On the emergence of random initial conditions in fluid limits

The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz~(1970), such processes, normalized by the carrying capacity, converge on finite intervals to the solutions of ordinary differential equations, also known as the fluid limit. When the initial population is small relative to carrying capacity, this limit is trivial. Here we show that, viewed at suitably chosen times increasing to infinity, the process converges to the fluid limit, governed by the same dynamics, but with a random initial condition. This random initial condition is related to the martingale limit of an associated linear birth and death process

Sickness certification system in the United Kingdom: qualitative study of views of general practitioners in Scotland

Objectives: To explore how general practitioners operate the sickness certification system, their views on the system, and suggestions for change. Design: Qualitative focus group study consisting of 11 focus groups with 67 participants. Setting: General practitioners in practices in Glasgow, Tayside, and Highland regions, Scotland. Sample: Purposive sample of general practitioners, with further theoretical sampling of key informant general practitioners to examine emerging themes. Results: General practitioners believed that the sickness certification system failed to address complex, chronic, or doubtful cases. They seemed to develop various operational strategies for its implementation. There appeared to be important deliberate misuse of the system by general practitioners, possibly related to conflicts about roles and incongruities in the system. The doctor-patient relationship was perceived to conflict with the current role of general practitioners in sickness certification. When making decisions about certification, the general practitioners considered a wide variety of factors. They experienced contradictory demands from other system stakeholders and felt blamed for failing to make impossible reconciliations. They clearly identified the difficulties of operating the system when there was no continuity of patient care. Many wished either to relinquish their gatekeeper role or to continue only with major changes. Conclusions: Policy makers need to recognise and accommodate the range and complexity of factors that influence the behaviour of general practitioners operating as gatekeepers to the sickness certification system, before making changes. Such changes are otherwise unlikely to result in improvement. Models other than the primary care gatekeeper model should be considered

Leptons, quarks, and their antiparticles from a phase-space perspective

It is argued that antiparticles may be interpreted in macroscopic terms without explicitly using the concept of time and its reversal. The appropriate framework is that of nonrelativistic phase space. It is recalled that a quantum version of this approach leads also, alongside the appearance of antiparticles, to the emergence of `internal' quantum numbers identifiable with weak isospin, weak hypercharge and colour, and to the derivation of the Gell-Mann-Nishijima relation, while simultaneously offering a preonless interpretation of the Harari-Shupe rishon model. Furthermore, it is shown that - under the assumption of the additivity of canonical momenta - the approach entails the emergence of string-like structures resembling mesons and baryons, thus providing a different starting point for the discussion of quark unobservability.Comment: Talk given at Fifth Int. Workshop DICE2010 Space-Time-Matter, Castiglioncello, Italy, September 13-17, 201

Universal transloader moves delicate equipment without stress

Transloader moves delicate or heavy items over irregular surfaces without transmitting stress to the load. The loader is supported on three pivot points which produce a wrap free base. The base is supported by an artificial four-wheel frame

The geometry of the Barbour-Bertotti theories II. The three body problem

We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations. Consequences of a conformal symmetry are exploited and the sectional curvatures of geometrically preferred surfaces are computed. The geodesic motions are integrated. Line configurations, which lead to curvature singularities for $N\neq 3$, are investigated. None of the independent scalars formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit

Connecting deterministic and stochastic metapopulation models

In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-015-0865-

Quenched QCD at finite density

Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon screening mass decreases linearly as $\mu$ increases predicting a critical chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation. The meson spectrum does not change as $\mu$ increases over the same range, from zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that there is phase transition at $\mu = m_\pi/2$. We provide alternative explanations for these results, and find a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to $m_N/3$. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte

Local approximation of a metapopulation's equilibrium

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at $z$ being occupied is shown to be close to $q_1(z)$, the equilibrium occupation probability in Levins's model, at any point $z \in \Omega$ not too close to the boundary, if the local colonization pressure and extinction rates appropriate to $z$ are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously

Interacting vector fields in Relativity without Relativity

Barbour, Foster and \'{O} Murchadha have recently developed a new framework, called here {\it{the 3-space approach}}, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of 3-dimensional metric--matter configurations. In fact gravity, the universal light cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity -- and more -- without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang--Mills fields minimally coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity (14 pages, no figures

A law of large numbers approximation for Markov population processes with countably many types

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are countably infinitely many possible types of individual. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove a law of large numbers for rather general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.Comment: revised version in response to referee comments, 34 page