In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spinglass model is analyzed (the p-spin spherical model) by using three different approaches. Thermodynamics, covering pure states, overlaps, overlap distribution, replica symmetry breaking, and the static transition. Dynamics, covering the generating functional method, generalized Langevin equation, equations for the correlation and the response, the Mode Coupling approximation, and the dynamical transition. And finally complexity, covering the mean-field (TAP) free energy, metastable states, entropy crisis, threshold energy, and saddles. Particular attention has been paid on the mutual consistency of the results obtained from the different methods.

HighlightsMedia attitude towards underpinning policy with evidence influences policy decision makers.Individual skills, attitudes, values of policy makers impact the extent evidence use.A solid research infrastructure is facilitating but not sufficient for evidence use.Factors that impact evidence use in policy making differ by country and policy context.Interventions connecting policy makers and researchers in the policy context seem most promising.

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: A replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when the temperature is varied. We give a full description of this constrained out of equilibrium behavior and we clarify the connection to the thermodynamics by computing (sub-dominant) tap states, constrained to the starting equilibrium configuration.PACS numbers: 75.10. Nr, 64.70.Pf, 75.50.Lk Many interesting physical systems live for very long times out of equilibrium, and, in this regime, they display highly non trivial behaviors which are still to be understood (e.g. rejuvenation and memory effects in spin glasses). In general, these systems fall out of equilibrium when some external parameter is changed. For example, fragile glassforming liquids undergo a dramatic slowing down of their relaxational dynamics when the temperature is dropped below the glass transition temperature 1 . This effect is sharpened in certain mean-field models where, at a critical temperature T d , a transition occurs from an equilibrium kind of dynamics to an off-equilibrium aging one 2 . The phenomenon is ubiquitous and can be found also in very different fields: e.g. in local search algorithms for solving hard optimization problems the time-complexity may become extremely large by varying a macroscopic parameter 3 . A better understanding of the mechanisms leading to the dramatic slowing down in out of equilibrium dynamics is a subject of broad interest and wide applicability.In describing the dynamical slowing down (and possible eventual arrest) the common view suggests that at a low temperature a huge number of metastable states appears (with energies higher than the equilibrium one, E 0 ), making relaxation to equilibrium very slow, and even impossible if interactions are long ranged and metastable states lifetimes diverge in the thermodynamic limit. This picture has been verified by solving the out of equilibrium Langevin dynamics of a particularly simple mean-field model, the so-called fully connected spherical p-spin, whose Hamiltonian is 4where the N spins σ i are continuous variables subject to the spherical constraint i σ 2 i = N and the couplings are i.i.d. random variables with zero mean and variance p!/(2N p−1 ). In this model (hereafter p ≥ 3) if we consider a quench, that is if we choose an initial configuration of high energy and let the system relax at a fixed value of the temperature T < T d (T d being the dynamic transition temperature), the asymptotic dynamics remains trapped at the energy level of the highest and most numerous metastable states, the so-called threshold states. Time-translation invariance and the dynamic fluctuation-dissipation relation are violated and aging is observed in correlation and response functions 5 .These features are intriguing and experimentally relevant, since aging behaviour has been observed in many disordered systems. Nevertheless, in order t...

BackgroundEnsuring health policies are informed by evidence still remains a challenge despite efforts devoted to this aim. Several tools and approaches aimed at fostering evidence-informed policy-making (EIPM) have been developed, yet there is a lack of availability of indicators specifically devoted to assess and support EIPM. The present study aims to overcome this by building a set of measurable indicators for EIPM intended to infer if and to what extent health-related policies are, or are expected to be, evidence-informed for the purposes of policy planning as well as formative and summative evaluations.MethodsThe indicators for EIPM were developed and validated at international level by means of a two-round internet-based Delphi study conducted within the European project ‘REsearch into POlicy to enhance Physical Activity’ (REPOPA). A total of 82 researchers and policy-makers from the six European countries (Denmark, Finland, Italy, the Netherlands, Romania, the United Kingdom) involved in the project and international organisations were asked to evaluate the relevance and feasibility of an initial set of 23 indicators developed by REPOPA researchers on the basis of literature and knowledge gathered from the previous phases of the project, and to propose new indicators.ResultsThe first Delphi round led to the validation of 14 initial indicators and to the development of 8 additional indicators based on panellists’ suggestions; the second round led to the validation of a further 11 indicators, including 6 proposed by panellists, and to the rejection of 6 indicators. A total of 25 indicators were validated, covering EIPM issues related to human resources, documentation, participation and monitoring, and stressing different levels of knowledge exchange and involvement of researchers and other stakeholders in policy development and evaluation.ConclusionThe study overcame the lack of availability of indicators to assess if and to what extent policies are realised in an evidence-informed manner thanks to the active contribution of researchers and policy-makers. These indicators are intended to become a shared resource usable by policy-makers, researchers and other stakeholders, with a crucial impact on fostering the development of policies informed by evidence.Electronic supplementary materialThe online version of this article (10.1186/s12961-018-0323-z) contains supplementary material, which is available to authorized users.

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Evidence shows that regular physical activity is enhanced by supporting environment. Studies are needed to integrate research evidence into health enhancing, cross-sector physical activity (HEPA) policy making. This article presents the rationale, study design, measurement procedures and the initial results of the first phase of six European countries in a five-year research project (2011-2016), REsearch into POlicy to enhance Physical Activity (REPOPA). REPOPA is programmatic research; it consists of linked studies; the first phase studied the use of evidence in 21 policies in implementation to learn more in depth from the policy making process and carried out 86 qualitative stakeholder interviews. The second, ongoing phase builds on the central findings of the first phase in each country; it consists of two sets of interventions: game simulations to study cross-sector collaboration and organizational change processes in the use of evidence and locally tailored interventions to increase knowledge integration. The results of the first two study phases will be tested and validated among policy makers and other stakeholders in the third phase using a Delphi process. Initial results from the first project phase showed the lack of explicit evidence use in HEPA policy making. Facilitators and barriers of the evidence use were the availability of institutional resources and support but also networking between researchers and policy makers. REPOPA will increase understanding use of research evidence in different contexts; develop guidance and tools and establish sustainable structures such as networks and platforms between academics and policy makers across relevant sectors.

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