Simulating Uniform Hashing in Constant Time and Optimal Space

Many algorithms and data structures employing hashing have been analyzed under the uniform hashing assumption, i.e., the assumption that hash functions behave like truly random functions. In this paper it is shown how to implement hash functions that can be evaluated on a RAM in constant time, and behave like truly random functions on any set of n inputs, with high probability. The space needed to represent a function is O(n) words, which is the best possible (and a polynomial improvement compared to previous fast hash functions). As a consequence, a broad class of hashing schemes can be implemented to meet, with high probability, the performance guarantees of their uniform hashing analysis

Local starburst galaxies and their descendants

Despite strong interest in the starburst (hereafter SB) phenomenon, the concept remains ill-defined. We use a strict definition of SB to examine the statistical properties of local SB and post-starburst (hereafter PB) galaxies. We also seek relationships to active galaxies. Potential SB galaxies are selected from the SDSS DR7 and their stellar content is analysed. We apply an age dependent dust attenuation correction and derive star formation rates (SFR), ages and masses of the young and old populations. The photometric masses nicely agree with dynamical masses derived from the H-alpha emission line width. To select SB galaxies, we use the birthrate parameter b=SFR/, requiring b>=3. The PB sample is selected from the citerion EW(Hdelta_abs)>=6 A. Only 1% of star-forming galaxies are found to be SB galaxies. They contribute 3-6% to the stellar production and are therefore unimportant for the local star formation activity. The median SB age is 70 Myr, roughly independent of mass. The b-parameter strongly depends on burst age. Values close to b=60 are found at ages ~10 Myr, while almost no SBs are found at ages >1 Gyr. The median baryonic burst mass fraction of sub-L* galaxies is 5%, decreasing slowly with mass. The median mass fraction of the recent burst in the PB sample is 5-10%. The age-mass distribution of the progenitors of the PBs is bimodal with a break at log(M)~10.6 above which the ages are doubled. The SB and PB luminosity functions (hereafter LFs) follow each other closely until M_r~-21, when AGNs begin to dominate. The PB LF continues to follow the AGN LF while SB loose significance. This suggests that the number of luminous SBs is underestimated by about one dex at high luminosities, due to large amounts of dust and/or AGN blending. It also indicates that the SB phase preceded the AGN phase. We also discuss the conditions for global gas outflow caused by stellar feedback.Comment: Accepted for publication in Astronomy and Astrophysics. This is an extended, substantially revised and corrected version with partly modified conclusion

Моделирование потребления активной мощности насосных агрегатов с изменяющимся режимом водопотребления

Материалы XX Междунар. науч.-техн. конф. студентов, аспирантов и молодых ученых, Гомель, 23–24 апр. 2020 г

FIGS: Spectral fitting constraints on the star formation history of massive galaxies since Cosmic Noon

We constrain the stellar population properties of a sample of 52 massive galaxies, with stellar mass log Ms>10.5, over the redshift range 0.5<z<2 by use of observer-frame optical and near-infrared slitless spectra from HST's ACS and WFC3 grisms. The deep exposures (~100 ks) allow us to target individual spectra of massive galaxies to F160W=22.5AB. Our spectral fitting approach uses a set of six base models adapted to the redshift and spectral resolution of each observation, and fits the weights of the base models, including potential dust attenuation, via an MCMC method. Our sample comprises a mixed distribution of quiescent (19) and star-forming galaxies (33). We quantify the width of the age distribution (Dt) that is found to dominate the variance of the retrieved parameters according to Principal Component Analysis. The population parameters follow the expected trend towards older ages with increasing mass, and Dt appears to weakly anti-correlate with stellar mass, suggesting a more efficient star formation at the massive end. As expected, the redshift dependence of the relative stellar age (measured in units of the age of the Universe at the source) in the quiescent sample rejects the hypothesis of a single burst (aka monolithic collapse). Radial colour gradients within each galaxy are also explored, finding a wider scatter in the star-forming subsample, but no conclusive trend with respect to the population parameters.Comment: 20 pages, 12+3 figures, 4+3 tables. MNRAS, in pres

The Science Case for Multi-Object Spectroscopy on the European ELT

This White Paper presents the scientific motivations for a multi-object spectrograph (MOS) on the European Extremely Large Telescope (E-ELT). The MOS case draws on all fields of contemporary astronomy, from extra-solar planets, to the study of the halo of the Milky Way and its satellites, and from resolved stellar populations in nearby galaxies out to observations of the earliest 'first-light' structures in the partially-reionised Universe. The material presented here results from thorough discussions within the community over the past four years, building on the past competitive studies to agree a common strategy toward realising a MOS capability on the E-ELT. The cases have been distilled to a set of common requirements which will be used to define the MOSAIC instrument, entailing two observational modes ('high multiplex' and 'high definition'). When combined with the unprecedented sensitivity of the E-ELT, MOSAIC will be the world's leading MOS facility. In analysing the requirements we also identify a high-multiplex MOS for the longer-term plans for the E-ELT, with an even greater multiplex (>1000 targets) to enable studies of large-scale structures in the high-redshift Universe. Following the green light for the construction of the E-ELT the MOS community, structured through the MOSAIC consortium, is eager to realise a MOS on the E-ELT as soon as possible. We argue that several of the most compelling cases for ELT science, in highly competitive areas of modern astronomy, demand such a capability. For example, MOS observations in the early stages of E-ELT operations will be essential for follow-up of sources identified by the James Webb Space Telescope (JWST). In particular, multi-object adaptive optics and accurate sky subtraction with fibres have both recently been demonstrated on sky, making fast-track development of MOSAIC feasible.Comment: Significantly expanded and updated version of previous ELT-MOS White Paper, so there is some textual overlap with arXiv:1303.002

Constructing Evolutionary Trees - Algorithms and Complexity

In this thesis three general problems concerning construction of evolutionary trees are considered. Algorithms for the problems are presented and the complexity of the problems is investigated. The thesis consists of three corresponding parts. The first part is devoted to the problem of constructing evolutionary trees in the experiment model. Different algorithms for the problem are given, including an optimal algorithm for constructing evolutionary trees and an optimal algorithm for merging two evolutionary trees. Matching lower bounds are also provided. The second part of the thesis presents results related to the inferred consensus tree problem. The optimization version of the problem is shown to be NP-complete and two heuristic algorithms are presented. Further, the ordered version of the problem is studied. In the last part of the thesis the complexity of the maximum homeomorphic subtree problem is examined. The problem is shown to be hard to approximate, unless P=NP, even for trees of constant height, whereas a constant approximation ratio is obtained in case of a constant number of trees of constant height

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