Despite notable scientific and medical advances, broader political, socioeconomic and behavioural factors continue to undercut the response to the COVID-19 pandemic1,2. Here we convened, as part of this Delphi study, a diverse, multidisciplinary panel of 386 academic, health, non-governmental organization, government and other experts in COVID-19 response from 112 countries and territories to recommend specific actions to end this persistent global threat to public health. The panel developed a set of 41 consensus statements and 57 recommendations to governments, health systems, industry and other key stakeholders across six domains: communication; health systems; vaccination; prevention; treatment and care; and inequities. In the wake of nearly three years of fragmented global and national responses, it is instructive to note that three of the highest-ranked recommendations call for the adoption of whole-of-society and whole-of-government approaches1, while maintaining proven prevention measures using a vaccines-plus approach2 that employs a range of public health and financial support measures to complement vaccination. Other recommendations with at least 99% combined agreement advise governments and other stakeholders to improve communication, rebuild public trust and engage communities3 in the management of pandemic responses. The findings of the study, which have been further endorsed by 184 organizations globally, include points of unanimous agreement, as well as six recommendations with >5% disagreement, that provide health and social policy actions to address inadequacies in the pandemic response and help to bring this public health threat to an end.

We generate an observable which relates the interspike time statistics in a noise driven excitable system with its phase space global properties. Experimental results from a semiconductor laser with optical feedback are analyzed within this framework. PACS numbers: 42.65.Sf, 05.40.Ca, 42.55.Px Escape problems from metastable states are ubiquitous in nature [1]. From biology to physics, several situations are adequately modeled through noise driven equations for which the dynamical output consists of a sequence of spike responses with a more or less complex interspike time distribution [2,3]. In these cases, efforts usually are devoted to the calculation of rate coefficients. Kramers made the seminal contribution to this program. He computed escape rates from both the local properties of the deterministic part of the model in the neighborhood of the metastable state and the noise level [4]. In Ref.[5], pseudoregular oscillations were found in noise driven excitable systems for a specific case: the infinitely dissipative regime. In this work, we analyze the consequences of the global properties of a general excitable system (presenting finite dissipation) in the interspike time distribution of its response to added noise. We find that the interspike distributions present a nontrivial structure. The global properties we refer to are the stable and unstable manifolds of the fixed points of the deterministic part of the model. In particular, we analyze the results of an experiment (a semiconductor laser with optical feedback close to the onset of a regime called low frequency fluctuations) [6][7][8], in terms of a simple model [9].The experimental setup is shown in Fig. 1(a). The diode laser used in our experiment is the single transverse-mode Sharp LT030MD0 (nominal wavelength l 750 nm; solitary laser threshold I th 36.66 mA). The temperature of the laser is stabilized to better than 0.01 ± C. The beam is collimated and directed toward a high reflection mirror (R 99%) located at 50 cm from the laser, which redirects the beam back to it. An antireflection coated lens ( f 25 cm) is placed within the cavity in order to focus the beam into the mirror, which seems to improve the coupling efficiency. The optical feedback strength is controlled by an acusto-optic modulator (AOM) placed inside the cavity, in such a way that a variable amount of light can be removed from the zero order thus reducing the feedback level. The intensity output is detected by a 1 GHz bandwidth photodiode and the signal is analyzed with a HP 54616B 500 MHz digital oscilloscope. In this work, we are interested in the slow dynamics, i.e., time scales much larger than the external cavity round-trip time (t ഠ 3 ns). Actually, the short-time dynamics are washed out by the use of a 30 MHz low-pass filter. Different dynamical scenarios are observed as the parameters (current, feedback) are varied, which are extensively described in the literature (see [6], and references therein).For pump values considerably smaller than the solitary laser threshold t...

Recently it was proposed that semiconductor lasers with optical feedback present a regime where they behave as noise driven excitable units. In this work we report on an experimental study in which we periodically force one of these lasers and we compare the results with the solutions of a simple model. The comparison is based on a topological analysis of experimental and theoretical solutions.

We study a quantum-mechanical system, prepared, at t = 0, in a model state, that subsequently decays into a sea of other states whose energy levels form a discrete spectrum with given statistical properties. An important quantity is the survival probability P(t), defined as the probability, at time t, to find the system in the original model state. Our main purpose is to analyze the influence of the discreteness and statistical properties of the spectrum on the behavior of P(t). Since P(t) itself is a statistical quantity, we restrict our attention to its ensemble average (P(t)}, which is calculated analytically using randommatrix techniques, within certain approximations discussed in the text. We find, for (P(t)}, an exponential decay, followed by a revival, governed by the two-point structure function of the statistical spectrum, thus giving a nonzero asymptotic value for large t's. The analytic result compares well with a number of computer simulations, over a time range discussed in the text.

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The dynamics and thermodynamics of a quantum time-dependent field coupled to a two-level system, well known as the Jaynes-Cummings Hamiltonian, is studied, using the maximum entropy principle. In the framework of this approach we found three di8'erent infinite sets of relevant operators that describe the dynamics of the system for any temporal dependence. These sets of relevant operators are connected by isomorphisms, which allow us to consider the case of mixed initial conditions. A consistent set of initial conditions is established using the maximum entropy principle density operator, obtaining restrictions to the physically feasible initial conditions of the system. The behavior of the population inversion is shown for difFerent time dependencies of the Hamiltonian and initial conditions. For the time-independent case, an explicit solution for the population inversion in terms of the relevant operators of one of the sets is given. It is also shown how the well known formulas for the population inversion are recovered for the special cases where the initial conditions correspond to a pure, coherent, and thermal field.PACS nuxnber(s): 42.50.DvPermanent address: Grupo de Sistemas Dinamicos, CentroRegional Norte, Universidad de Buenos Aires, C.C. 2, 1638 V. Lopez, Buenos Aires, Argentina.work the complete dynamics was described in terms of the mean value of four relevant operators. A consistent set of initial conditions (CSIC) [20] was established using the MEP density operator, obtaining restrictions to the physically feasible initial conditions (IC) of the system. In this paper we study a generalization of the quantum two-level system to the time-dependent case [14, 22 -27]. Since we are interested in obtaining a description to be used in difFerent fields of physics, we shall describe the system in terms of three diH'erent sets of relevant operators, which are straightforwardly obtained by use of the MEP. These sets of operators are connected via linear transformations which allows us to change from one set to another. For the Jaynes-Cummings Hamiltonian (JCH) the operator sets are infinite and in consequence the dynamics is described by an infi'nite set of ordinary differential equations for the mean values of the relevant operators, making evident the quantum character of the field. As we have shown before, the IC for the dynamical set of equations cannot be arbitrarily chosen [17,18]. The CSIC is properly obtained using the MEP density matrix. The purpose is achieved introducing the Hamiltonian as a relevant operator for constructing our density matrix. This fact, leads to a quantum thermodynamical description of the problem [28]. The time-independent case is studied in detail in order to reduce our general results to previous ones. A general solution for the population number of one of the levels is obtained and the results for a pure, coherent, and thermal state are recovered [29 -32]. We compare an approximate time evolution of the mean value of the level population with the one obtained by the series so...