Faces of weight polytopes and a generalization of a theorem of Vinberg

The paper is motivated by the study of graded representations of Takiff algebras, cominuscule parabolics, and their generalizations. We study certain special subsets of the set of weights (and of their convex hull) of the generalized Verma modules (or GVM's) of a semisimple Lie algebra \lie g. In particular, we extend a result of Vinberg and classify the faces of the convex hull of the weights of a GVM. When the GVM is finite-dimensional, we ask a natural question that arises out of Vinberg's result: when are two faces the same? We also extend the notion of interiors and faces to an arbitrary subfield \F of the real numbers, and introduce the idea of a weak \F-face of any subset of Euclidean space. We classify the weak \F-faces of all lattice polytopes, as well as of the set of lattice points in them. We show that a weak \F-face of the weights of a finite-dimensional \lie g-module is precisely the set of weights lying on a face of the convex hull.Comment: Statement changed in Section 4. Typos fixed and some proofs updated. Submitted to "Algebra and Representation Theory." 18 page

Lack of trust in maternal support is associated with negative interpretations of ambiguous maternal behavior

Attachment theory assumes that children who lack trust in maternal availability for support are more inclined to interpret maternal behavior in congruence with their expectation that mother will remain unavailable for support. To provide the first test of this assumption, early adolescents (9-13 years old) were asked to assess whether ambiguous interactions with mother should be interpreted in a positive or a negative way. In our sample (n = 322), results showed that early adolescents' lack of trust in their mother's availability for support was related to more negative interpretations of maternal behavior. The associations remained significant after controlling for depressive mood. The importance of these findings for our understanding of attachment theory, attachment stability, and clinical practice are discussed

Analyses showing how religiosity, social activities, and drug-related beliefs mediate relationships between post-high school experiences and substance use

https://deepblue.lib.umich.edu/bitstream/2027.42/137877/1/occ50.pd

Variations in social contexts and their effect on adolescent inhalant use: a latent profile investigation.

The social contexts surrounding the use and abuse of inhalants are poorly understood. The aim of this study was to utilize latent profile analysis (LPA) to identify specific subgroups of adolescents based on social contextual effects surrounding inhalant use episodes in a sample of 279 adolescent inhalant users. Findings revealed that a three-class solution exhibited the best empirical and conceptual fit with the data. Identified classes represented a gradient of low, moderate, and high levels of contextual effects where approximately one third of adolescent inhalant users reported high levels of inhalant use in response to social contextual influences. Subsequent validation analysis showed that these gradient-based classes were directly correspondent with severity in measures of psychopathology, past drug use, variety of inhalants used, and measures of impulsivity and fearlessness. Results indicate heterogeneity in contextual effects on inhalant use and suggest that follow-up studies should examine the role that susceptibility and exposure to contextual effects has on inhalant use.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61150/1/Context Variations.pd

State trust in middle childhood: an experimental manipulation of maternal support

A

Simulated Warming Differentially Affects the Growth and Competitive Ability of Centaurea maculosa Populations from Home and Introduced Ranges

Climate warming may drive invasions by exotic plants, thereby raising concerns over the risks of invasive plants. However, little is known about how climate warming influences the growth and competitive ability of exotic plants from their home and introduced ranges. We conducted a common garden experiment with an invasive plant Centaurea maculosa and a native plant Poa pratensis, in which a mixture of sand and vermiculite was used as a neutral medium, and contrasted the total biomass, competitive effects, and competitive responses of C. maculosa populations from Europe (home range) and North America (introduced range) under two different temperatures. The warming-induced inhibitory effects on the growth of C. maculosa alone were stronger in Europe than in North America. The competitive ability of C. maculosa plants from North America was greater than that of plants from Europe under the ambient condition whereas this competitive ability followed the opposite direction under the warming condition, suggesting that warming may enable European C. maculosa to be more invasive. Across two continents, warming treatment increased the competitive advantage instead of the growth advantage of C. maculosa, suggesting that climate warming may facilitate C. maculosa invasions through altering competitive outcomes between C. maculosa and its neighbors. Additionally, the growth response of C. maculosa to warming could predict its ability to avoid being suppressed by its neighbors

Interference competition and invasion: spatial structure, novel weapons and resistance zones

Certain invasive plants may rely on interference mechanisms (allelopathy, e.g.) to gain competitive superiority over native species. But expending resources on interference presumably exacts a cost in another life-history trait, so that the significance of interference competition for invasion ecology remains uncertain. We model ecological invasion when combined effects of preemptive and interference competition govern interactions at the neighborhood scale. We consider three cases. Under "novel weapons," only the initially rare invader exercises interference. For "resistance zones" only the resident species interferes, and finally we take both species as interference competitors. Interference increases the other species' mortality, opening space for colonization. However, a species exercising greater interference has reduced propagation, which can hinder its colonization of open sites. Interference never enhances a rare invader's growth in the homogeneously mixing approximation to our model. But interference can significantly increase an invader's competitiveness, and its growth when rare, if interactions are structured spatially. That is, interference can increase an invader's success when colonization of open sites depends on local, rather than global, species densities. In contrast, interference enhances the common, resident species' resistance to invasion independently of spatial structure, unless the propagation-cost is too great. Increases in background mortality (i.e., mortality not due to interference) always reduce the effectiveness of interference competition

A review of the phytochemical support for the shifting defence hypothesis

Several theories have been developed to explain why invasive species are very successful and develop into pest species in their new area. The shifting defence hypothesis (SDH) argues that invasive plant species quickly evolve towards new defence levels in the invaded area because they lack their specialist herbivores but are still under attack by local (new) generalist herbivores. The SDH predicts that plants should increase their cheap, toxic defence compounds and lower their expensive digestibility reducing compounds. As a net result resources are saved that can be allocated to growth and reproduction giving these plants a competitive edge over the local plant species. We conducted a literature study to test whether toxic defence compounds in general are increased in the invaded area and if digestibility reducing compounds are lowered. We specifically studied the levels of pyrrolizidine alkaloids, a toxin which is known for its beneficial and detrimental impact against specialists and generalists, respectively. Digestibility reducers did not show a clear trend which might be due to the small number of studies and traits measured. The meta analysis showed that toxic compounds in general and pyrrolizidine alkaloid levels specifically, increased significantly in the invaded area, supporting the predictions of the SDH that a fast evolution takes place in the allocation towards defence