Optimal Approximation for Submodular and Supermodular Optimization with Bounded Curvature

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or minimize a monotone decreasing supermodular function with a bounded total curvature c. Intuitively, the parameter c represents how nonlinear a function f is: when c = 0, f is linear, while for c = 1, f may be an arbitrary monotone increasing submodular function. For the case of submodular maximization with total curvature c, we obtain a (1 − c/e)-approximation—the first improvement over the greedy algorithm of of Conforti and Cornuéjols from 1984, which holds for a cardinality constraint, as well as a recent analogous result for an arbitrary matroid constraint. Our approach is based on modifications of the continuous greedy algorithm and nonoblivious local search, and allows us to approximately maximize the sum of a nonnegative, monotone increasing submodular function and a (possibly negative) linear function. We show how to reduce both submodular maximization and supermodular minimization to this general problem when the objective function has bounded total curvature. We prove that the approximation results we obtain are the best possible in the value oracle model, even in the case of a cardinality constraint. We define an extension of the notion of curvature to general monotone set functions and show a (1 − c)-approximation for maximization and a 1/(1 − c)-approximation for minimization cases. Finally, we give two concrete applications of our results in the settings of maximum entropy sampling, and the column-subset selection problem

Complicated variations of early optical afterglow of GRB 090726

We report on a detection of an early rising phase of optical afterglow (OA) of a long GRB 090726. We resolve a complicated profile of the optical light curve. We also investigate the relation of the optical and X-ray emission of this event. We make use of the optical photometry of this OA obtained by the 0.5 m telescope of AI AS CR, supplemented by the data obtained by other observers, and the X-ray Swift/XRT data. The optical emission peaked at ~ 17.5 mag (R) at t-T0 ~ 500 s. We find a complex profile of the light curve during the early phase of this OA: an approximately power-law rise, a rapid transition to a plateau, a weak flare superimposed on the center of this plateau, and a slowly steepening early decline followed by a power-law decay. We discuss several possibilities to explain the short flare on the flat top of the optical light curve at t-T0 ~ 500 s; activity of the central engine is favored although reverse shock cannot be ruled out. We show that power-law outflow with Theta_obs/Theta_c > 2.5 is the best case for OA of GRB 090726. The initial Lorentz factor is Gamma_0 ~ 230-530 in case of propagation of the blast wave in a homogeneous medium, while propagation of this wave in a wind environment gives Gamma_0 ~ 80-300. The value of Gamma_0 in GRB 090726 thus falls into the lower half of the range observed in GRBs and it may even lie on the lower end. We also show that both the optical and X-ray emission decayed simultaneously and that the spectral profile from X-ray to the optical band did not vary. This OA belongs to the least luminous ones in the phase of its power-law decay corresponding to that observed for the ensemble of OAs of long GRBs.Comment: 5 pages, 5 figures, accepted to A&

Properties and nature of Be stars: 29. Orbital and long-term spectral variations of \gamma\ Cassiopei\ae

A detailed analysis of more than 800 electronic high-resolution spectra of gamma Cas, which were obtained during a time interval of over 6000 days (16.84 yrs) at several observatories, documents the smooth variations in the density and/or extend of its circumstellar envelope. We found a clear anticorrelation between the peak intensity and FWHM of the H alpha emission, which seems to agree with recent models of such emission lines. The main result of this study is a confirmation of the binary nature of the object, determination of a reliable linear ephemeris T_{min.RV} = HJD (2452081.9$\pm$0.6) + (203.52$\pm$0.08)*E, and a rather definitive set of orbital elements. We clearly demonstrated that the orbit is circular within the limits of accuracy of our measurements and has a semi-amplitude of radial-velocity curve of 4.30$\pm$0.09 (km/s). No trace of the low-mass secondary was found. The time distribution of our spectra does not allow a reliable investigation of rapid spectral variations, which are undoubtedly present in the spectra. We postpone this investigation for a future study, based on series of dedicated whole-night spectral observations

Empiric Models of the Earth's Free Core Nutation

Free core nutation (FCN) is the main factor that limits the accuracy of the modeling of the motion of Earth's rotational axis in the celestial coordinate system. Several FCN models have been proposed. A comparative analysis is made of the known models including the model proposed by the author. The use of the FCN model is shown to substantially increase the accuracy of the modeling of Earth's rotation. Furthermore, the FCN component extracted from the observed motion of Earth's rotational axis is an important source for the study of the shape and rotation of the Earth's core. A comparison of different FCN models has shown that the proposed model is better than other models if used to extract the geophysical signal (the amplitude and phase of FCN) from observational data.Comment: 8 pages, 3 figures; minor update of the journal published versio

Properties and nature of Be stars: 27. Orbital and recent long-term variations of the Pleiades Be star Pleione = BU Tauri

