Deflationary Language

In the following recessionary story, numbers and letters deflate instead of inflate, and any word that has a comparative element is changed to its lower or lesser counterpart

Disturbing Verbing and Pre-verbing

Humorous commentary on the English language trend of creating verbs out of nouns which he calls verbing.

Integrable Lattice Models for Conjugate An(1)A^{(1)}_n

A new class of $A^{(1)}_n$ integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the $A^{(1)}_n$ conjugate modular invariants, there being a model for each value of the rank and level. The Boltzmann weights are parameterized by elliptic theta functions and satisfy the Yang-Baxter equation for any fixed value of the elliptic nome q. At q=0, the models provide representations of the Hecke algebra and are expected to lead in the continuum limit to coset conformal field theories related to the $A^{(1)}_n$ conjugate modular invariants.Comment: 18 pages. v2: minor changes, such as page 11 footnot

Aggregate Demand and Supply

This paper is part of a broader project that provides a microfoundation to the General Theory of J.M. Keynes. I call this project 'old Keynesian economics' to distinguish it from new-Keynesian economics, a theory that is based on the idea that to make sense of Keynes we must assume that prices are sticky. I describe a multi-good model in which I interpret the definitions of aggregate demand and supply found in the General Theory through the lens of a search theory of the labor market. I argue that Keynes' aggregate supply curve can be interpreted as the aggregate of a set of first order conditions for the optimal choice of labor and, using this interpretation, I reintroduce a diagram that was central to the textbook teaching of Keynesian economics in the immediate post-war period.

Solutions of the boundary Yang-Baxter equation for ADE models

We present the general diagonal and, in some cases, non-diagonal solutions of the boundary Yang-Baxter equation for a number of related interaction-round-a-face models, including the standard and dilute A_L, D_L and E_{6,7,8} models.Comment: 32 pages. Sections 7.2 and 9.2 revise

Higher Spin Alternating Sign Matrices

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The case r=1 gives standard alternating sign matrices, while the case in which all matrix entries are nonnegative gives semimagic squares. We show that the higher spin alternating sign matrices of size n are the integer points of the r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices are the standard alternating sign matrices of size n. It then follows that, for fixed n, these matrices are enumerated by an Ehrhart polynomial in r.Comment: 41 pages; v2: minor change

Osculating Paths and Oscillating Tableaux

The combinatorics of certain osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. More specifically, the paths being considered have fixed start and end points on respectively the lower and right boundaries of a rectangle in the square lattice, each path can take only unit steps rightwards or upwards, and two different paths are permitted to share lattice points, but not to cross or share lattice edges. Such paths correspond to configurations of the six-vertex model of statistical mechanics with appropriate boundary conditions, and they include cases which correspond to alternating sign matrices and various subclasses thereof. Referring to points of the rectangle through which no or two paths pass as vacancies or osculations respectively, the case of primary interest is tuples of paths with a fixed number $l$ of vacancies and osculations. It is then shown that there exist natural bijections which map each such path tuple $P$ to a pair $(t,\eta)$, where $\eta$ is an oscillating tableau of length $l$ (i.e., a sequence of $l+1$ partitions, starting with the empty partition, in which the Young diagrams of successive partitions differ by a single square), and $t$ is a certain, compatible sequence of $l$ weakly increasing positive integers. Furthermore, each vacancy or osculation of $P$ corresponds to a partition in $\eta$ whose Young diagram is obtained from that of its predecessor by respectively the addition or deletion of a square. These bijections lead to enumeration formulae for osculating paths involving sums over oscillating tableaux.Comment: 65 pages; expanded versio

Ichthyoplankton Adjacent to Live-Bottom Habitats in Onslow Bay, North Carolina

The abundance and distribution of ichthyoplankton adjacent to live-bottom habitats (rock outcroppings containing rich, sessile invertebrate communities and many species of tropical and subtropical fishes) in open-shelf waters « 55-m isobath) in Onslow Bay, North Carolina, were investigated. Larvae of reef-associated genera, especially the economically important subtropical and tropical members of the families Haemulidae (Haemulon), Lutjanidae (Lutjanus and Rltomboplites), Serranidae (Mycteroperca and Epinephelus), and Sparidae (Calamus and Pagrus) were targeted. Larvae representing 40 families were collected in neuston tows. Commonly collected reef-associated families were Balistidae, Blenniidae (dominated by the reef-associated Parablennius marmoreus) , Mullidae, and Gobiidae. Larvae representing 70 families were collected in subsurface tows. Reef-associated families commonly collected included Apogonidae, Balistidae, Gobiidae, Haemulidae, LutJanidae, Scaridae, and Serranidae. Larval Haemulon sp (p)., Lutjanus sp(p)., and Rltomboplites aurorubens were commonly collected and thus it is likely that these taxa spawn in Onslow Bay and recruit to live-bottom sites within the area. Other families of fishes commonly collected but generally not considered reef-associated included Bothidae, Callionymidae, Carangidae, Clupeidae, Engraulidae, and Ophidiidae. Estuarine-dependent species (e.g. the clupeid Brevoortia tyrannus and the sciaenids Leiostomus xanthurus and Micropogonias undulatus) were an important component of the ichthyoplankton during late fall and winter. The frequent occurrence of larvae from oceanic species (e.g. gonostomatids and myctophids) indicated that Gulf Stream waters had intruded onto the shelf, transporting these larvae to open-shelf waters off North Carolina.(PDF file containes 36 pages.

Fractional Perfect b-Matching Polytopes. I: General Theory

The fractional perfect b-matching polytope of an undirected graph G is the polytope of all assignments of nonnegative real numbers to the edges of G such that the sum of the numbers over all edges incident to any vertex v is a prescribed nonnegative number b_v. General theorems which provide conditions for nonemptiness, give a formula for the dimension, and characterize the vertices, edges and face lattices of such polytopes are obtained. Many of these results are expressed in terms of certain spanning subgraphs of G which are associated with subsets or elements of the polytope. For example, it is shown that an element u of the fractional perfect b-matching polytope of G is a vertex of the polytope if and only if each component of the graph of u either is acyclic or else contains exactly one cycle with that cycle having odd length, where the graph of u is defined to be the spanning subgraph of G whose edges are those at which u is positive.Comment: 37 page

Graptemys pearlensis

Number of Pages: 4Integrative BiologyGeological Science