Relational Width of First-Order Expansions of Homogeneous Graphs with Bounded Strict Width

Solving the algebraic dichotomy conjecture for constraint satisfaction problems over structures first-order definable in countably infinite finitely bounded homogeneous structures requires understanding the applicability of local-consistency methods in this setting. We study the amount of consistency (measured by relational width) needed to solve CSP(?) for first-order expansions ? of countably infinite homogeneous graphs ? := (A; E), which happen all to be finitely bounded. We study our problem for structures ? that additionally have bounded strict width, i.e., for which establishing local consistency of an instance of CSP(?) not only decides if there is a solution but also ensures that every solution may be obtained from a locally consistent instance by greedily assigning values to variables, without backtracking. Our main result is that the structures ? under consideration have relational width exactly (2, ?_?) where ?_? is the maximal size of a forbidden subgraph of ?, but not smaller than 3. It beats the upper bound: (2 m, 3 m) where m = max(arity(?)+1, ?, 3) and arity(?) is the largest arity of a relation in ?, which follows from a sufficient condition implying bounded relational width given in [Manuel Bodirsky and Antoine Mottet, 2018]. Since ?_? may be arbitrarily large, our result contrasts the collapse of the relational bounded width hierarchy for finite structures ?, whose relational width, if finite, is always at most (2,3)

Smooth Approximations and Relational Width Collapses

We prove that relational structures admitting specific polymorphisms (namely, canonical pseudo-WNU operations of all arities n ? 3) have low relational width. This implies a collapse of the bounded width hierarchy for numerous classes of infinite-domain CSPs studied in the literature. Moreover, we obtain a characterization of bounded width for first-order reducts of unary structures and a characterization of MMSNP sentences that are equivalent to a Datalog program, answering a question posed by Bienvenu et al.. In particular, the bounded width hierarchy collapses in those cases as well

MOA-2019-BLG-008Lb : a new microlensing detection of an object at the planet/brown dwarf boundary

Funding: R.A.S. and E.B. gratefully acknowledge support from NASA grant 80NSSC19K0291. Y.T. and J.W. acknowledge the support of DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (WA 1047/11-1). K.H. acknowledges support from STFC grant ST/R000824/1. J.C.Y. acknowledges support from NSF grant No. AST-2108414. Work by C.H. was supported by the grants of the National Research Foundation of Korea (2019R1A2C2085965 and 2020R1A4A2002885). D.M.B. acknowledges the support of the NYU Abu Dhabi Research Enhancement Fund under grant RE124. This work was partly supported by the National Science Foundation of China (grant Nos. 11333003, 11390372, and 11761131004 to S.M.). The MOA project is supported by JSPS KAKENHI grant Nos. JSPS24253004, JSPS26247023, JSPS23340064, JSPS15H00781, JP16H06287, and JP17H02871.We report on the observations, analysis and interpretation of the microlensing event MOA-2019-BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite-source effects were observed. Therefore, the angular Einstein ring radius θE cannot be measured from the light curve alone. However, the large event duration, tE ∼ 80 days, allows a precise measurement of the microlensing parallax πE. In addition to the constraints on the angular radius θ* and the apparent brightness Is of the source, we employ the Besançon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two galactic models: the companion is likely a resident of the brown dwarf desert with a mass Mp ∼ 30 MJup, and the host is a main-sequence dwarf star. The lens lies along the line of sight to the Galactic bulge, at a distance of ≤4 kpc. We estimate that in about 10 yr the lens and source will be separated by ∼55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground- or space-based observatories.Publisher PDFPeer reviewe

Brown dwarf companions in microlensing binaries detected during the 2016-2018 seasons

Aims. With the aim of finding microlensing binaries containing brown dwarf (BD) companions, we investigate the microlensing survey data collected during the 2016-2018 seasons.Methods. For this purpose, we first modeled lensing events with light curves exhibiting anomaly features that are likely to be produced by binary lenses. We then sorted out BD companion binary-lens events by applying the criterion that the companion-to-primary mass ratio is q less than or similar to 0.1. With this procedure, we identify six binaries with candidate BD companions: OGLE-2016-BLG-0890L, MOA-2017-BLG-477L, OGLE-2017-BLG-0614L, KMT-2018-BLG-0357L, OGLE-2018-BLG-1489L, and OGLE-2018-BLG-0360L.Results. We estimated the masses of the binary companions by conducting Bayesian analyses using the observables of the individual lensing events. According to the Bayesian estimation of the lens masses, the probabilities for the lens companions of the events OGLE-2016-BLG-0890, OGLE-2017-BLG-0614, OGLE-2018-BLG-1489, and OGLE-2018-BLG-0360 to be in the BD mass regime are very high with P-BD > 80%. For MOA-2017-BLG-477 and KMT-2018-BLG-0357, the probabilities are relatively low with P-BD = 61% and 69%, respectively

MOA-2019-BLG-008Lb: A New Microlensing Detection of an Object at the Planet/Brown Dwarf Boundary

We report on the observations, analysis and interpretation of the microlensing event MOA-2019-BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite-source effects were observed. Therefore, the angular Einstein ring radius theta (E) cannot be measured from the light curve alone. However, the large event duration, t (E) similar to 80 days, allows a precise measurement of the microlensing parallax pi (E). In addition to the constraints on the angular radius theta (*) and the apparent brightness I ( s ) of the source, we employ the Besancon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two galactic models: the companion is likely a resident of the brown dwarf desert with a mass M ( p ) similar to 30 M (Jup), and the host is a main-sequence dwarf star. The lens lies along the line of sight to the Galactic bulge, at a distance of <= 4 kpc. We estimate that in about 10 yr the lens and source will be separated by similar to 55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground- or space-based observatories