Radial-velocity variations of the H-alpha emission measured on the steep wings of the H-alpha line, prewhitened for the long-time changes, vary periodically with a period of (218.025 +/- 0.022)d, confirming the suspected binary nature of the bright Be star Pleione, a member of the Pleiades cluster. The orbit seems to have a high eccentricity over 0.7, but we also briefly discuss the possibility that the true orbit is circular and that the eccentricity is spurious owing to the phase-dependent effects of the circumstellar matter. The projected angular separation of the spectroscopic orbit is large enough to allow the detection of the binary with large optical interferometers, provided the magnitude difference primary - secondary is not too large. Since our data cover the onset of a new shell phase up to development of a metallic shell spectrum, we also briefly discuss the recent long-term changes. We confirm the formation of a new envelope, coexisting with the previous one, at the onset of the new shell phase. We find that the full width at half maximum of the H-alpha profile has been decreasing with time for both envelopes. In this connection, we briefly discuss Hirata's hypothesis of precessing gaseous disk and possible alternative scenarios of the observed long-term changes

Streaming Algorithms for Submodular Function Maximization

We consider the problem of maximizing a nonnegative submodular set function $f:2^{\mathcal{N}} \rightarrow \mathbb{R}^+$ subject to a $p$-matchoid constraint in the single-pass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are {\em non-monotone}. We describe deterministic and randomized algorithms that obtain a $\Omega(\frac{1}{p})$-approximation using $O(k \log k)$-space, where $k$ is an upper bound on the cardinality of the desired set. The model assumes value oracle access to $f$ and membership oracles for the matroids defining the $p$-matchoid constraint.Comment: 29 pages, 7 figures, extended abstract to appear in ICALP 201

Report of the IAU/IAG Joint Working Group on Theory of Earth Rotation and Validation

This report focuses on some selected scientific outcomes of the activities developed by the IAU/IAG Joint Working Group on Theory of Earth rotation and validation along the term 2015–2019. It is based on its end-of-term report to the IAG Commission 3 published in the Travaux de l’IAG 2015–2019, which in its turn updates previous reports to the IAG and IAU, particularly the triennial report 2015–2018 to the IAU Commission A2, and the medium term report to the IAG Commission 3 (2015–2017). The content of the report has served as a basis for the IAG General Assembly to adopt Resolution 5 on Improvement of Earth rotation theories and models.JMF, AE, and JG were partially supported by Spanish Project AYA2016-79775-P (AEI/FEDER, UE). The work of RSG described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Support for that work was provided by the Earth Surface and Interior Focus Area of NASA’s Science Mission Directorate

New crustose Teloschistaceae in Central Europe

Central Europe in general is poor in Teloschistaceae lichen crusts (Caloplaca s. lat.). Diversity of these lichens is increased by the occurrence of some Arctic, Mediterranean and continental species, which are here close to the limits of their range. Examples include: 1) Caloplaca interfulgens, previously known from arid territories of northern Africa and western Asia, is recorded, surprisingly, from Austria, Czech Republic, Germany, Slovakia and southern Russia. In Central Europe, it is restricted to scattered xerothermic limestone outcrops. 2) Caloplaca scabrosa, previously known only from Svalbard, is recorded from the Sudetes in the Czech Republic. It is similar to, but not conspecific with, C. furfuracea. Its diagnostic characters include a blastidiate thallus and the presence of atranorin. Our results show that atranorin is absent in the majority of taxa related to C. furfuracea with only two exceptions: the sample from Eastern Carpathians, here called C. aff. scabrosa, and in one Sudetan sample identified as C. crenularia. 3) Caloplaca emilii, newly described below, is closely related to the Mediterranean C. areolata. We consider C. emilii a Mediterranean species rarely occurring in higher latitudes in Austria, the Czech Republic and Germany. It is distinguished from C. areolata mainly by the presence of vegetative diaspores (blastidia); a possible role of blastidia in the distribution pattern of C. emilii is discussed below. Status of the names Caloplaca areolata, C. isidiigera and C. spalatensisis, formerly used for the new taxon, is clarified. 4) Caloplaca molariformis, newly described below, belongs to the Pyrenodesmia group (a lineage of Caloplaca without anthraquinones). It is a continental species, frequently collected on limestone or lime-rich tuffs in steppes or deserts in Turkey, Iran, western Kazakhstan and southern Russia, and is also known from eastern Ukraine and southern Slovakia. Caloplaca molariformis is characterized by its thick thallus with fungal and algal tissues arranged in high stacks. 5) Caloplaca substerilis, newly described below, is distinguished from the closely related C. ulcerosa by its endophloeodal or minutely squamulose thallus with soralia formed in bark crevices or on margins of squamules. While C. ulcerosa has a maritime distribution in Europe, C. substerilis is typically a continental species. North American continental lichens called C. ulcerosa are phylogenetically closer and more similar to C. substerilis. The positions within Teloschistaceae of the taxa considered are demonstrated by ITS phylogenies. The distributions of C. areolata, C. emilii and C. interfulgens are mapped. The new species are fully described using more than a hundred phenotype characters, and diagnostic characters are indicated separately. Copyright © British Lichen Society 2013