Updown categories: Generating functions and universal covers

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to covering relations, and possibly nontrivial automorphism groups. We call such a category an "updown category". In this paper we give a precise definition of such categories and develop a theory for them. We also give a detailed account of ten examples, including updown categories of integer partitions, integer compositions, planar rooted trees, and rooted trees.Comment: arXiv admin note: substantial text overlap with arXiv:math/040245

Herpetofaunal Inventory of Arkansas Post National Memorial, Arkansas County, Arkansas

The Arkansas Post National Memorial (ARPO) is a unique historical landmark with an interesting herpetofaunal community. We conducted an amphibian and reptile inventory of this national park from 2000-2002. We found eight amphibian and 21 reptilian species inhabiting the park. These included eight species not previously identified at ARPO. Overall species richness was highest at Alligator Slough, although the northern portion of ARPO was relatively rich. Aquatic trophic guilds included 7 (36.8%) piscivores, 7 (36.8%) omnivores, 4 (21.1%) insectivores, and one (5.3%) carnivore. The terrestrial trophic guilds included 13 (76.5%) insectivores, 2 (11.8%) carnivores, and 1 (5.9%) each of omnivores and generalized carnivores. We provide a species list, analysis of the distributions, diversity relationships and the trophic guilds present at ARPO, including management recommendations for the conservation of the herpetofauna community at ARPO

Versican Expression during Synovial Joint Morphogenesis

The extracellular matrix (ECM) plays a critical role in governing cell behavior and phenotype during limb skeletogenesis. Chondroitin sulfate proteoglycans (Cspgs) are highly expressed in the ECM of precartilage mesenchymal condensations and are important to limb chondrogenesis and cartilage structure, but little is known regarding their involvement in formation of synovial joints in the embryonic limb. Matrix versican Cspg expression has previously been reported in the epiphysis of developing long bones and presumptive joint; however, detailed analysis has not yet been conducted. In the present study we immunolocalized versican and aggrecan Cspgs during chick elbow joint morphogenesis between HH st25-41 of development. In this study we show that versican and aggrecan expression initially overlapped in the incipient cartilage model of long bones in the wing, but versican was also highly expressed in the perichondrium and presumptive joint interzone during early stages of morphogenesis (HH st25-34). By HH st36-41 versican localization was restricted to the future articular surfaces of the developing joint and surrounding joint capsule while aggrecan localized in an immediately adjacent and predominately non-overlapping region of chondrogenic cells at the epiphyses. These results suggest a potential role for versican proteoglycan in development and maintenance of the synovial joint interzone

Promotion and Rowmotion

We present an equivariant bijection between two actions--promotion and rowmotion--on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and recent work of D. Armstrong, C. Stump, and H. Thomas on root posets and noncrossing partitions. We apply this bijection to several classes of posets, obtaining equivariant bijections to various known objects under rotation. We extend the same idea to give an equivariant bijection between alternating sign matrices under rowmotion and under B. Wieland's gyration. Finally, we define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions.Comment: 25 pages, 22 figures; final versio

The African honey bee: Factors contributing to a successful biological invasion

The African honey bee subspecies Apis mellifera scutellata has colonized much of the Americas in less than 50 years and has largely replaced European bees throughout its range in the New World. The African bee therefore provides an excellent opportunity to examine the factors that influence invasion success. We provide a synthesis of recent research on the African bee, concentrating on its ability to displace European honey bees. Specifically, we consider (a) the genetic composition of the expanding population and the symmetry of gene flow between African and European bees, (b) the mechanisms that favor the preservation of the African genome, and (c) the possible range and impact of the African bee in the United States

Universalism vs. Particularism: On the Limits of Major Power Order

Relations between major powers can be described as shifting between universalism and particularism. In periods of universalism, major powers try to work out acceptable rules of behavior among one another, whereas in periods of particularism, they emphasize special interests of special powers. The way historians see shifts in major power relations since 1816 largely follows such a classification. By comparing the policies pursued during four periods of universalism and four periods of particularism, as well as analysing what ended or initiated such periods, the limits of major power universalism can be evaluated. Particularly, the short-comings of the recent period of detente are illuminated. Also some principles for a more enduring form of universalism are suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68816/2/10.1177_002234338402100304.pd