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Yayın Spectral renormalization group for the Gaussian model and 𝜓4 theory on nonspatial networks(American Physical Society, 2015-08-06) Tuncer, Aslı; Erzan, AyşeWe implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, (d) over tilde. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At (d) over tilde = 2, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a psi(4) perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2 < <(d)over tilde> < 4.Yayın Evolutionary route to diploidy and sex(National Academy of Sciences, 2001-11-20) Tüzel, Erkan; Sevim, Volkan; Erzan, AyşeBy using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust that even the accidental conversion and pairing of only two diploids give rise to a sexual population.Yayın Strategies for the evolution of sex(American Physical Soc, One Physics Ellipse, 2001-12) Tüzel, Erkan; Sevim, Volkan; Erzan, AyşeWe find that the hypothesis made by Jan, Stauffer, and Moseley [Theory Biosci. 119, 166 (2000)] for the evolution of sex, namely, a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multistable regime. On the other hand, in the limit of extremely slow drive. another transition takes place to a different steady state distribution. with fewer deleterious mutations within the population.
