Non-Nudgable Subgroups of Permutations

Motivated by a problem from behavioral economics, we study subgroups of permutation groups that have a certain strong symmetry. Given a fixed permutation, consider the set of all permutations with disjoint inversion sets. The group is called non-nudgable, if the cardinality of this set always remains the same when replacing the initial permutation with its inverse. It is called nudgable otherwise. We show that all full permutation groups, standard dihedral groups, half of the alternating groups, and any abelian subgroup are non-nudgable. In the right probabilistic sense, it is thus quite likely that a randomly generated subgroup is non-nudgable. However, the other half of the alternating groups are nudgable. We also construct a smallest possible nudgable group, a 6-element subgroup of the permutation group on 4 elements.Comment: new version contains some simplifications and extension

On semidefinite representations of non-closed sets

Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in semidefinite programming. There are several recent results on the question which sets are semidefinite representable. So far, all results focus on the case of closed sets. In this work we develop a new method to prove semidefinite representability of sets which are not closed. For example, the interior of a semidefinite representable set is shown to be semidefinite representable. More general, one can remove faces of a semidefinite representable set and preserve semidefinite representability, as long as the faces are parametrized in a suitable way.Comment: 13 page

X-ray Continuum Slope and X-ray Spectral Features in NLS1 Galaxies

The idea that some of the unusual features in the X-ray spectra of Narrow-Line Seyfert 1 galaxies (NLS1s) are due to the steep X-ray continuum is tested by comparing photoionization model calculations with various observed properties of Seyfert 1 galaxies. A meaningful comparison must involve the careful use of the right X-ray ionization parameter, designated here U(oxygen). When this is done, it is found that the strength of the continuum absorption features is insensitive to the exact slope of the 0.1-50 keV continuum. It is also shown that the complex of iron L-shell lines near 1 keV can produce strong absorption and emission features, depending on the gas distribution and line widths. While this may explain some unusual X-ray features in AGN, the predicted intensity of the features do not distinguish NLS1 from broader line sources. Finally, acceleration of highly ionized gas, by X-ray radiation pressure, is also not sensitive to the exact slope of the X-ray continuum.Comment: Invited talk presented at the Joint MPE,AIP,ESO workshop on NLS1s, Bad Honnef, Dec. 1999, to appear in New Astronomy Reviews; also available at http://wave.xray.mpe.mpg.de/conferences/nls1-worksho

Reverberation Mapping of High-z, High-luminosity Quasars

We present Reverberation Mapping results after monitoring a sample of 17 high-z, high-luminosity quasars for more than 10 years using photometric and spectroscopic capabilities. Continuum and line emission flux variability is observed in all quasars. Using cross-correlation analysis we successfully determine lags between the variations in the continuum and broad emission lines for several sources. Here we present a highlight of our results and the determined radius--luminosity relations for Ly_alpha and CIV.Comment: Contributed talk at conference "Quasars at all cosmic epochs", held in Padova 2-7 April 2017, published in Frontiers in Astronomy and Space Science

The effect of radiation pressure on emission line profiles and black hole mass determination in active galactic nuclei

We present a new analysis of the motion of broad line region (BLR) clouds in active galactic nuclei (AGNs) taking into account the combined influence of gravity and radiation pressure force. We calculate cloud orbits under a large range of conditions and include the effect of a changing column density as a function of location. The dependence of radiation pressure force on the level of ionization and the column density are accurately computed. The main results are: a. The mean cloud location r(BLR) and the line widths (FWHMs) are combined in such a way that the simple virial mass estimate, r{BLR} FWHM^2/G, gives a reasonable approximation to the black hole mass M even when radiation pressure force is important. The reason is that L/M rather than L is the main parameter affecting the planar cloud motion. b. Reproducing the observed mean radius, FWHM and intensity of H-beta and CIV 1549 requires at least two different populations of clouds. c. The cloud location is a function of both L^{1/2} and L/M. Given this we suggest a new approximation for r(BLR) which, when inserted into the BH mass equation, results in a new approximation for M. The new expression involves L^{1/2}, FWHM and two constants that are obtained from a comparison with available M-sigma mass estimates. It deviates only slightly from the old mass estimate at all luminosities. d. The quality of present black hole mass estimators depends, critically, on the way the present M-sigma AGN sample (16 objects) represents the AGN population, in particular the distribution of Eddington ratios.Comment: Accepted for publication in ApJ, 11 pages, 9 figure

Evolution of Time Preferences and Attitudes Towards Risk

This paper explores a general model of the evolution and adaption of hedonic utility. It is shown that optimal utility will be increasing strongly in regions where choices have to be made often and decision mistakes have a severe impact on fitness. Several applications are suggested. In the context of intertemporal preferences, the model offers an evolutionary explanation for the existence of conflicting short- and long-run interests that lead to dynamic inconsistency. Concerning attitudes towards risk, an evolutionary explanation is given for S-shaped value functions that adjust to the decision-maker’s environment.Evolution of Utility, Risk Attitudes, Time Preferences

Black Hole Growth to z = 2 - I: Improved Virial Methods for Measuring M_BH and L/L_Edd

We analyze several large samples of AGN in order to establish the best tools required to study the evolution of black hole mass (M_BH) and normalized accretion rate (L/L_Edd). The data include spectra from the SDSS, 2QZ and 2SLAQ surveys at z<2, and a compilation of smaller samples with 0<z<5. We critically evaluate the usage of the MgII(2798A) and CIV(1549A) lines, and adjacent continuum bands, as estimators of M_BH and L/L_Edd, by focusing on sources where one of these lines is observed together with Hbeta. We present a new, luminosity-dependent bolometric correction for the monochromatic luminosity at 3000A, L_3000, which is lower by a factor of 1.75 than those used in previous studies. We also re-calibrate the use of L_3000 as an indicator for the size of the broad emission line region (R_BLR) and find that R_BLR is proportional to L_3000^0.62. We find that FWHM(MgII)\simeqFWHM(Hb) for all sources with FWHM(MgII)<6000 km/s. Beyond this FWHM, the MgII line width seems to saturate. The spectral region of the MgII line can thus be used to reproduce Hb-based estimates of M_BH and L/L_Edd, with negligible systematic differences and a scatter of 0.3 dex. The width of the CIV line, on the other hand, shows no correlation with either that of the Hb or the MgII lines and we could not identify the reason for this discrepancy. The scatter of M_BH(CIV), relative to M_BH(Hb) is of almost 0.5 dex. Moreover, 46% of the sources have FWHM(CIV)<FWHM(Hb), in contrast with the basic premise of the virial method, which predicts FWHM(CIV)/FWHM(Hbeta)~1.9. Thus, the CIV line cannot be used to obtain precise estimates of M_BH. We conclude by presenting the observed evolution of M_BH and L/L_Edd with cosmic epoch. The steep rise of L/L_Edd with redshift up to z~1 flattens towards the expected maximal value of L/L_Edd~1, with lower-M_BH sources showing higher values of L/L_Edd at all redshifts. [Abridged]Comment: 23 pages, including 2 appendices and 18 figures. Accepted for publication in MNRAS (minor corrections