A Conceptual Probabilistic Framework for Annotation Aggregation of Citizen Science Data

Over the last decade, hundreds of thousands of volunteers have contributed to science by collecting or analyzing data. This public participation in science, also known as citizen science, has contributed to significant discoveries and led to publications in major scientific journals. However, little attention has been paid to data quality issues. In this work we argue that being able to determine the accuracy of data obtained by crowdsourcing is a fundamental question and we point out that, for many real-life scenarios, mathematical tools and processes for the evaluation of data quality are missing. We propose a probabilistic methodology for the evaluation of the accuracy of labeling data obtained by crowdsourcing in citizen science. The methodology builds on an abstract probabilistic graphical model formalism, which is shown to generalize some already existing label aggregation models. We show how to make practical use of the methodology through a comparison of data obtained from different citizen science communities analyzing the earthquake that took place in Albania in 2019.

Analytical halo models of cosmic tidal fields

ABSTRACT The non-linear cosmic web environment of dark matter haloes plays a major role in shaping their growth and evolution, and potentially also affects the galaxies that reside in them. We develop an analytical (halo model) formalism to describe the tidal field of anisotropic halocentric density distributions, as characterized by the halocentric tidal tensor $\left\langle \, T_{ij}\, \right\rangle (\lt R)$ spherically averaged on scale R ∼ 4Rvir for haloes of virial radius Rvir. We focus on axisymmetric anisotropies, which allows us to explore simple and intuitive toy models of (sub)halo configurations that exemplify some of the most interesting anisotropies in the cosmic web. We build our models around the spherical Navarro–Frenk–White profile after describing it as a Gaussian mixture, which leads to almost fully analytical expressions for the ‘tidal anisotropy’ scalar α(< 4Rvir) extracted from the tidal tensor. Our axisymmetric examples include (i) a spherical halo at the axis of a cylindrical filament, (ii) an off-centred satellite in a spherical host halo, and (iii) an axisymmetric halo. Using these, we demonstrate several interesting results. For example, the tidal tensor at the axis of a pure cylindrical filament gives α(fil)(< R) = 1/2 exactly, for any R. Also, α(< 4Rvir,sat) for a satellite of radius Rvir,sat as a function of its hostcentric distance is a sensitive probe of dynamical mass-loss of the satellite in its host environment. Finally, we discuss a number of potentially interesting extensions and applications of our formalism that can deepen our understanding of the multiscale phenomenology of the cosmic web.

Simple halo model formalism for the cosmic infrared background and its correlation with the thermal Sunyaev-Zel’dovich effect

Modelling the anisotropies in the cosmic infrared background (CIB) on all the scales is a challenging task because the nature of the galaxy evolution is complex and too many parameters are therefore often required to fit the observational data. We present a new halo model for the anisotropies of the CIB using only four parameters. Our model connects the mass accretion on the dark matter haloes to the star formation rate. Despite its relative simplicity, it is able to fit both the Planck and Herschel CIB power spectra and is consistent with the external constraints for the obscured star formation history derived from infrared deep surveys used as priors for the fit. Using this model, we find that the halo mass with the maximum efficiency for converting the accreted baryons into stars is log10Mmax = 12.94-0.02+0.02 M⊙, consistent with other studies. Accounting for the mass loss through stellar evolution, we find for an intermediate-age galaxy that the star formation efficiency defined as M⋆(z)/Mb(z) is equal to 0.19 and 0.21 at redshift 0.1 and 2, respectively, which agrees well with the values obtained by previous studies. A CIB model is used for the first time to simultaneously fit Planck and Herschel CIB power spectra. The high angular resolution of Herschel allows us to reach very small scales, making it possible to constrain the shot noise and the one-halo term separately, which is difficult to do using the Planck data alone. However, we find that large angular scale Planck and Herschel data are not fully compatible with the small-scale Herschel data (for ℓ > 3000). The CIB is expected to be correlated with the thermal Sunyaev-Zel’dovich (tSZ) signal of galaxy clusters. Using this halo model for the CIB and a halo model for the tSZ with a single parameter, we also provide a consistent framework for calculating the CIB × tSZ cross correlation, which requires no additional parameter. To a certain extent, the CIB at high frequencies traces galaxies at low redshifts that reside in the clusters contributing to the tSZ, giving rise to the one-halo term of this correlation, while the two-halo term comes from the overlap in the redshift distribution of the tSZ clusters and CIB galaxies. The CIB × tSZ correlation is thus found to be higher when inferred with a combination of two widely spaced frequency channels (e.g. 143 × 857 GHz). We also find that even at ℓ ∼ 2000, the two-halo term of this correlation is still comparable to the one-halo term and has to be accounted for in the total cross-correlation. The CIB, tSZ, and CIB × tSZ act as foregrounds when the kinematic SZ (kSZ) power spectrum is measured from the cosmic microwave background power spectrum and need to be removed. Because of its simplistic nature and the low number of parameters, the halo model formalism presented here for these foregrounds is quite useful for such an analysis to measure the kSZ power spectrum accurately.

Precedent Comparison in the Precedent Model Formalism: A Technical Note

We outline a formalization of precedent comparison in the precedent model formalism.

Jahn–Teller coupling to moiré phonons in the continuum model formalism for small-angle twisted bilayer graphene

We show how to include the Jahn–Teller coupling of moiré phonons to the electrons in the continuum model formalism which describes small-angle twisted bilayer graphene. These phonons, which strongly couple to the valley degree of freedom, are able to open gaps at most integer fillings of the four flat bands around the charge neutrality point. Moreover, we derive the full quantum mechanical expression of the electron–phonon Hamiltonian, which may allow accessing phenomena such as the phonon-mediated superconductivity and the dynamical Jahn–Teller effect.

Sofic entropy of Gaussian actions

Associated to any orthogonal representation of a countable discrete group, is a probability measure-preserving action called the Gaussian action. Using the Polish model formalism we developed before, we compute the entropy (in the sense of Bowen [J. Amer. Math. Soc.23(2010) 217–245], Kerr and Li [Invent. Math.186(2011) 501–558]) of Gaussian actions when the group is sofic. Computation of entropy for Gaussian actions has only been done when the acting group is abelian and thus our results are new, even in the amenable case. Fundamental to our approach are methods of non-commutative harmonic analysis and$C^{\ast }$-algebras which replace the Fourier analysis used in the abelian case.

Hyperspherical three-body model calculation for the bound 3,1S-states of Coulombic systems

In this paper, hyperspherical three-body model formalism has been applied for the calculation of energies of the low-lying bound [Formula: see text]-states of neutral helium and helium like Coulombic three-body systems having nuclear charge (z) in the range [Formula: see text]. Energies of [Formula: see text]-states are also calculated for those having nuclear charge in the range [Formula: see text]. The calculation of the coupling potential matrix elements of the two-body potentials has been simplified by the use of Raynal–Revai Coefficients (RRC). The three-body wave function in the Schrödinger equation when expanded in terms of hyperspherical harmonics (HH), leads to an infinite set of coupled differential equation (CDE) which for practical purposes is truncated to a finite set and the truncated set of CDE’s are solved by renormalized Numerov method (RNM) to get the energy (E). The calculated energy is compared with the ones of the literature.