Four generated, squarefree, monomial ideals

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 201

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Effect of Grazing, Mowing, or Herbicide on Leafy Spurge Control

Leafy spurge (euphorbia esula L.) is an herbaceous perennial which is deep rooted and can reproduce by seeds and rhizomes. First introduced into North America in the 1800’s from Europe, it now covers 25 states in the USA and several provinces in Canada. It is a major concern in North Dakota, South Dakota, Wyoming, Montana, and Nebraska. Leafy spurge is considered a noxious weed that is extremely competitive, establishing itself in pastureland and roadsides. Bangsund et al. (1997) estimated that by 2005, uncontrolled leafy spurge acres would reach 18.5 million in the Northern Great Plains. The cost of leafy spurge is estimated to be in the 100’s of millions of dollars due to lost grazing through a reduction of available AUM’s (animal unit months) and treatment costs which may not be economically feasible. This is impart due to the fact that cattle avoid eating leafy spurge because of post-ingestive negative feedbacks from plant toxins (Kronberg et al., 1993) and avoid grazing in areas where leafy spurge canopy cover is high, thus reducing grass production and utilization (Hein and Miller, 1992). Do to the high costs of herbicides and their ineffective control in the long-term (Lym and Messersmith, 1985), biological controls such as sheep and goats as well as the flea beetle have become more popular tools in controlling leafy spurge (Bangsund et al., 2000). In a pasture setting sheep and goats readily graze forbs and do not experience the build up of toxins that cattle do, making small ruminants ideal biological controls for leafy spurge. The object of this trial was to measure the effectiveness of various control methods on leafy spurge

Citizen participation in news

The process of producing news has changed significantly due to the advent of the Web, which has enabled the increasing involvement of citizens in news production. This trend has been given many names, including participatory journalism, produsage, and crowd-sourced journalism, but these terms are ambiguous and have been applied inconsistently, making comparison of news systems difficult. In particular, it is problematic to distinguish the levels of citizen involvement, and therefore the extent to which news production has genuinely been opened up. In this paper we perform an analysis of 32 online news systems, comparing them in terms of how much power they give to citizens at each stage of the news production process. Our analysis reveals a diverse landscape of news systems and shows that they defy simplistic categorisation, but it also provides the means to compare different approaches in a systematic and meaningful way. We combine this with four case studies of individual stories to explore the ways that news stories can move and evolve across this landscape. Our conclusions are that online news systems are complex and interdependent, and that most do not involve citizens to the extent that the terms used to describe them imply

Absolutely Koszul algebras and the Backelin-Roos property

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property

Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

Dielectric multilayer waveguides for TE and TM mode matching

We analyse theoretically for the first time to our knowledge the perfect phase matching of guided TE and TM modes with a multilayer waveguide composed of linear isotropic dielectric materials. Alongside strict investigation into dispersion relations for multilayer systems, we give an explicit qualitative explanation for the phenomenon of mode matching on the basis of the standard one-dimensional homogenization technique, and discuss the minimum number of layers and the refractive index profile for the proposed device scheme. Direct applications of the scheme include polarization-insensitive, intermodal dispersion-free planar propagation, efficient fibre-to-planar waveguide coupling and, potentially, mode filtering. As a self-sufficient result, we present compact analytical expressions for the mode dispersion in a finite, N-period, three-layer dielectric superlattice.Comment: 13 pages with figure

Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids

To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (or defined for a matroid in general) from various sets of Betti numbers of Stanley-Reisner rings of simplicial complexes associated to the matroid