Pattern classes and priority queues

When a set of permutations comprising a pattern class C is submitted as input to a priority queue the resulting output is again a pattern class C'. The basis of C' is determined for pattern classes C whose basis elements have length 3, and is finite in these cases. An example is given of a class C with basis 2431 for which C is not finitely based

Permutation Classes of Polynomial Growth

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue of all such sets of forbidden permutations having three or fewer elements is provided together with bounds on the degrees of the associated enumerating polynomials.Comment: 17 pages, 4 figure

g_1 at low x and low Q^2 with Polarized ep Colliders

Measurements of g_1 at low x and low Q^2 are expected to provide a sensitive probe of the transition from Regge to perturbative QCD dynamics, offering a new testing ground for models of small x physics. We discuss the potential of polarized ep colliders (Polarized HERA and eRHIC) to investigate this physics --- varying Q^2 between 0.01 and 1 GeV^2 --- and to constrain the high-energy part of the Drell-Hearn-Gerasimov sum-rule for polarized photoproduction.Comment: 18 pages, 2 figure

Waiting times of entangled electrons in normal-superconducting junctions

We consider a normal-superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from spliting of Cooper pairs at the interface and demonstrate a significant enhancement of the probability to detect two consecutive electrons in a short time interval. Finally, we discuss the electronic waiting time distribution in the more realistic situation of partial entanglement

Sorting with a forklift

A fork stack is a generalised stack which allows pushes and pops of several items at a time. We consider the problem of determining which input streams can be sorted using a single forkstack, or dually, which permutations of a fixed input stream can be produced using a single forkstack. An algorithm is given to solve the sorting problem and the minimal unsortable sequences are found. The results are extended to fork stacks where there are bounds on how many items can be pushed and popped at one time. In this context we also establish how to enumerate the collection of sortable sequences.Comment: 24 pages, 2 figure

Development expenditures and the local financing constraint

Focusing on the local financing constraint sheds new light on issues of aid, fiscal reform, and the management of public spending. The fungibility of aid need not translate into resource flows to fill the local financing gap. Indeed, project aid can widen the local financing gap. To augment direct local financing of development, aid must be nonproject aid that can generate local currency. In the longer term, project aid's effect on local financing lies in its impact on growth and on expanding the base for tax revenues, seigniorage, and borrowing. When inadequate local financing limits project implementation and effective use of aid, local currency funds are more valuable than project aid, at the margin--and it becomes important to reallocate local funds, to leverage project aid, and to raise the quality of investment projects. A persistent gap in local financing complicates programs of fiscal reform. For such programs to be effective, the local financing gap has to be confronted directly by matching planned local fund expenditures against expected local fund receipts. This requires a transparent database to develop indicators and to monitor the allocation and use of local resources.Development Economics&Aid Effectiveness,Economic Theory&Research,Environmental Economics&Policies,Payment Systems&Infrastructure,Fiscal&Monetary Policy,Environmental Economics&Policies,Development Economics&Aid Effectiveness,National Governance,Fiscal&Monetary Policy,Economic Theory&Research

Isomorphisms between pattern classes

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.Comment: 11 page