Is the growth of the Scottish economy the 'first priority' for public spending in Scotland

The Scottish Executive, notably the First Minister, has frequently stated that the growth and development of the Scottish Economy is the first priority of government in Scotland

Pattern formation in individual-based systems with time-varying parameters

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model parameters are varied slowly, whereas fast sweeps produce a large number of small domains. The symmetry breaking is triggered by intrinsic noise, originating from the discrete dynamics at the micro-level. Based on a linear-noise approximation, we calculate the characteristic length scale of these patterns. We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation. Our theoretical estimates are confirmed in simulations. In further numerical work, we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.Comment: 16 pages, 9 figures. Published version. Corrected missing appendix link from previous versio

Stochastic tunneling and metastable states during the somatic evolution of cancer

Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic of much investigation. The phenomenon of stochastic tunneling, where an intermediate mutant in a sequence does not reach fixation in a population before generating a double mutant, has been studied using a variety of computational and mathematical methods. However, the field still lacks a comprehensive analytical description since theoretical predictions of fixation times are only available for cases in which the second mutant is advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing the deterministic dynamics of large populations we systematically identify the parameter regimes captured by existing approaches. Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states. These are landscapes in which the final mutant is not the most advantageous in the sequence, and resulting metastable states are a consequence of a mutation-selection balance. The escape from these states is driven by intrinsic noise, and their location affects the probability of tunneling. Existing methods no longer apply. In these regimes it is the escape from the metastable states that is the key bottleneck; fixation is no longer limited by the emergence of a successful mutant lineage. We used the so-called Wentzel-Kramers-Brillouin method to compute fixation times in these parameter regimes, successfully validated by stochastic simulations. Our work fills a gap left by previous approaches and provides a more comprehensive description of the acquisition of multiple mutations in populations of somatic cells.Comment: 33 pages, 7 figure

When the mean is not enough: Calculating fixation time distributions in birth-death processes

Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.Comment: Published in PRE. 14 pages, 6 figure

Nuclear recoil energy scale in liquid xenon with application to the direct detection of dark matter

We show for the first time that the quenching of electronic excitation from nuclear recoils in liquid xenon is well-described by Lindhard theory, if the nuclear recoil energy is reconstructed using the combined (scintillation and ionization) energy scale proposed by Shutt {\it et al.}. We argue for the adoption of this perspective in favor of the existing preference for reconstructing nuclear recoil energy solely from primary scintillation. We show that signal partitioning into scintillation and ionization is well-described by the Thomas-Imel box model. We discuss the implications for liquid xenon detectors aimed at the direct detection of dark matter

Devolution and the economy : a Scottish perspective

In their interesting and challenging chapter John Adams and Peter Robinson assess the consequences for economic development policy of the devolution measures enacted by the UK Labour government post 1997. Their chapter ranges widely over current UK regional disparities, the link between devolution and economic growth, the balance of responsibilities in policy between Whitehall and the devolved administrations, and finally, they raise questions about the developing "quasi-federal" role of Whitehall in regulating or coordinating the new devolved policy landscape. In response, we propose to focus on four issues that we believe are key to understanding the economic consequences of devolution both at the Scottish and UK levels. First, we argue that the view of Scotland's devolutionary experience in economic policy is partial and so does not fully capture the nature and extent of change post 1999. Secondly, we examine the role of devolution in regional economic performance. There is much in their paper on this topic with which we agree but we contend that there are significant omissions in the analysis, which are important for policy choice. Our third section highlights an area not discussed in depth by Adams and Robinson's paper: the funding of the devolution settlement. Here we consider some of the implications of funding arrangements for economic performance and the options for a new funding settlement. Finally, we deal with the difficult issue of co-ordination between the centre and the devolved regions. We contend that co-ordination is largely conspicuous by its absence. Moreover, where coordination is deployed it reflects an inadequate understanding of the extent to which the economies of the regions and devolved territories of the UK are linked

Effects of spin vacancies on magnetic properties of the Kitaev-Heisenberg model

We study the ground state properties of the Kitaev-Heisenberg model in a magnetic field and explore the evolution of spin correlations in the presence of non-magnetic vacancies. By means of exact diagonalizations, the phase diagram without vacancies is determined as a function of the magnetic field and the ratio between Kitaev and Heisenberg interactions. We show that in the (antiferromagnetic) stripe ordered phase the static susceptibility and its anisotropy can be described by a spin canting mechanism. This accounts as well for the transition to the polarized phase when including quantum fluctuations perturbatively. Effects of spin vacancies depend sensitively on the type of the ground state. In the liquid phase, the magnetization pattern around a single vacancy in a small field is determined, and its spatial anisotropy is related to that of non-zero further neighbor correlations induced by the field and/or Heisenberg interactions. In the stripe phase, the joint effect of a vacancy and a small field breaks the six-fold symmetry of the model and stabilizes a particular stripe pattern. Similar symmetry-breaking effects occur even at zero field due to effective interactions between vacancies. This selection mechanism and intrinsic randomness of vacancy positions may lead to spin-glass behavior.Comment: 13 pages, 10 figure

Low-Temperature Hall Effect in Substituted Sr2RuO4

We report the results of a study of the Hall effect and magnetoresistance in single crystals of Sr2RuO4 in which Sr^(2+) has been substituted by La^(3+) (Sr(2-y)La(y)RuO(4)) or Ru^(4+) by Ti^(4+) (Sr(2)Ru(1-x)Ti(x)O(4)). For undoped Sr2RuO4, the purity is so high that the strong-field Hall coefficient can be measured for fields above 4 T. The conventional weak-field Hall coefficient as a function of doping shows a sharp jump and sign change at y ~ 0.01 that is unrelated to either a sharp change in Fermi-surface topography or a magnetic instability. The implications of these results are discussed.Comment: 5 pages, 4 figure

Fixation in finite populations evolving in fluctuating environments

The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments