Prioritizing the First Doses of SARS-CoV-2 Vaccine to Save the Elderly: The Case Study of Italy.

SARS-CoV-2 is currently causing hundreds of deaths every day in European countries, mostly in not yet vaccinated elderly. Vaccine shortage poses relevant challenges to health authorities, called to act promptly with a scarcity of data. We modeled the mortality reduction of the elderly according to a schedule of mRNA SARS-CoV-2 vaccine that prioritized first dose administration. For the case study of Italy, we show an increase in protected individuals up to 53.4% and a decrease in deaths up to 19.8% in the cohort of over 80's compared with the standard vaccine recalls after 3 or 4 weeks. This model supports the adoption of vaccination campaigns that prioritize the administration of the first doses in the elderly.

Formation of disks with long-lived spiral arms from violent gravitational dynamics.

By means of simple dynamical experiments we study the combined effect of gravitational and gas dynamics in the evolution of an initially out-of-equilibrium, uniform, and rotating massive overdensity thought of as in isolation. The rapid variation of the system mean-field potential makes the pointlike particles (PPs), which interact only via Newtonian gravity, form a quasistationary thick disk dominated by rotational motions surrounded by far out-of-equilibrium spiral arms. On the other side, the gas component is subjected to compression shocks and radiative cooling so as to develop a much flatter disk, where rotational motions are coherent and the velocity dispersion is smaller than that of PPs. Around such gaseous disk long-lived, but nonstationary, spiral arms form: these are made of gaseous particles that move coherently because have acquired a specific phase-space correlation during the gravitational collapse phase. Such a phase-space correlation represents a signature of the violent origin of the arms and implies both the motion of matter and the transfer of energy. On larger scales, where the radial velocity component is significantly larger than the rotational one, the gas follows the same out-of-equilibrium spiral arms traced by PPs. We finally outline the astrophysical and cosmological implications of our results.

Long-lived transient structure in collisionless self-gravitating systems.

The evolution of self-gravitating systems, and long-range interacting systems more generally, from initial configurations far from dynamical equilibrium is often described as a simple two-phase process: a first phase of violent relaxation bringing it to a quasistationary state in a few dynamical times, followed by a slow adiabatic evolution driven by collisional processes. In this context the complex spatial structure evident, for example, in spiral galaxies is understood either in terms of instabilities of quasistationary states or as a result of dissipative nongravitational interactions. We illustrate here, using numerical simulations, that purely self-gravitating systems evolving from quite simple initial configurations can in fact give rise easily to structures of this kind, of which the lifetime can be large compared to the dynamical characteristic time but short compared to the collisional relaxation timescale. More specifically, for a broad range of nonspherical and nonuniform rotating initial conditions, gravitational relaxation gives rise quite generically to long-lived nonstationary structures of a rich variety, characterized by spiral-like arms, bars, and even ringlike structures in special cases. These structures are a feature of the intrinsically out-of-equilibrium nature of the system's collapse, associated with a part of the system's mass while the bulk is well virialized. They are characterized by predominantly radial motions in their outermost parts, but also incorporate an extended flattened region which rotates coherently about a well-virialized core of triaxial shape with an approximately isotropic velocity dispersion. We characterize the kinematical and dynamical properties of these complex velocity fields and we briefly discuss the possible relevance of these simple toy models to the observed structure of real galaxies, emphasizing the difference between dissipative and dissipationless disk formation.

The Scientific Competitiveness of Nations.

We use citation data of scientific articles produced by individual nations in different scientific domains to determine the structure and efficiency of national research systems. We characterize the scientific fitness of each nation-that is, the competitiveness of its research system-and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification. We find that technological leading nations, beyond having the largest production of scientific papers and the largest number of citations, do not specialize in a few scientific domains. Rather, they diversify as much as possible their research system. On the other side, less developed nations are competitive only in scientific domains where also many other nations are present. Diversification thus represents the key element that correlates with scientific and technological competitiveness. A remarkable implication of this structure of the scientific competition is that the scientific domains playing the role of "markers" of national scientific competitiveness are those not necessarily of high technological requirements, but rather addressing the most "sophisticated" needs of the society.