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Ultraviolet (UV) wavelength observations have made a significant contribution to our understanding of hot stellar populations of star clusters. Multi-wavelength spectral energy distributions (SEDs) of stars, including ultraviolet observations, have proven to be an excellent tool for discovering unresolved hot companions in exotic stars such as blue straggler stars (BSS), thereby providing helpful clues to constrain their formation mechanisms. Melotte 66 is a 3.4 Gyr old open cluster located at a distance of 4810 pc. We identify the cluster members by applying the ML-MOC algorithm on Gaia EDR3 data. Based on our membership identification, we find 1162 members, including 14 BSS candidates, 2 yellow straggler candidates (YSS), and one subdwarf B candidate (sdB). We generated SEDs for 11 BSS candidates and the sdB candidate using Swift/UVOT data combined with other archival data in the optical and IR wavelengths. We discover a hot companion of one BSS candidate, BSS3, with temperature of 38000$_{-6000}^{+7000}$ K, luminosity of 2.99$_{-1.86}^{+5.47}$ L$_\odot$, and radius of 0.04$_{-0.005}^{+0.008}$ R$_\odot$. This hot companion is a likely low-mass WD with an estimated mass of 0.24 $\text{-}$ 0.44 M$_\odot$. We report one BSS candidate, BSS6, as an Algol-type eclipsing binary with a period of 0.8006 days, based on the Gaia DR3 variability classification. We suggest that BSS3 is formed via either the Case A or Case B mass-transfer channel, whereas BSS6 is formed via the Case A mass transfer.

We consider classes of non-manipulable social choice functions with range of cardinality at most two within a set of at least two alternatives. We provide the functional form for each of the classes we consider. This functional form is a characterization that explicitly describes how a social choice function of that particular class selects the collective choice corresponding to a profile. We provide a unified formulation of these characterizations using the new concept of "character". The choice of the character, depending on the class of social choice functions, gives the functional form of all social choice functions of the class., Comment: JEL Code: D71

We present a variety of refined conditions for $\sigma$ algebras $\mathcal{A}$ (on a set $X$), $\mathcal{F}, \mathcal{G}$ (on a set $U$) such that the distributivity equation $$(\mathcal{A}\otimes\mathcal{F})\cap(\mathcal{A}\otimes\mathcal{G})=\mathcal{A}\otimes\left(\mathcal{F}\cap\mathcal{G}\right),$$ holds -- or is violated. \\ The article generalizes the results in arXiv:2007.06095 and includes a positive result for $\sigma$ algebras generated by at most countable partitions, was not covered before. We also present a proof that counterexamples may be constructed whenever $X$ is uncountable and there exist two $\sigma$-algebras on $X$ which are both countably separated, but their intersection is not. We present examples of such structures. In the last section, we extend Theorem 3.3 of arXiv:2007.06095 from analytic to the setting of Blackwell spaces., Comment: 8 Pages

We report the laser-plasma accelerator-based X-ray sources development at ELI beamlines. One of the main objectives of ELI Beamlines is to provide beams of ultrashort particle and complex X-ray sources to users from various research fields. Two hard X-ray betatron sources with high photon flux based on laser-plasma acceleration (LPA) are being commissioned. The first source is the Gammatron beamline located in Experimental Hall E2. It provides X-ray pulses of energies from 1-100 keV in betatron and up to a MeV in Compton scheme. A novel X-ray optics has been designed as a focusing optics of these hard X-ray sources for the user application. The second hard X-ray source based on LPA is being developed in the ELI plasma physics platform (P3) that will serve as an active diagnostics HED and Laboratory astrophysics, multi-beam experiments, and fundamental research. This source is now being commissioned, we will present the first experimental results. Besides, we have proposed a novel scheme for enhancing the X-ray flux based on betatron oscillations enhanced from nonlinear resonances due to interaction with a two-color laser field. In addition, we will introduce a novel optical probing technique with high sensitivity to characterize a low-density gas target for a laser-plasma accelerator. It has been achieved by employing multiple passes of the probe beam through the object and relay-imaging of the object between the individual passes., Comment: 48th EPS Conference on Plasma Physics

Melody extraction is a vital music information retrieval task among music researchers for its potential applications in education pedagogy and the music industry. Melody extraction is a notoriously challenging task due to the presence of background instruments. Also, often melodic source exhibits similar characteristics to that of the other instruments. The interfering background accompaniment with the vocals makes extracting the melody from the mixture signal much more challenging. Until recently, classical signal processing-based melody extraction methods were quite popular among melody extraction researchers. The ability of the deep learning models to model large-scale data and the ability of the models to learn automatic features by exploiting spatial and temporal dependencies inspired many researchers to adopt deep learning models for melody extraction. In this paper, an attempt has been made to review the up-to-date data-driven deep learning approaches for melody extraction from polyphonic music. The available deep models have been categorized based on the type of neural network used and the output representation they use for predicting melody. Further, the architectures of the 25 melody extraction models are briefly presented. The loss functions used to optimize the model parameters of the melody extraction models are broadly categorized into four categories and briefly describe the loss functions used by various melody extraction models. Also, the various input representations adopted by the melody extraction models and the parameter settings are deeply described. A section describing the explainability of the block-box melody extraction deep neural networks is included. The performance of 25 melody extraction methods is compared. The possible future directions to explore/improve the melody extraction methods are also presented in the paper., Comment: 72 pages