From Monomials to Words to graphs

Given a finite alphabet X and an ordering on the letters, the map \sigma sends each monomial on X to the word that is the ordered product of the letter powers in the monomial. Motivated by a question on Groebner bases, we characterize ideals I in the free commutative monoid (in terms of a generating set) such that the ideal generated by \sigma(I) in the free monoid is finitely generated. Whether there exists an ordering such that is finitely generated turns out to be NP-complete. The latter problem is closely related to the recognition problem for comparability graphs.Comment: 27 pages, 2 postscript figures, uses gastex.st

Discrete Dynamical Systems: A Brief Survey

Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization

Semi-empirical analysis of Sloan Digital Sky Survey galaxies III. How to distinguish AGN hosts

We consider the techniques to distinguish normal star forming (NSF) galaxies and active galactic nuclei (AGN) hosts using optical spectra. The observational data base is a set of 20000 galaxies extracted from the Sloan Digital Sky Survey, for which we have determined the emission line intensities after subtracting the stellar continuum obtained from spectral synthesis. Our analysis is based on photoionization models computed using the stellar ionizing radiation predicted by Starburst 99 and, for the AGNs, a broken power-law spectrum. We explain why, among the four classical emission line diagnostic diagrams, the [OIII]/Hb vs [NII]/Ha one works best. We show however, that none of these diagrams is efficient in detecting AGNs in metal poor galaxies, should such cases exist. We propose a new divisory line between ``pure'' NSF galaxies and AGN hosts. We also show that a classification into NSF and AGN galaxies using only [NII]/Ha is feasible and useful. Finally, we propose a new classification diagram, the DEW diagram, plotting D_n(4000) vs max(EW[OII],EW[NeIII]). This diagram can be used with optical spectra for galaxies with redshifts up to z = 1.3, meaning an important progress over classifications proposed up to now. Since the DEW diagram requires only a small range in wavelength, it can also be used at even larger redshifts in suitable atmospheric windows. It also has the advantage of not requiring stellar synthesis analysis to subtract the stars and of allowing one to see ALL the galaxies in the same diagram, including passive galaxies.Comment: 14 pages, 9 figures, accepted for publication in MNRAS (replaced on august 3, 2006, eqs 6 and 7 corrected

Retired galaxies: not to be forgotten in the quest of the star formation -- AGN connection

We propose a fresh look at the Main Galaxy Sample of the Sloan Digital Sky Survey by packing the galaxies in stellar mass and redshift bins. We show how important it is to consider the emission-line equivalent widths, in addition to the commonly used emission-line ratios, to properly identify retired galaxies (i.e. galaxies that have stopped forming stars and are ionized by their old stellar populations) and not mistake them for galaxies with low-level nuclear activity. We find that the proportion of star-forming galaxies decreases with decreasing redshift in each mass bin, while that of retired galaxies increases. Galaxies with $M_\star > 10^{11.5} M_\odot$ have formed all their stars at redshift larger than 0.4. The population of AGN hosts is never dominant for galaxy masses larger than $10^{10} M_\odot$. We warn about the effects of stacking galaxy spectra to discuss galaxy properties. We estimate the lifetimes of active galactic nuclei (AGN) relying entirely on demographic arguments --- i.e. without any assumption on the AGN radiative properties. We find upper-limit lifetimes of about 1--5 Gyr for detectable AGN in galaxies with masses between $10^{10}$--$10^{12} M_\odot$. The lifetimes of the AGN-dominated phases are a few $10^8$ yr. Finally, we compare the star-formation histories of star-forming, AGN and retired galaxies as obtained by the spectral synthesis code STARLIGHT. Once the AGN is turned on it inhibits star formation for the next $\sim$ 0.1 Gyr in galaxies with masses around $10^{10} M_\odot$, $\sim$ 1 Gyr in galaxies with masses around $10^{11} M_\odot$.Comment: accepted for MNRAS figure resolution has been degraded with respect to what will be published in MNRA

Comment on "Fisheries Management"

The recent article by O’Leary et al. (2011) raises an important question about the relationship between science and those who manage fisheries. They contend that fishery managers do not give due cognisance to scientific advice and consistently set Total Allowable Catches (TACs) above values advised by scientists (which they define as ‘‘political adjustment’’). The authors claim that the consequence of this is that there is a high probability of stock collapse in the next 40 years. They use a simulation model to argue that this probability may exceed 80% at the mean level of political adjustment adopted by managers, depending on the degree of environmental variability and life history strategy of the fish