On covers of cyclic acts over monoids

In (Bull. Lond. Math. Soc. 33:385–390, 2001) Bican, Bashir and Enochs finally solved a long standing conjecture in module theory that all modules over a unitary ring have a flat cover. The only substantial work on covers of acts over monoids seems to be that of Isbell (Semigroup Forum 2:95–118, 1971), Fountain (Proc. Edinb. Math. Soc. (2) 20:87–93, 1976) and Kilp (Semigroup Forum 53:225–229, 1996) who only consider projective covers. To our knowledge the situation for flat covers of acts has not been addressed and this paper is an attempt to initiate such a study. We consider almost exclusively covers of cyclic acts and restrict our attention to strongly flat and condition (P) covers. We give a necessary and sufficient condition for the existence of such covers and for a monoid to have the property that all its cyclic right acts have a strongly flat cover (resp. (P)-cover). We give numerous classes of monoids that satisfy these conditions and we also show that there are monoids that do not satisfy this condition in the strongly flat case. We give a new necessary and sufficient condition for a cyclic act to have a projective cover and provide a new proof of one of Isbell’s classic results concerning projective covers. We show also that condition (P) covers are not unique, unlike the situation for projective covers

Do Proto-Jovian Planets Drive Outflows?

We discuss the possibility that gaseous giant planets drive strong outflows during early phases of their formation. We consider the range of parameters appropriate for magneto-centrifugally driven stellar and disk outflow models and find that if the proto-Jovian planet or accretion disk had a magnetic field of >~ 10 Gauss and moderate mass inflow rates through the disk of less than 10^-7 M_J/yr that it is possible to drive an outflow. Estimates based both on scaling from empirical laws observed in proto-stellar outflows and the magneto-centrigugal disk and stellar+disk wind models suggest that winds with mass outflow rates of 10^-8 M_J/yr and velocities of order ~ 20 km/s could be driven from proto-Jovian planets. Prospects for detection and some implications for the formation of the solar system are briefly discussed.Comment: AAS Latex, accepted for Ap

Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

Statistical relational learning with soft quantifiers

Quantification in statistical relational learning (SRL) is either existential or universal, however humans might be more inclined to express knowledge using soft quantifiers, such as ``most'' and ``a few''. In this paper, we define the syntax and semantics of PSL^Q, a new SRL framework that supports reasoning with soft quantifiers, and present its most probable explanation (MPE) inference algorithm. To the best of our knowledge, PSL^Q is the first SRL framework that combines soft quantifiers with first-order logic rules for modelling uncertain relational data. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results

Demography and Life Histories of Sympatric Patas Monkeys, Erythrocebus patas, and Vervets, Cercopithecus aethiops, in Laikipia, Kenya

Mortality patterns are thought to be strong selective forces on life history traits, with high adult mortality and low immature mortality favoring early and rapid reproduction. Patas monkeys (Erythrocebus patas) have the highest potential rates of population increase for their body size of any haplorhine primate because they reproduce both earlier and more often. We report here 10 yr of comparative demographic data on a population of patas monkeys and a sympatric population of vervet monkeys (Cercopithecus aethiops), a closely related species differing in aspects of social system, ecology, and life history. The data reveal that 1) adult female patas monkeys have significantly higher mortality than adult female vervets; 2) infant mortality in patas monkeys is relatively low compared to the norm for mammals because it is not significantly different from that of adult female patas monkeys; and 3) infant mortality is significantly higher than adult female mortality in vervets. For both species, much of the mortality could be attributed to predation. An epidemic illness was also a major contributor to the mortality of adult female patas monkeys whereas chronic exposure to pathogens in a cold and damp microenvironment may have contributed to the mortality of infant vervets. Both populations experienced large fluctuations during the study period. Our results support the prediction from demographic models of life history evolution that high adult mortality relative to immature mortality selects for early maturation

Bucolic Complexes

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In particular, we characterize bucolic complexes by some properties of their 2-skeleta and 1-skeleta (that we call bucolic graphs), by which several known results are generalized. We also show that locally-finite bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties.Comment: 45 pages, 4 figure

Food site residence time and female competitive relationships in wild gray-cheeked mangabeys (Lophocebus albigena)

Authors of socioecological models propose that food distribution affects female social relationships in that clumped food resources, such as fruit, result in strong dominance hierarchies and favor coalition formation with female relatives. A number of Old World monkey species have been used to test predictions of the socioecological models. However, arboreal forest-living Old World monkeys have been understudied in this regard, and it is legitimate to ask whether predominantly arboreal primates living in tropical forests exhibit similar or different patterns of behavior. Therefore, the goal of our study was to investigate female dominance relationships in relation to food in gray-cheeked mangabeys (Lophocebus albigena). Since gray-cheeked mangabeys are largely frugivorous, we predicted that females would have linear dominance hierarchies and form coalitions. In addition, recent studies suggest that long food site residence time is another important factor in eliciting competitive interactions. Therefore, we also predicted that when foods had long site residence times, higher-ranking females would be able to spend longer at the resource than lower-ranking females. Analyses showed that coalitions were rare relative to some other Old World primate species, but females had linear dominance hierarchies. We found that, contrary to expectation, fruit was not associated with more agonism and did not involve long site residence times. However, bark, a food with a long site residence time and potentially high resource value, was associated with more agonism, and higher-ranking females were able to spend more time feeding on it than lower-ranking females. These results suggest that higher-ranking females may benefit from higher food and energy intake rates when food site residence times are long. These findings also add to accumulating evidence that food site residence time is a behavioral contributor to female dominance hierarchies in group-living species

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum dimension of a bounded face, then the number of vertices of the polyhedron is O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For inputs in general position the number of bounded faces is O(n^d). For any fixed d, we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a polynomial number of linear programs

Species richness, but not phylogenetic diversity, influences community biomass production and temporal stability in a re‐examination of 16 grassland biodiversity studies

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111813/1/fec12432.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/111813/2/fec12432-sup-0002-Suppinfo.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/111813/3/fec12432-sup-0001-LaySummary.pd