Economic modelling using constraint logic programming

This paper investigates the use of constraint logic programming (CLP) in economic modelling through the design and implementation of two economic models. The first model, the Desai- Henry model contains only linear equations while the second model, constructed by the author, contains non-linear elements. In order to implement the second model, a non-linear constraint solver was constructed. This was necessary because, although CLP is a very powerful programming paradigm, currently available implementations lack any on-linear constraint solving mechanisms

The Digrams of Webster\u27s Unabridged Dictionary

For many years word buffs at these laboratories have made a game out of finding words which contain strange digrams (pairs of letters side-by-side). The problem, as originally posed by M.D. McIlroy, was to complete a table with 26 rows and 26 columns, labeled by the letters A, B, ... , Z. The space where row L crossed column L\u27 was to be filled by a word containing the digram LL\u27

The algebra of rewriting for presentations of inverse monoids

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianised kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel - the module of identities - uses further facts about pseudoregular groupoids.Comment: 22 page

Parafermionic phases with symmetry-breaking and topological order

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates. These two properties are shown to be topologically robust, and applicable to a wider family of topologically-ordered Hamiltonians than has been previously considered. An an application of these edge modes, we formulate a new notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain groundstate is topological, i.e., it originates from the topological manifold of degenerate states on the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalizes Cooper pairing in superconductors. The stability of these condensates are investigated on both open and closed chains.Comment: 27 pages, 9 figure

Modelling alternative strategies for delivering hepatitis B vaccine in prisons : the impact on the vaccination coverage of the injecting drug user population

Since 2001 hepatitis B vaccination has been offered to prisoners on reception into prisons in England and Wales. However, short campaigns of vaccinating the entire population of individual prisons have achieved high vaccination coverage for limited periods, suggesting that short campaigns may be a preferable way of vaccinating prisoners. A model is used that describes the flow of prisoners through prisons stratified by injecting status to compare a range of vaccination scenarios that describe vaccination on prison reception or via regular short campaigns. Model results suggest that vaccinating on prison reception can capture a greater proportion of the injecting drug user (IDU) population than the comparable campaign scenarios (63% vs. 55 . 6% respectively). Vaccination on prison reception is also more efficient at capturing IDUs for vaccination than vaccination via a campaign, although vaccination via campaigns may have a role with some infections for overall control

Differential Expression Of Gap Junction mRNAs And Proteins In The Developing Murine Kidney And In Experimentally Induced Nephric Mesenchymes

The expression of three gap junction (GJ) proteins, alpha-1 (Cx43), beta-1 (Cx32), and beta-2 (Cx26), and their transcripts were examined during the ontogeny of the mouse and rat kidney. These proteins were expressed in two non-overlapping patterns. The alpha-1 GJ protein was first observed in mesenchymal cells in the 12-day mouse kidney. By day 14 and thereafter, the ai protein was detected in the transient S-shaped bodies, but not in the podocytes of the maturing glomeruli. After birth the antigen was retained in a small subset of secretory tubules.The beta-1 and beta-2 GJ proteins were similar in their developmental patterns. They were first detected in a small subset of secretory tubules in the subcortical zone of day 17 embryos. These tubules were identified by immunohistochemical markers to be proximal. At birth, practically all proximal tubules expressed the two antigens.This analysis of GJ proteins was consistent with the results of S1 nuclease protection assays showing that, while the alpha-1 mRNA appeared early during kidney development and declined around birth, the two beta mRNAs appeared later and became intensified during the last days of intrauterine development.In experimentally induced metanephric mesenchymes, a transient expression of the alpha-1 GJ protein was seen during the segregation of the tubular anlagen. beta-1 and beta-2 GJ proteins were not detected in such induced mesenchymes cultivated up to 7 days.These observations provide evidence for the cell-specific utilization of different GJ genes during different stages of kidney organogenesis. The alpha-1 gene is activated during the early segregation of the secretory tubule and might contribute to its compartmentalization, while the beta-1 and beta-2 gene products are not detected until advanced stages of development. The latter gene products might be correlated with the physiological activity of the proximal tubules in vivo, as they are not expressed in experimentally induced tubules detectable with markers for proximal tubules

Elemental Abundances in M31: Alpha and Iron Element Abundances from Low-Resolution Resolved Stellar Spectroscopy in the Stellar Halo

Measurements of [Fe/H] and [$\alpha$/Fe] can probe the minor merging history of a galaxy, providing a direct way to test the hierarchical assembly paradigm. While measurements of [$\alpha$/Fe] have been made in the stellar halo of the Milky Way, little is known about detailed chemical abundances in the stellar halo of M31. To make progress with existing telescopes, we apply spectral synthesis to low-resolution DEIMOS spectroscopy (R $\sim$ 2500 at 7000 Angstroms) across a wide spectral range (4500 Angstroms $<$ $\lambda$ $<$ 9100 Angstroms). By applying our technique to low-resolution spectra of 170 giant stars in 5 MW globular clusters, we demonstrate that our technique reproduces previous measurements from higher resolution spectroscopy. Based on the intrinsic dispersion in [Fe/H] and [$\alpha$/Fe] of individual stars in our combined cluster sample, we estimate systematic uncertainties of $\sim$0.11 dex and $\sim$0.09 dex in [Fe/H] and [$\alpha$/Fe], respectively. We apply our method to deep, low-resolution spectra of 11 red giant branch stars in the smooth halo of M31, resulting in higher signal-to-noise per spectral resolution element compared to DEIMOS medium-resolution spectroscopy, given the same exposure time and conditions. We find $\langle$[$\alpha$/Fe]$\rangle$ = 0.49 $\pm$ 0.29 dex and $\langle$[Fe/H]$\rangle$ = 1.59 $\pm$ 0.56 dex for our sample. This implies that---much like the Milky Way---the smooth halo of M31 is likely composed of disrupted dwarf galaxies with truncated star formation histories that were accreted early in the halo's formation.Comment: 21 pages, 14 figures, accepted to Ap