ﻻ يوجد ملخص باللغة العربية
We present a new non-Archimedean model of evolutionary dynamics, in which the genomes are represented by p-adic numbers. In this model the genomes have a variable length, not necessarily bounded, in contrast with the classical models where the length is fixed. The time evolution of the concentration of a given genome is controlled by a p-adic evolution equation. This equation depends on a fitness function f and on mutation measure Q. By choosing a mutation measure of Gibbs type, and by using a p-adic version of the Maynard Smith Ansatz, we show the existence of threshold function M_{c}(f,Q), such that the long term survival of a genome requires that its length grows faster than M_{c}(f,Q). This implies that Eigens paradox does not occur if the complexity of genomes grows at the right pace. About twenty years ago, Scheuring and Poole, Jeffares, Penny proposed a hypothesis to explain Eigens paradox. Our mathematical model shows that this biological hypothesis is feasible, but it requires p-adic analysis instead of real analysis. More exactly, the Darwin-Eigen cycle proposed by Poole et al. takes place if the length of the genomes exceeds M_{c}(f,Q).
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that
We introduced a more general predator-prey model to analyze the paradox of enrichment. We hope the results obtained for the model can guide us on identifying real field paradox of enrichment.
Policy gradient and actor-critic algorithms form the basis of many commonly used training techniques in deep reinforcement learning. Using these algorithms in multiagent environments poses problems such as nonstationarity and instability. In this pap
We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at
We continue the study in [21] of the linearizability near an indif- ferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz [13] in 1981 that Siegels linearization theore