The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

PSR J1641+3627F: a low-mass He white dwarf orbiting a possible high-mass neutron star in the globular cluster M13

We report on the discovery of the companion star to the millisecond pulsar J1631+3627F in the globular cluster M13. By means of a combination of optical and near-UV high-resolution observations obtained with the Hubble Space Telescope, we identified the counterpart at the radio source position. Its location in the color-magnitude diagrams reveals that the companion star is a faint (V \sim 24.3) He-core white dwarf. We compared the observed companion magnitudes with those predicted by state-of-the-art binary evolution models and found out that it has a mass of 0.23 \pm 0.03 Msun, a radius of 0.033^+0.004_-0.005 Rsun and a surface temperature of 11500^+1900_-1300 K. Combining the companion mass with the pulsar mass function is not enough to determine the orbital inclination and the neutron star mass; however, the last two quantities become correlated: we found that either the system is observed at a low inclination angle, or the neutron star is massive. In fact, assuming that binaries are randomly aligned with respect to the observer line of sight, there is a \sim 70% of probability that this system hosts a neutron star more massive than 1.6 Msun. In fact, the maximum and median mass of the neutron star, corresponding to orbital inclination angles of 90 deg and 60 deg, are M_NS,max = 3.1 \pm 0.6 Msun and M_NS,med = 2.4 \pm 0.5 Msun, respectively. On the other hand, assuming also an empirical neutron star mass probability distribution, we found that this system could host a neutron star with a mass of 1.5 \pm 0.1 Msun if orbiting with a low-inclination angle around 40 deg.Comment: Accepted for publication by Ap

Гастро-эзофагиальная рефлюксная болезнь: атипичные клинические проявления и влияние на качество жизни больных

Spitalul Clinic al Ministerului Sănătăţii, Chişinău, Catedra Medicină internă nr. 6, USMF „Nicolae Testemiţanu”, Spitalul Feroviar, Chişinău, Conferinţa Ştiinţifico-Practică „Medicina modernă, actualităţi şi perspective”, consacrată aniversării de 40 de ani ai Spitalului Clinic al Ministerului Sănătăţii, 27-28 mai, 2010, Chişinău, Republica MoldovaIn this work data are presented about the influence of gastro-esophageal reflux disease on patient’s lifestyle, having an obscure evolution, but sometimes with severe atypical evolution and complications (hemorrhages, perforations, esophageal cancer) which may lead to death.В настоящем обзоре литературы приводятся данные о влиянии гастро-эзофагиальной рефлюксной болезни на качество жизни больных, которая может протекать со стертой клинической картиной, а иногда с тяжелым атипичным течением и развитием различных тяжелых осложнений (кровотечения, перфорации, рак пищевода) приводящих к смерти

Stellar archaeology with Gaia: the Galactic white dwarf population

Gaia will identify several 1e5 white dwarfs, most of which will be in the solar neighborhood at distances of a few hundred parsecs. Ground-based optical follow-up spectroscopy of this sample of stellar remnants is essential to unlock the enormous scientific potential it holds for our understanding of stellar evolution, and the Galactic formation history of both stars and planets.Comment: Summary of a talk at the 'Multi-Object Spectroscopy in the Next Decade' conference in La Palma, March 2015, to be published in ASP Conference Series (editors Ian Skillen & Scott Trager

An irradiated-Jupiter analogue hotter than the Sun

Planets orbiting close to hot stars experience intense extreme-ultraviolet radiation, potentially leading to atmosphere evaporation and to thermal dissociation of molecules. However, this extreme regime remains mainly unexplored due to observational challenges. Only a single known ultra-hot giant planet, KELT-9b, receives enough ultraviolet radiation for molecular dissociation, with a day-side temperature of ~4,600K. An alternative approach uses irradiated brown dwarfs as hot-Jupiter analogues. With atmospheres and radii similar to those of giant planets, brown dwarfs orbiting close to hot Earth-sized white-dwarf stars can be directly detected above the glare of the star. Here we report observations revealing an extremely irradiated low-mass companion to the hot white dwarf WD0032-317. Our analysis indicates a day-side temperature of ~8,000K, and a day-to-night temperature difference of ~6,000K. The amount of extreme-ultraviolet radiation (with wavelengths 100-912\r{A}) received by WD0032-317B is equivalent to that received by planets orbiting close to stars as hot as a late B-type stars, and about 5,600 times higher than that of KELT-9b. With a mass of ~75-88 Jupiter masses, this near-hydrogen-burning-limit object is potentially one of the most massive brown dwarfs known.Comment: Authors' version of the article published in Nature Astronomy (DOI https://doi.org/10.1038/s41550-023-02048-z

Resonant Tunneling in Photonic Double Quantum Well Heterostructures

Here, we study the resonant photonic states of photonic double quantum well (PDQW) heterostructures composed of two different photonic crystals. The heterostructure is denoted as B/A/B/A/B, where photonic crystals A and B act as photonic wells and barriers, respectively. The resulting band structure causes photons to become confined within the wells, where they occupy discrete quantized states. We have obtained an expression for the transmission coefficient of the PDQW heterostructure using the transfer matrix method and have found that resonant states exist within the photonic wells. These resonant states occur in split pairs, due to a coupling between degenerate states shared by each of the photonic wells. It is observed that when the resonance energy lies at a bound photonic state and the two photonic quantum wells are far away from each other, resonant states appear in the transmission spectrum of the PDQW as single peaks. However, when the wells are brought closer together, coupling between bound photonic states causes an energy-splitting effect, and the transmitted states each have two peaks. Essentially, this means that the system can be switched between single and double transparent states. We have also observed that the total number of resonant states can be controlled by varying the width of the photonic wells, and the quality factor of transmitted peaks can be drastically improved by increasing the thickness of the outer photonic barriers. It is anticipated that the resonant states described here can be used to develop new types of photonic-switching devices, optical filters, and other optoelectronic devices