Replicator dynamics with turnover of players.

We study adaptive dynamics in games where players abandon the population at a given rate and are replaced by naive players characterized by a prior distribution over the admitted strategies. We demonstrate how such a process leads macroscopically to a variant of the replicator equation, with an additional term accounting for player turnover. We study how Nash equilibria and the dynamics of the system are modified by this additional term for prototypical examples such as the rock-paper-scissors game and different classes of two-action games played between two distinct populations.

Equilibrium strategy and population-size effects in lowest unique bid auctions.

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies.

Protein localization with flexible DNA or RNA.

Localization of activity is ubiquitous in life, and also within sub-cellular compartments. Localization provides potential advantages as different proteins involved in the same cellular process may supplement each other on a fast timescale. It might also prevent proteins from being active in other regions of the cell.

Structural correlations in bacterial metabolic networks.

Background: Evolution of metabolism occurs through the acquisition and loss of genes whose products acts as enzymes in metabolic reactions, and from a presumably simple primordial metabolism the organisms living today have evolved complex and highly variable metabolisms. We have studied this phenomenon by comparing the metabolic networks of 134 bacterial species with known phylogenetic relationships, and by studying a neutral model of metabolic network evolution.

Results: We consider the 'union-network' of 134 bacterial metabolisms, and also the union of two smaller subsets of closely related species.

Flow improvement caused by agents who ignore traffic rules.

A system of agents moving along a road in both directions is studied numerically within a cellular-automata formulation. An agent steps to the right with probability q or to the left with 1-q when encountering other agents. Our model is restricted to two agent types, traffic-rule abiders (q=1) and traffic-rule ignorers (q=1/2) , and the traffic flow, resulting from the interaction between these two types of agents, which is obtained as a function of density and relative fraction.

One hub-one process: a tool based view on regulatory network topology.

Background: The relationship between the regulatory design and the functionality of molecular networks is a key issue in biology. Modules and motifs have been associated to various cellular processes, thereby providing anecdotal evidence for performance based localization on molecular networks.

Results: To quantify structure-function relationship we investigate similarities of proteins which are close in the regulatory network of the yeast Saccharomyces Cerevisiae.

The blind watchmaker network: scale-freeness and evolution.

It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects a ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent gamma>/=2.

Optimization and scale-freeness for complex networks.

Complex networks are mapped to a model of boxes and balls where the balls are distinguishable. It is shown that the scale-free size distribution of boxes maximizes the information associated with the boxes provided configurations including boxes containing a finite fraction of the total amount of balls are excluded. It is conjectured that for a connected network with only links between different nodes, the nodes with a finite fraction of links are effectively suppressed.

Degree landscapes in scale-free networks.

We generalize the degree-organizational view of real-world networks with broad degree distributions in a landscape analog with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes correspond to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains.

Models and average properties of scale-free directed networks.

We extend the merging model for undirected networks by Kim [Eur. Phys. J.