Topological features of gene regulatory networks can be successfully reproduced by a model population evolving under selection for short dynamical attractors. The evolved population of networks exhibit motif statistics, summarized by significance profiles, which closely match those of E. coli, S. cerevsiae and B. subtilis, in such features as the excess of linear motifs and feed-forward loops, and deficiency of feedback loops. The slow relaxation to stasis is a hallmark of a rugged fitness landscape, with independently evolving populations exploring distinct valleys strongly differing in network properties.

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We study the discrete-time quantum walk on the line with a single phase impurity. The spread and localisation properties of discrete-time walks initialized at the impurity site are affected by the appearance of bound states and their reflection symmetry. Here, we measure localisation by means of an effective localisation length and an effective participation ratio, which are obtained by averaging over all eigenstates and over all initial states, respectively. We observe that the reduced coin system dynamics undergoes oscillations in the long-time limit with the frequencies determined by the sublattice operator and the bound state quasi-energy differences. The oscillations give rise to non-Markovian evolution, which we quantify using the trace distance and entanglement based measures of non-Markovianity. Indeed, we reveal that the degree of the non-Markovian behaviour is closely related to the emergence of bound states due to the phase impurity. We also show that the considered measures give qualitatively different results depending on the number and symmetries of supported bound states. Finally, comparing localisation and non-Markovianity measures, we demonstrate that the degree of non-Markovianity becomes maximum when the walker is most localised in position space.

We study metanetworks arising in genotype and phenotype spaces, in the context of a model population of Boolean graphs evolved under selection for short dynamical attractors. We define the adjacency matrix of a graph as its genotype, which gets mutated in the course of evolution, while its phenotype is its set of dynamical attractors. Metanetworks in the genotype and phenotype spaces are formed, respectively, by genetic proximity and by phenotypic similarity, the latter weighted by the sizes of the basins of attraction of the shared attractors. We find that populations of evolved networks form giant clusters in genotype space, have Poissonian degree distributions but exhibit hierarchically organized κ-core decompositions. Nevertheless, at large scales, they form tree-like expander graphs. Random populations of Boolean graphs are typically so far removed from each other genetically that they cannot form a metanetwork. In phenotype space, the metanetworks of evolved populations are super robust both under the elimination of weak connections and random removal of nodes.

Thermal expansion coefficient of nickel bulk is investigated at temperatures 75-125K. Elastic minimum image convention is used to simulate thermal effects on the sample. Thermal expansion coefficient and specific heat of the nickel sample attained after simulations are compared to experimental data in the literature.