Generalizations of Eulerian partially ordered sets, flag numbers, and the Mobius function

A partially ordered set is r-thick if every nonempty open interval contains at least r elements. This paper studies the flag vectors of graded, r-thick posets and shows the smallest convex cone containing them is isomorphic to the cone of flag vectors of all graded posets. It also defines a k-analogue of the Mobius function and k-Eulerian posets, which are 2k-thick. Several characterizations of k-Eulerian posets are given. The generalized Dehn-Sommerville equations are proved for flag vectors of k-Eulerian posets. A new inequality is proved to be valid and sharp for rank 8 Eulerian posets

The Growth of Red Sequence Galaxies in a Cosmological Hydrodynamic Simulation

We examine the cosmic growth of the red sequence in a cosmological hydrodynamic simulation that includes a heuristic prescription for quenching star formation that yields a realistic passive galaxy population today. In this prescription, halos dominated by hot gas are continually heated to prevent their coronae from fueling new star formation. Hot coronae primarily form in halos above \sim10^12 M\odot, so that galaxies with stellar masses \sim10^10.5 M\odot are the first to be quenched and move onto the red sequence at z > 2. The red sequence is concurrently populated at low masses by satellite galaxies in large halos that are starved of new fuel, resulting in a dip in passive galaxy number densities around \sim10^10 M\odot. Stellar mass growth continues for galaxies even after joining the red sequence, primarily through minor mergers with a typical mass ratio \sim1:5. For the most massive systems, the size growth implied by the distribution of merger mass ratios is typically \sim2\times the corresponding mass growth, consistent with observations. This model reproduces mass-density and colour-density trends in the local universe, with essentially no evolution to z = 1, with the hint that such relations may be washed out by z \sim 2. Simulated galaxies are increasingly likely to be red at high masses or high local overdensities. In our model, the presence of surrounding hot gas drives the trends with both mass and environment.Comment: 15 pages, 8 figures. MNRAS accepte

Finding complex balanced and detailed balanced realizations of chemical reaction networks

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che

Finding weakly reversible realizations of chemical reaction networks using optimization

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph theory and important former results on the dense realizations of CRNs. The proposed method is also capable of determining if no dynamically equivalent weakly reversible structure exists for a given reaction network with a previously fixed complex set.Comment: 18 pages, 9 figure