABSTRACTWe show that the crystal rotation method for measuring the difference between splay and bend flexoelectric coefficients (e1–e3) [Outram and Elston, Liq. Cryst. 39, 149 (2012)] can be improved by using AC instead of DC fields. The field frequency is small (~0.05 Hz), yet sufficient to get rid of the difficulties connected with the migration of charge carriers. The method is sensitive enough so as to use fields with amplitudes as small as 1 V/mm. This has the advantage of avoiding the consideration of the interaction due to the dielectric anisotropy, and greatly simplifies the analysis of data. The results are extracted from a simple fitting scheme, which involves two parameters. In particular (e1–e3) is obtained from a scale factor in a one-parameter fit. Measurements of the temperature dependence of (e1–e3) are presented for two classical nematic materials.

Determination of aerodynamic parameters of urban surfaces: methods and results revisited

Estimates of aerodynamic parameters, in particular roughness length z0 and displacement height d, are important for the analysis of the roughness of an urban surface, which affects processes that occur within the urban boundary layer such as pollutant dispersion and urban ventilation. Findings regarding the aerodynamic effects of various configurations of urban arrays were compiled from various studies. Several experimental, numerical and semi-empirical studies to estimate z0 and d were reviewed and compared with each other. The results can be summarized as follows: (1) the influence of the frontal area index (λf) on z0 is significant and their relationship has been confirmed by both experimental and numerical data; (2) compared to one-parameter and two-parameter fitting methods, the three-parameter fitting method is the least accurate; (3) the physical meaning of d remains vague because its definition as the height where surface drag acts may not be accurate for sharp-edged roughness blocks and (4) the peak values of z0 for uniform and heterogeneous block heights indicate presence of skimming or wake-interference flow effects, which may influence surface roughness. Finally, the semi-empirical models were found to be limited to cases derived from available experimental data, which normally involve uniform arrays of cubes.

Scaling in the correlation energies of atomic ions

We show through numerical investigations that the ground-state correlation energies of atomic ions follow an unexpectedly simple scaling relation, ${E}_{c}\ensuremath{\approx}{Z}^{4/3}{f}_{c}(Z/N)$, where $N$ is the number of electrons, $Z$ is the atomic number, and ${f}_{c}$ is a universal function, for which an analytic expression with a one-parameter fit can be provided. The relation agrees well with several sets of correlation energies obtained from different methods for atomic ions with $N=2,...,18$ and $Z=2,...,28$. Moreover, our relation gives a good agreement with neutral atoms up to $N\ensuremath{\approx}90$. Our main result is readily applicable to estimating correlation energies of heavy elements, for which there are no available data in the literature. The simplicity of the relation may also have implications in the development of correlation functionals within density-functional theory.

AN IMPROVED PREDICTION OF DCT-BASED IMAGE FILTERS EFFICIENCY USING REGRESSION ANALYSIS

Efficiency of DCT-based filters for a wide-class of images is investigated. The study is carried out for additive white Gaussian noise (AWGN) case with several intensity levels. Local DCT-based filter is used as basic denoising technique. Nonlocal BM3D filter known as the state-of-the-art technique for AWGN removal is also exploited. A precise prediction method of denoising efficiency for several quality metrics is proposed. It is shown that statistics of DCT coefficients provides useful information. Regression models for analyzed filters and metrics are presented. The obtained dependence approximations of quality metrics on DCT statistics have high goodness of fit. One-parameter and multi-parameter fitting cases are considered. The most valuable DCT statistics are found.

Zero-Point Corrections for Isotropic Coupling Constants for Cyclohexadienyl Radical, C6H7 and C6H6Mu: Beyond the Bond Length Change Approximation

Zero-point vibrational level averaging for electron spin resonance (ESR) and muon spin resonance (µSR) hyperfine coupling constants (HFCCs) are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of H by D on 13C-NMR chemical shifts is used. DFT methods are used to compute the change in energy and HFCCs when the geometry is changed from the equilibrium values for the stretch and both bend degrees of freedom. This variation is then averaged over the probability distribution for each degree of freedom. The method is tested using data for the methylene group of C6H7, cyclohexadienyl radical and its Mu analog. Good agreement is found for the difference between the HFCCs for Mu and H of CHMu and that for H of CHMu and CH2 of the parent radical methylene group. All three of these HFCCs are the same in the absence of the zero point average, a one-parameter fit of the static HFCC, a(0), can be computed. That value, 45.2 Gauss, is compared to the results of several fixed geometry electronic structure computations. The HFCC values for the ortho, meta and para H atoms are then discussed.

Galaxy rotation curves in the Grumiller's modified gravity

The effective potential in the Grumiller's modified gravity includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration a ≈ 0.30 × 10−10 m s−2. We do a two-parameter fit first, with the mass-to-light ratio (ϒ*) and the Rindler acceleration (a) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range 0 ≲ r ≲ 40 kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value |$\bar{a}\approx 0.30\times 10^{-10}\,{\rm m\,s}^{-2}$|⁠. Inspired by this fact, we then carry out a one-parameter (ϒ*) fit to the six galaxies, with a fixed at |$\bar{a}$|⁠, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgrom's modified Newtonian dynamics. For the rest two galaxies, NGC 5055 and DDO 154, the fitting results are significantly improved if the photometric scale length (h) is included as another free parameter.

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Motivated by the statistical fluctuation of Dirac spectrum of QCD-like theories subjected to (pseudo)reality-violating perturbations and in the epsilon-regime, we compute the smallest eigenvalue distribution and the level spacing distribution of chiral and non-chiral parametric random matrix ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nystrom method to numerically evaluate the Fredholm Pfaffian of the integral kernel for the chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and universality of our results by comparing them with several lattice models, namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched lattice gauge theory under the twisted boundary condition (imaginary chemical potential) or perturbed by phase noise. Both in the zero-virtuality region and in the spectral bulk, excellent one-parameter fitting is achieved already on a small 4^4 lattice. Anticipated scaling of the fitting parameter with the twisting phase, mean level spacing, and the system size allows for precise determination of the pion decay (diffusion) constant F in the low-energy effective Lagrangian.

DATA TAKING STRATEGY FOR THE PHASE STUDY IN ψ′→K+K-

The study of the relative phase between strong and electromagnetic amplitudes is of great importance for understanding the dynamics of charmonium decays. The information of the phase can be obtained model-independently by fitting the scan data of some special decay channels, one of which is ψ′ →K+K-. To find out the optimal data taking strategy for a scan experiment in the measurement of the phase in ψ′ →K+ K-, the minimization process is analyzed from a theoretical point of view. The result indicates that for one-parameter fit, only one data taking point in the vicinity of a resonance peak is sufficient to acquire the optimal precision. Numerical results are obtained by fitting simulated scan data. Besides the results related to the relative phase between strong and electromagnetic amplitudes, the method is extended to analyze the fits of other resonant parameters, such as the mass and the total decay width of ψ′.