How to manage the post pandemic opening? A Pontryagin Maximum Principle approach

The COVID-19 pandemic has completely disrupted the operation of our societies. Its elusive transmission process, characterized by an unusually long incubation period, as well as a high contagion capacity, has forced many countries to take quarantine and social isolation measures that conspire against the performance of national economies. This situation confronts decision makers in different countries with the alternative of reopening the economies, thus facing the unpredictable cost of a rebound of the infection. This work tries to offer an initial theoretical framework to handle this alternative.Comment: 10 page

A Solvable Sequence Evolution Model and Genomic Correlations

We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations in the composition of letters as long as the sequence length is growing, i.e., the combined rates of duplications and insertions are higher than the deletion rate. For constant sequence length, on the other hand, all initial correlations decay exponentially. These results are obtained analytically and by simulations. They are compared with the long-range correlations observed in genomic DNA, and the implications for genome evolution are discussed.Comment: 4 pages, 4 figure

Millikelvin magnetic relaxation measurements of alpha-Fe2O3 antiferromagnetic particles

In this paper we report magnetic relaxation data for antiferromagnetic alpha-Fe2O3 particles of 5 nm mean diameter in the temperature range 0.1 K to 25 K. The average spin value of these particles S=124 and the uniaxial anisotropy constant D=1.6x10^-2 K have been estimated from the experimental values of the blocking temperature and anisotropy field. The observed plateau in the magnetic viscosity from 3 K down to 100 mK agrees with the occurrence of spin tunneling from the ground state Sz = S. However, the scaling M vs Tln(nu t) is broken below 5 K, suggesting the occurrence of tunneling from excited states below this temperature.Comment: 4 pages (two columns), 4 figure

Correlation between magnetic interactions and domain structure in A1 FePt ferromagnetic thin films

We have investigated the relationship between the domain structure and the magnetic interactions in a series of FePt ferromagnetic thin films of varying thickness. As-made films grow in the magnetically soft and chemically disordered A1 phase that may have two distinct domain structures. Above a critical thickness $d_{cr}\sim 30$ nm the presence of an out of plane anisotropy induces the formation of stripes, while for $d<d_{cr}$ planar domains occur. Magnetic interactions have been characterized using the well known DCD-IRM remanence protocols, $\delta M$ plots, and magnetic viscosity measurements. We have observed a strong correlation between the domain configuration and the sign of the magnetic interactions. Planar domains are associated with positive exchange-like interactions, while stripe domains have a strong negative dipolar-like contribution. In this last case we have found a close correlation between the interaction parameter and the surface dipolar energy of the stripe domain structure. Using time dependent magnetic viscosity measurements, we have also estimated an average activation volume for magnetic reversal, $\langle V_{ac}\rangle \sim 1.37\times 10^{4}$ nm$^{3},$ which is approximately independent of the film thickness or the stripe period.Comment: 25 pages, 11 figure