In the last few years, the importance of neoantigens in the development of personalized antitumor vaccines has increased remarkably. In order to study whether bioinformatic tools are effective in detecting neoantigens that generate an immune response, DNA samples from patients with cutaneous melanoma in different stages were obtained, resulting in a total of 6048 potential neoantigens gathered. Thereafter, the immunological responses generated by some of those neoantigens ex vivo were tested, using a vaccine designed by a new optimization approach and encapsulated in nanoparticles. Our bioinformatic analysis indicated that no differences were found between the number of neoantigens and that of non-mutated sequences detected as potential binders by IEDB tools. However, those tools were able to highlight neoantigens over non-mutated peptides in HLA-II recognition (p-value 0.03). However, neither HLA-I binding affinity (p-value 0.08) nor Class I immunogenicity values (p-value 0.96) indicated significant differences for the latter parameters. Subsequently, the new vaccine, using aggregative functions and combinatorial optimization, was designed. The six best neoantigens were selected and formulated into two nanoparticles, with which the immune response ex vivo was evaluated, demonstrating a specific activation of the immune response. This study reinforces the use of bioinformatic tools in vaccine development, as their usefulness is proven both in silico and ex vivo.

We study metabelian groups 𝐺 given by full rank finite presentations ${⟨A\mid R⟩}_M$ in the variety ℳ of metabelian groups. We prove that 𝐺 is a product of a free metabelian subgroup of rank $\max \{0,\left|A\right|-\left|R\right|\}$ and a virtually abelian normal subgroup, and that if $\left|R\right|\le \left|A\right|-2$, then the Diophantine problem of 𝐺 is undecidable, while it is decidable if $\left|R\right|\ge \left|A\right|$. We further prove that if $\left|R\right|\le \left|A\right|-1$, then, in any direct decomposition of 𝐺, all factors, except one, are virtually abelian. Since finite presentations have full rank asymptotically almost surely, metabelian groups finitely presented in the variety of metabelian groups satisfy all the aforementioned properties asymptotically almost surely.

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.