Large butterfly Cayley graphs and digraphs

We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large $k$ and for values of $d$ taken from a large interval, the largest known Cayley graphs and digraphs of diameter $k$ and degree $d$. Another method yields, for sufficiently large $k$ and infinitely many values of $d$, Cayley graphs and digraphs of diameter $k$ and degree $d$ whose order is exponentially larger in $k$ than any previously constructed. In the directed case, these are within a linear factor in $k$ of the Moore bound.Comment: 7 page

The permutation classes Av(1234,2341) and Av(1243,2314)

We investigate the structure of the two permutation classes defined by the sets of forbidden patterns \{{1234, 2341}\} and \{{1243, 2314}\}. By considering how the Hasse graphs of permutations in these classes can be built from a sequence of rooted source graphs, we determine their algebraic generating functions. Our approach is similar to that of “adding a slice”, used previously to enumerate various classes of polyominoes and other combinatorial structures. To solve the relevant functional equations, we make extensive use of the kernel method

Growth rates of geometric grid classes of permutations

Geometric grid classes of permutations have proven to be key in investigations of classical permutation pattern classes. By considering the representation of gridded permutations as words in a trace monoid, we prove that every geometric grid class has a growth rate which is given by the square of the largest root of the matching polynomial of a related graph. As a consequence, we characterise the set of growth rates of geometric grid classes in terms of the spectral radii of trees, explore the influence of "cycle parity" on the growth rate, compare the growth rates of geometric grid classes against those of the corresponding monotone grid classes, and present new results concerning the effect of edge subdivision on the largest root of the matching polynomial

The Fiscal Dimensions of Ethiopia's Transition and Reconstruction

sub-Saharan Africa, Ethiopia, conflict, economic reform

Helper T cells for cytotoxic T lymphocytes need not be I region restricted.

We investigated the antigenic requirements for restimulation of H-2- restricted cytolytic T lymphocytes (CTL) in vitro to determine whether H-2 I region-restricted helper T cells are required in these responses. In one set of experiments, we studied the in vitro response of (responder x nonresponder)F(1) female T cells to the male antigen H-Y. We chose to examine this response because it has been suggested that the defect in nonresponder strains is a failure of helper T cells to recognize H-Y in association with nonresponder I region determinants. However, we find that nonresponder male stimulator cells are as effective as F(1) male stimulator cells at inducing H-Y-specific CTL responses. This finding calls into question reports that secondary CTL responses to H-Y are dependent upon the activation of H-Y- specific helper T cells restricted to responder type I region determinants. In a second set of experiments, we examined the requirements for restimulation of H-2-restricted T cells specific for minor-histocompatibility antigens from long-term mixed lymphocyte cultures. These cultures were established by repeatedly restimulating cultures of specific T cells with H- 2-matched stimulator cells expressing foreign minor histocompatibility antigens. We found that H-2D-restricted T ceils, including CTL, could be restimulated with cells that were matched with the responding cells at only the D region genes. This response did not appear to result from positive allogeneic effects or from antigen processing and representation by responder type APC that might contaminate the cultures. Thus, we find no evidence for a requirement for I region-restricted helper T cells in these CTL responses. However, helper T cells are required because we find that CTL lines derived by limit-dilution cloning from these long-term MLC are absolutely dependent upon exogenous helper factors for growth. The most simple interpretation of these results is that the helper cells are restricted to H-2 antigens other than I region antigens or to antigens that code outside of the H-2 complex. Finally, we show that factor-dependent CTL lines must recognize their specific antigen to proliferate, even in the presence of exogenous factors. The requirement of activated CTL for antigen to proliferate provides an explanation for how specific CTL can be selectively enriched in MLC by specific antigen stimulation. Furthermore, it is at variance with reports that memory CTL or activated CTL require only interleukin 2 for restimulation

Aid, Public Expenditure and Dutch Disease

Contemporary policy debates on the macroeconomics of aid often concentrate on short-run Dutch disease effects, ignoring the possible supply side impact of aidâfinanced public expenditure. We develop a simple model of aid and public expenditure in which public infrastructure capital generates an inter-temporal productivity spillover for both tradable and non-tradable sectors, where these productivity effects may display sector-specific biases. The model also allows for non-homothetic demands. We then use an extended version of this model, calibrated to contemporary conditions in Uganda, to simulate the effect of a step increase in net aid flows. Our simulations show that beyond the short-run, where Dutch disease effects are present, the relationship between enhanced aid flows, real exchange rates and welfare is less straightforward than simple models of aid suggest. We show that public infrastructure which generates a productivity bias in favour of non-tradable production delivers the largest aggregate return to aid, with the real exchange rate appreciation reduced or reversed and enhanced export performance, but it does so at the cost of a deterioration in the income distribution. Income gains accrue predominantly to urban skilled and unskilled households, leaving the rural poor relatively worse off. Under plausible parameterizations of the model the rural poor may also be worse ff in absolute terms.Aid, Dutch Disease, Public Expenditure, Africa

Large circulant graphs of fixed diameter and arbitrary degree

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circulant graphs which enables us to improve the current best known asymptotic orders for every diameter. As an application, we use our constructions in the directed case to obtain upper bounds on the minimum size of a subset A of a cyclic group of order n such that the k-fold sumset kA is equal to the whole group. We also present a revised table of largest known circulant graphs of small degree and diameter

The permutation class Av(4213,2143)

We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its left. We use this characterisation to establish the generating function enumerating these permutations. We also investigate the properties of a typical large permutation in the class and prove that if a large permutation that avoids 4213 and 2143 is chosen uniformly at random, then it is more likely than not to avoid 2413 as well

Fiscal Policy Design in Low-Income Countries

Fiscal policy, Macro-economic stabilization, Sub-Saharan Africa

Intervals of permutation class growth rates

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θB ≈ 2.35526, and that it also contains every value at least λB ≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λA ≈ 2.48187. Thus, we also refute his conjecture that the set of growth rates below λA is nowhere dense. Our proof is based upon an analysis of expansions of real numbers in non-integer bases, the study of which was initiated by Rényi in the 1950s. In particular, we prove two generalisations of a result of Pedicini concerning expansions in which the digits are drawn from sets of allowed values