Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems

Let \(\mathcal{C}\) be a uniform clutter and let A be the incidence matrix of \(\mathcal{C}\). We denote the column vectors of A by v ₁,…,v _q . Under certain conditions we prove that \(\mathcal{C}\) is vertex critical. If \(\mathcal{C}\) satisfies the max-flow min-cut property, we prove that A diagonalizes over ? to an identity matrix and that v ₁,…,v _q form a Hilbert basis. We also prove that if \(\mathcal{C}\) has a perfect matching such that \(\mathcal{C}\) has the packing property and its vertex covering number is equal to 2, then A diagonalizes over ? to an identity matrix. If A is a balanced matrix we prove that any regular triangulation of the cone generated by v ₁,…,v _q is unimodular. Some examples are presented to show that our results only hold for uniform clutters. These results are closely related to certain algebraic properties, such as the normality or torsion-freeness, of blowup algebras of edge ideals and to finitely generated abelian groups. They are also related to the theory of Gröbner bases of toric ideals and to Ehrhart rings.     

Insects on urban plants: contrasting the flower head feeding assemblages on native and exotic hosts

Exotic plant species very often comprise a large proportion of urban floras. Because herbivorous insects depend on the presence of suitable host plants to maintain their populations, it is imperative to elucidate the relative importance of native and exotic hosts to understand the response of herbivorous guilds to urbanization. By using a plant-herbivore system composed of Asteraceae hosts and flower-head endophagous insects, we investigated whether the diversity and composition of herbivorous insects differs between native and exotic host-plant species in an urban environment. Although we found only seven exotic Asteraceae among the 30 species recorded, the overall abundance of exotics was considerably greater than that of native host plants. Overall, the exotic host species supported a small subset of the herbivore assemblage found on the native ones. The number of herbivore species per host species was significantly higher among the native plants, but we did not find a difference in herbivore abundance. Moreover, the higher taxonomic composition of herbivores on exotic Asteraceae was reduced, being composed of only three genera and two families from a total of 16 genera and six families of herbivores. These results provide support for the idea that plants outside of their original geographic distribution have lower loads of enemies than phylogenetically related native species. Our findings indicate that native host plants in urban areas play a critical role in supporting the native herbivorous insect fauna.     

THE MONOPOLY OF VIOLENCE: EVIDENCE FROM COLOMBIA

Many states in Latin America, Africa, and Asia lack the monopoly of violence, even though this was identified by Max Weber as the foundation of the state, and thus the capacity to govern effectively. In this paper we develop a new perspective on the establishment of the monopoly of violence. We build a model to explain the incentive of central states to eliminate nonstate armed actors (paramilitaries) in a democracy. The model is premised on the idea that paramilitaries may choose to and can influence elections. Since paramilitaries have preferences over policies, this reduces the incentives of the politicians they favor to eliminate them. We then investigate these ideas using data from Colombia between 1991 and 2006. We first present regression and case study evidence supporting our postulate that paramilitary groups can have significant effects on elections for the legislature and the executive. Next, we show that the evidence is also broadly consistent with the implication of the model that paramilitaries tend to persist to the extent that they deliver votes to candidates for the executive whose preferences are close to theirs and that this effect is larger in areas where the presidential candidate would have otherwise not done as well. Finally, we use roll‐call votes to illustrate a possible “quid pro quo” between the executive and paramilitaries in Colombia.     

Building Financial Satisfaction

This paper aims to contribute further research on the conceptualization of individual financial satisfaction as a particular domain of satisfaction with life as a whole. Based on the 2003 Survey on Living Conditions and Poverty for Andalucía (Spain) and using a self-reported measure of welfare, ordered probit models are used to analyze the extent to which individual financial satisfaction can be solely explained by income in absolute terms, or alternatively, by taking into account the importance of relative income in its two dimensions: (1) personal aspirations as individual’s adaptation to previous and future income levels (intra-individual comparisons), and (2) social comparisons as individual’s concern for her peer’s income (inter-personal dependency).     

LETTER GRADING GOVERNMENT EFFICIENCY

We mailed letters to non‐existent business addresses in 159 countries (10 per country), and measured whether they come back to the return address in the United States and how long it takes. About 60% of the letters were returned, taking over six months, on average. The results provide new objective indicators of government efficiency across countries, based on a simple and universal service, and allow us to shed light on its determinants. The evidence suggests that both technology and management quality influence government efficiency, just as they do that of the private sector.     

Comparisons of coherent systems with non-identically distributed components

The signature-based mixture representations for coherent systems are a good way to obtain distribution-free comparisons of systems. Unfortunately, these representations only hold for systems whose component lifetimes are independent and identically distributed (IID) or exchangeable (i.e., their joint distribution is invariant under permutations). In this paper we obtain comparison results for generalized mixtures, that is, for reliability functions that can be written as linear combinations of some baseline reliability functions with positive and negative coefficients. These results are based on some concepts in Graph Theory. We apply these results to obtain new comparison results for coherent systems without the IID or exchangeability assumptions by using their generalized mixture representations based on the minimal path sets.     

A maximum likelihood estimator for left-truncated lifetimes based on probabilistic prior information about time of occurrence

In forestry, many processes of interest are binary and they can be modeled using lifetime analysis. However, available data are often incomplete, being interval- and right-censored as well as left-truncated, which may lead to biased parameter estimates. While censoring can be easily considered in lifetime analysis, left truncation is more complicated when individual age at selection is unknown. In this study, we designed and tested a maximum likelihood estimator that deals with left truncation by taking advantage of prior knowledge about the time when the individuals enter the experiment. Whenever a model is available for predicting the time of selection, the distribution of the delayed entries can be obtained using Bayes' theorem. It is then possible to marginalize the likelihood function over the distribution of the delayed entries in the experiment to assess the joint distribution of time of selection and time to event. This estimator was tested with continuous and discrete Gompertz-distributed lifetimes. It was then compared with two other estimators: a standard one in which left truncation was not considered and a second estimator that implemented an analytical correction. Our new estimator yielded unbiased parameter estimates with empirical coverage of confidence intervals close to their nominal value. The standard estimator leaded to an overestimation of the long-term probability of survival.