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We study the evolutionary robustness of strategies in infinitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator…
We show that sparse spherical harmonic expansions can be efficiently recovered from a small number of randomly chosen samples on the sphere. To establish the main result, we verify the restricted isometry property of an associated…
We introduce the concept of self-healing in the field of complex networks. Obvious applications range from infrastructural to technological networks. By exploiting the presence of redundant links in recovering the connectivity of the…
Let $M$ be a matroid. We study the expansions of $M$ mainly to see how the combinatorial properties of $M$ and its expansions are related to each other. It is shown that $M$ is a graphic, binary or a transversal matroid if and only if an…
As biomedical sciences discover new layers of complexity in the mechanisms of life and disease, mathematical models trying to catch up with these developments become mathematically intractable. As a result, in the grand scheme of things,…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms.…
Competing risks models for a repairable system subject to several failure modes are discussed. Under minimal repair, it is assumed that each failure mode has a power law intensity. An orthogonal reparametrization is used to obtain an…
We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely continuous is very small - of co-dimension at least one in…
Modern networks are large, highly complex and dynamic. Add to that the mobility of the agents comprising many of these networks. It is difficult or even impossible for such systems to be managed centrally in an efficient manner. It is…
The results of modeling of radiation defects formation and evolution on the surface and in the volume of a crystal are presented in this article. Statistical properties are calculated for the investigated system. It is revealed that defects…
We investigate the effect of spatial range expansions on the evolution of fitness when beneficial and deleterious mutations co-segregate. We perform individual-based simulations of a uniform linear habitat and complement them with…
We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular…
We study how maximal regularity estimates with respect to the continuous functions improve automatically in cases where the spatial norm is fundamentally different from the supremum norm. More precisely, we invoke properties such as weak…
We resort to variational methods to evaluate the asymptotic behavior of fine metamaterials as a function of cell size. To zeroth order, the metamaterial behaves as a micropolar continuum with both displacement and rotation degrees of…
Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…
We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated…
With the discovery of gravitational waves and fast radio bursts, wave optics has become increasingly relevant in astrophysics. This paper studies the behaviour of random gravitational and plasma lenses, presenting the refractive and…
Suppose $M$ is a compact Riemannian manifold and $p\in M$ an arbitrary point. We employ estimates on the volume growth around $p$ to prove that the only conformal compactification of $M\setminus\{p\}$ is $M$ itself.
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…