Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition. We find the following: SI (but not divergence) is inversely proportional to sequence length for a random sequence but is length-independent for genomes; the genomic SI is always greater and, for shorter words and longer sequences, hundreds to thousands times greater than the SI in a random sequence whose length and composition match those of the genome; genomic SIs appear to have word-length dependent universal values. The universality is inferred to be an evolution footprint of a universal mode for genome growth.

We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.

Biological systems, from macromolecules to whole organisms, are robust if they continue to function, survive, or reproduce when faced with mutations, environmental change, and internal noise. I focus here on biological systems that are robust to mutations and ask whether such systems are more or less evolvable, in the sense that they can acquire novel properties. The more robust a system is, the more mutations in it are neutral, that is, without phenotypic effect. I argue here that such neutral change - and thus robustness - can be a key to future evolutionary innovation, if one accepts that neutrality is not an essential feature of a mutation. That is, a once neutral mutation may cause phenotypic effects in a changed environment or genetic background. I argue that most, if not all, neutral mutations are of this sort, and that the essentialist notion of neutrality should be abandoned. This perspective reconciles two opposing views on the forces dominating organismal evolution, natural selection and random drift: Neutral mutations occur and are especially abundant in robust systems, but they do not remain neutral indefinitely, and eventually become visible to natural selection, where some of them lead to evolutionary innovations.

We present a model for the emergence of collective decision in a system composed of interacting agents, each of whom is free to choose one of two possible alternatives at every time instant. The choice of each agent is influenced by those of its neighbors, as well as by its personal preference. The agent's preference, in turn, is not fixed, but adjusts to changing circumstances, based on the choices it has made previously (adaptation), as well as whether such choices accorded with those of the majority (learning). We observe a phase transition in the distribution of the collective decision in the presence of learning dynamics. The system gets polarized although individuals may continue to alternate among the choices. This indicates the existence of long-range correlations among the behavior of agents, and is observed in two-dimensional lattices as spatial patterns in the shape of vortices or spirals. Results of our model corroborate with empirical data on movie popularity, financial markets and voting behavior.

Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared to the concept of funnels in the potential energy landscape. Two existing algorithms have been used to find community structure, one involving removing edges with high betweenness, the other involving optimization of the modularity. The definition of the modularity has been refined, making it more appropriate for networks such as these where multiple edges and self-connections are not included. The optimization algorithm has also been improved, using Monte Carlo methods with simulated annealing and basin hopping, both often used successfully in other optimization problems. In addition to the small clusters, two examples with known heterogeneous landscapes, LJ_13 with one labelled atom and LJ_38, were studied with this approach. The network methods found communities that are comparable to those expected from landscape analyses. This is particularly interesting since the network model does not take any barrier heights or energies of minima into account. For comparison, the network associated with a two-dimensional hexagonal lattice is also studied and is found to have high modularity, thus raising some questions about the interpretation of the community structure associated with such partitions.