A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays

Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the delays distributions, a quenched or averaged propagation of chaos takes place in these networks, and that the network equations converge towards a delayed McKean-Vlasov equation with distributed delays. Our approach is mostly fitted to neuroscience applications. We instantiate in particular a classical neuronal model, the Wilson and Cowan system, and show that the obtained limit equations have Gaussian solutions whose mean and standard deviation satisfy a closed set of coupled delay differential equations in which the distribution of delays and the noise levels appear as parameters. This allows to uncover precisely the effects of noise, delays and coupling on the dynamics of such heterogeneous networks, in particular their role in the emergence of synchronized oscillations. We show in several examples that not only the averaged delay, but also the dispersion, govern the dynamics of such networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and clarified a regularity hypothesis (remark 1

Ethical issues in implementation research: a discussion of the problems in achieving informed consent

Background: Improved quality of care is a policy objective of health care systems around the world. Implementation research is the scientific study of methods to promote the systematic uptake of clinical research findings into routine clinical practice, and hence to reduce inappropriate care. It includes the study of influences on healthcare professionals' behaviour and methods to enable them to use research findings more effectively. Cluster randomized trials represent the optimal design for evaluating the effectiveness of implementation strategies. Various codes of medical ethics, such as the Nuremberg Code and the Declaration of Helsinki inform medical research, but their relevance to cluster randomised trials in implementation research is unclear. This paper discusses the applicability of various ethical codes to obtaining consent in cluster trials in implementation research. Discussion: The appropriate application of biomedical codes to implementation research is not obvious. Discussion of the nature and practice of informed consent in implementation research cluster trials must consider the levels at which consent can be sought, and for what purpose it can be sought. The level at which an intervention is delivered can render the idea of patient level consent meaningless. Careful consideration of the ownership of information, and rights of access to and exploitation of data is required. For health care professionals and organizations, there is a balance between clinical freedom and responsibility to participate in research. Summary: While ethical justification for clinical trials relies heavily on individual consent, for implementation research aspects of distributive justice, economics, and political philosophy underlie the debate. Societies may need to trade off decisions on the choice between individualized consent and valid implementation research. We suggest that social sciences codes could usefully inform the consideration of implementation research by members of Research Ethics Committees

Direct flux and current vector control for induction motor drives using model predictive control theory

The study presents the direct flux and current vector control of an induction motor (IM) drive, which is a relatively newer and promising control strategy, through the use of model predictive control (MPC) techniques. The results highlight that the fast flux control nature of direct flux control strategy is further enhanced by MPC. Predictive control is applied in two of its variants, namely the finite control set and modulated MPC, and the advantages and limitations of the two are underlined. This work also highlights, through experimental results, the importance of prioritising the flux part of the cost function which is particularly significant in the case of an IM drive. The performance of the MPC-based approach is compared with the proportional-integral controller, which also prioritises the flux control loop, under various operating regions of the drive such as in the flux-weakening regime. Simulations show the performance expected with different control strategies which is then verified through experiments

A hierarchical model for aging

We present a one dimensional model for diffusion on a hierarchical tree structure. It is shown that this model exhibits aging phenomena although no disorder is present. The origin of aging in this model is therefore the hierarchical structure of phase space.Comment: 10 pages LaTeX, 4 postscript-figures include

Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

Sub-Doppler spectroscopy of Rb atoms in a sub-micron vapor cell in the presence of a magnetic field

We report the first use of an extremely thin vapor cell (thickness ~ 400 nm) to study the magnetic-field dependence of laser-induced-fluorescence excitation spectra of alkali atoms. This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced-fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine states, we observe a nonlinear Zeeman effect for each sublevel, a substantial modification of the transition probabilities between different magnetic sublevels, and the appearance of transitions that are strictly forbidden in the absence of the magnetic field. For the case of right- and left- handed circularly polarized laser excitation, the fluorescence spectra differs qualitatively. Well pronounced magnetic field induced circular dichroism is observed. These observations are explained with a standard approach that describes the partial decoupling of I and J states

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees