Homogeneous spectrum and mixing transformations

Tikhonov, S. V.

doi:10.1134/s1064562411010224

Cited by 23 publications

(32 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1) as the input in the unfolding procedure. We use a least-squares method with Tikhonov regularization [10] as implemented in the TUnfold package [11]. The best value of the regularization strength (τ 2 ) is obtained via implementing the L-curve scan in TUnfoldDensity.…”

Section: Raw Event-plane Dependent Correlationsmentioning

confidence: 99%

Event-plane dependent away-side jet-like correlation shape in Au+Au collisions at $\sqrt{s_{\rm NN}}$=200 GeV from STAR

Zhang

2019

Proceedings of International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions — PoS(HardProbes20

View full text Add to dashboard Cite

We employ a data-driven method to subtract the flow background of all harmonics by calculating the difference of the two-particle correlations between the close-region and far-region, determined depending on the pseudo-rapidity (η) distance from the region where an enhanced recoil transverse momentum (P x ) from a high-p T trigger particle is selected. We analyze the correlation shape as a function of the trigger particle azimuthal angle relative to the event-plane (EP) reconstructed from the beam-beam counters (BBCs) which are displaced by several units in η from the mid-rapidity region. The large η gap can effectively eliminate the auto-correlation between trigger particles and EP. We correct for the relatively large resolution effect from the BBC EP determination via an unfolding procedure. The width of unfolded away-side jet-like correlation increases with longer path-length, which is an indication of jet-medium interactions.

show abstract

Section: Raw Event-plane Dependent Correlationsmentioning

confidence: 99%

Event-plane dependent away-side jet-like correlation shape in Au+Au collisions at $\sqrt{s_{\rm NN}}$=200 GeV from STAR

Zhang

2019

Proceedings of International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions — PoS(HardProbes20

View full text Add to dashboard Cite

show abstract

“…L 2 R MÂM is a regularization matrix, > 0 is a regularization parameter and k Á k indicates the Euclidean norm. Equation (3) is known as Tikhonov regularization (Tikhonov, 1963;Tikhonov & Arsenin, 1977) and was independently discovered by Glatter (1977) in the context of the inverse Fourier transform. JðwÞ can be interpreted within a Bayesian inference approach as well as within a frequentist one; both are explained below.…”

Section: Indirect Fourier Transform (Ift)mentioning

confidence: 99%

Indirect Fourier transform in the context of statistical inference

et al. 2016

View full text Add to dashboard Cite

Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.

show abstract

“…Physical maps are seldom uncorrelated, but the correlation can be easily accounted for via the reference map (see Section 2.2.4). Alternatively, the Tikhonov functional S( f ) = f 2 (Tikhonov 1963) and its derivatives, which measure the smoothness of the image, are also used in some cases (e.g. Piskunov, Tuominen & Vilhu 1990).…”

Section: Eclipse Mapping Of Surface Patternsmentioning

confidence: 99%

“…Pulsations, however, cause a periodic variation in the stellar shape, and hence also in the local gravity and other atmospheric conditions. Their inclusion would require not only a detailed atmospheric model (see Buta & Smith 1979;Townsend 1997), but also the knowledge of the pulsation modes themselves. Obviously, this is not feasible.…”

Section: Assumptionsmentioning

confidence: 99%

Photometric mode identification methods of non-radial pulsations in eclipsing binaries - I. Dynamic eclipse mapping

Bíró¹,

Nuspl

2011

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

We present the dynamic eclipse mapping method designed specifically to reconstruct the surface intensity patterns of non‐radial stellar oscillations on components of eclipsing binaries. The method needs a geometric model of the binary, accepts the light curve and the detected pulsation frequencies on input, and on output yields estimates of the pulsation patterns, in the form of images, thus allowing a direct identification of the surface mode numbers (ℓ, m). Since it has minimal modelling requirements and can operate on photometric observations in arbitrary wavelength bands, dynamic eclipse mapping is well suited to analyse the wide‐band time series collected by space observatories. We have investigated the performance and the limitations of the method through extensive numerical tests on simulated data, in which almost all photometrically detectable modes with a latitudinal complexity ℓ− |m| ≤ 4 were properly restored. The method is able by its nature to simultaneously reconstruct multimode pulsations from data covering a sufficient number of eclipses as well as pulsations on components with a tilted rotation axis of a known direction. It can also be applied in principle to isolate the contribution of hidden modes from the light curve. Sensitivity tests show that moderate errors in the geometric parameters and the assumed limb darkening can be partially tolerated by the inversion, in the sense that the lower degree modes are still recoverable. Tidally induced or mutually resonant pulsations, however, are an obstacle that neither the eclipse mapping nor any other inversion technique can ever surpass. We conclude that, with reasonable assumptions, dynamic eclipse mapping could be a powerful tool for mode identification, especially in moderately close eclipsing binary systems, where the pulsating component is not seriously affected by tidal interactions so that the pulsations are intrinsic to them, and not a consequence of the binarity.

show abstract

Homogeneous spectrum and mixing transformations

Cited by 23 publications

References 7 publications

Event-plane dependent away-side jet-like correlation shape in Au+Au collisions at $\sqrt{s_{\rm NN}}$=200 GeV from STAR

Event-plane dependent away-side jet-like correlation shape in Au+Au collisions at $\sqrt{s_{\rm NN}}$=200 GeV from STAR

Indirect Fourier transform in the context of statistical inference

Photometric mode identification methods of non-radial pulsations in eclipsing binaries - I. Dynamic eclipse mapping

Contact Info

Product

Resources

About