Vote Leave’s position on EU and Irish citizens post-Brexit raises more questions than it answers

On 1 June, Vote Leave issued a statement outlining its plans for a post-Brexit immigration policy. Among other matters, the statement sought to give reassurance on two status issues that would arise in the event of withdrawal: the position of resident EU citizens, and the future rights of Irish citizens. According to Bernard Ryan, their position on migrants’ rights after a Brexit raises more questions than it answers

Polychromatic Colorings on the Integers

We show that for any set $S\subseteq \mathbb{Z}$, $|S|=4$ there exists a 3-coloring of $\mathbb{Z}$ in which every translate of $S$ receives all three colors. This implies that $S$ has a codensity of at most $1/3$, proving a conjecture of Newman [D. J. Newman, Complements of finite sets of integers, Michigan Math. J. 14 (1967) 481--486]. We also consider related questions in $\mathbb{Z}^d$, $d\geq 2$.Comment: 16 pages, improved presentatio

Polychromatic Colorings on the Hypercube

Given a subgraph G of the hypercube Q_n, a coloring of the edges of Q_n such that every embedding of G contains an edge of every color is called a G-polychromatic coloring. The maximum number of colors with which it is possible to G-polychromatically color the edges of any hypercube is called the polychromatic number of G. To determine polychromatic numbers, it is only necessary to consider a structured class of colorings, which we call simple. The main tool for finding upper bounds on polychromatic numbers is to translate the question of polychromatically coloring the hypercube so every embedding of a graph G contains every color into a question of coloring the 2-dimensional grid so that every so-called shape sequence corresponding to G contains every color. After surveying the tools for finding polychromatic numbers, we apply these techniques to find polychromatic numbers of a class of graphs called punctured hypercubes. We also consider the problem of finding polychromatic numbers in the setting where larger subcubes of the hypercube are colored. We exhibit two new constructions which show that this problem is not a straightforward generalization of the edge coloring problem.Comment: 24 page

Nitrous Oxide Emissions

End of project reportNitrous oxide (N2O) is one of the three most important greenhouse gases (GHG). Nitrous oxide emissions currently account for approximately one third of GHG emissions from agriculture in Ireland. Emissions of N2O arise naturally from soil sources and from the application of nitrogen (N) in the form of N fertilizers and N in dung and urine deposition by grazing animals at pasture. Nitrous oxide emission measurements were conducted at three different scales. Firstly, a large-scale field experiment was undertaken to compare emission rates from a pasture receiving three different rates of N fertilizer application and to identify the effects of controlling variables over a two-year period. Variation in emission rates was large both within and between years. Two contrasting climatic years were identified. The cooler and wetter conditions in year 1 gave rise to considerably lower emission levels than the warmer and drier year 2. However, in both years, peak emissions were associated with fertilizer N applications coincident with rainfall events in the summer months. A small-plot study was conducted to identify the individual and combined effects of fertilizer, dung and urine applications to grassland. Treatment effects were however, difficult to obtain due to the overriding effects of environmental variables. Thirdly, through the use of a small-scale mini-lysimeter study, the diurnal nature of N2O emission rates was identified for two distinct periods during the year. The occurrence of a diurnal pattern has important implications for the identification of a measurement period during the day which is representative of the true daily flux. The research presented aims to identify the nature and magnitude of N2O emissions and the factors which affect emission rates from a grassland in Ireland. Further work is required to integrate the effects of different soil types and contrasting climatic regimes across soil types on N2O emissions.Environmental Protection Agenc

ON POTENTIALIZED PARTIAL FINITE DIFFERENCE EQUATIONS: ANALYZING THE COMPLEXITY OF KNOWLEDGE-BASED SPATIAL ECONOMIC DEVELOPMENTS

Knowledge-based regional and urban studies are plentiful; some systematics might be in order at this junction, so first the different links between economic production units in geographical space have to be clearly defined. Then a tool to represent the dynamics of those links should be selected; potentialized partial differential equations (PPDEs) are an appropriate tool to represent space-time relations in pre-geographical space. In practice, however, only discrete data are available, hence the question of how finite differences could generate PPFDEs (potentialized partial finite difference equations). A case has been worked out and simulated, showing a high degree of spatio-temporal complexity. Spatial econometric estimation is possible, as other work has shown; so an application to empirical data for France could be presented. Different versions of the latter have been worked out; they are presented in succession, followed by a last exercise on US data.COMPLEXITY, SPATIAL ECONOMETRICS, POTENTIAL, FINITE DIFFERENCES

Lattice QCD at the end of 2003

I review recent developments in lattice QCD. I first give an overview of its formalism, and then discuss lattice discretizations of fermions. We then turn to a description of the quenched approximation and why it is disappearing as a vehicle for QCD phenomenology. I describe recent claims for progress in simulations which include dynamical fermions and the interesting theoretical problems they raise. I conclude with brief descriptions of the calculations of matrix elements in heavy flavor systems and for kaons.Comment: Review for Int J Mod Phys A. 58 pages, latex, WSPC macros,, 22 postscript figure