Balancing the benefits of vaccination: An envy-free strategy.

The Covid-19 pandemic revealed the difficulties of vaccinating a population under the circumstances marked by urgency and limited availability of doses while balancing benefits associated with distinct guidelines satisfying specific ethical criteria. We offer a vaccination strategy that may be useful in this regard. It relies on the mathematical concept of envy-freeness. We consider finding balance by allocating the resource among individuals that seem heterogeneous concerning the direct and indirect benefits of vaccination, depending on age. The proposed strategy adapts a constructive approach in the literature based on Sperner's Lemma to point out an approximate division of doses guaranteeing that both benefits are optimized each time a batch becomes available. Applications using data about population age distributions from diverse countries suggest that, among other features, this strategy maintains the desired balance, throughout the entire vaccination period. We discuss complementary aspects of the method in the context of epidemiological models of age-stratified Susceptible - Infected - Recovered (SIR) type.

Fast and slow axonal transport: A unified approach based on cargo and molecular motor coupled dynamics.

The origins of the large differences observed in the rates at which diverse particles are conveyed along axonal microtubules are still a matter of debate in the literature. There is evidence that certain neurodegenerative diseases may be triggered by disturbances in the related transport processes. Motivated by this, we employ a model to investigate mobility properties of certain cargoes whose dynamics are coupled with that of molecular motors on crowded microtubules. For certain initial and boundary conditions, we use the method of characteristics to resolve perturbatively the pair of equations of Burgers type resulting from a mean-field approach to the original microscopic stochastic model. Extensions to nonperturbative limits are explored numerically. In this context, we are able to figure out conditions under which the cargoes' average velocities may differ up to orders of magnitude just by changing the number of motors on the considered track. We then discuss possibilities to connect these theoretical predictions with available experimental data about axon transport.

A phenomenological analysis of eco-evolutionary coupling under dilution.

Evolutionary dynamics experienced by mixed microbial populations of cooperators and cheaters has been examined in experiments in the literature using a protocol of periodic dilution to investigate the properties of resilience and adaptability to environmental changes. Data depicted on an appropriate phase diagram indicate, among other features, a stable equilibrium point at which cooperators and cheaters coexist (Sanchez and Gore, 2013). We present here a phenomenological analysis of these data focusing on an eco-evolutionary-game perspective. To that end, we work on an extension of the model proposed in Tao and Cressman (2007). It's original version takes into account changes of the total population density while the individuals experience a pairwise Prisoners Dilemma game. The extension devised here contains a dilution parameter to conform with the experimental procedure, in addition to a term accounting for Allee effects. In contrast to other descriptions proposed in similar contexts, however, the model here does not account for assortative encounters, group or kin selection. Nonetheless, it describes surprisingly well both qualitatively and quantitatively the features of the observed phase diagram. We discuss these results in terms of the behavior of an effective payoff matrix defined accordingly.

On the analysis of large-scale genomic structures.

We apply methods from statistical physics (histograms, correlation functions, fractal dimensions, and singularity spectra) to characterize large-scale structure of the distribution of nucleotides along genomic sequences. We discuss the role of the extension of noncoding segments ("junk DNA") for the genomic organization, and the connection between the coding segment distribution and the high-eukaryotic chromatin condensation. The following sequences taken from GenBank were analyzed: complete genome of Xanthomonas campestri, complete genome of yeast, chromosome V of Caenorhabditis elegans, and human chromosome XVII around gene BRCA1. The results are compared with the random and periodic sequences and those generated by simple and generalized fractal Cantor sets.

The efficiency of photolyase and indole complexes to repair DNA containing dimers of pyrimidine: a theoretical analysis of the electron transfer reactions.

We analyze the effects of competing reactions to the efficiency of enzymatic splitting of pyrimidine dimers formed in DNA by the incidence of ultraviolet radiation. This is accomplished with the aid of a formula that expresses the efficiency of the repair in terms of parameters that regulate the reaction rates for primary and for back long-range electron transfers taking place in the process. Comparison of experimental data with estimations on account of this formula supports early conjectures in the literature that attribute the relative high performance of the enzymatic complexes of photolyase to its ability to suppress the back reaction.