We study a simplified, solvable model of a fully-connected metabolic network with constrained quenched disorder to mimic the conservation laws imposed by stoichiometry on chemical reactions. Within a spin-glass type of approach, we show that in prese
nce of a conserved metabolic pool the flux state corresponding to maximal growth is stationary independently of the pool size. In addition, and at odds with the case of unconstrained networks, the volume of optimal flux configurations remains finite, indicating that the frustration imposed by stoichiometric constraints, while reducing growth capabilities, confers robustness and flexibility to the system. These results have a clear biological interpretation and provide a basic, fully analytical explanation to features recently observed in real metabolic networks.
We explore the effect of discounting and experimentation in a simple model of interacting adaptive agents. Agents belong to either of two types and each has to decide whether to participate a game or not, the game being profitable when there is an ex
cess of players of the other type. We find the emergence of large fluctuations as a result of the onset of a dynamical instability which may arise discontinuously (increasing the discount factor) or continuously (decreasing the experimentation rate). The phase diagram is characterized in detail and noise amplification close to a bifurcation point is identified as the physical mechanism behind the instability.
The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents learning rules. Here we study how the standard scenario is a
ffected in a mixed population game in which agents with the `optimal learning rule (i.e. the one leading to efficiency) coexist with ones whose adaptive dynamics is sub-optimal. Our generic finding is that any non-vanishing intensive fraction of optimal agents guarantees the existence of an efficient phase. Specifically, we calculate the dependence of the critical point on the fraction $q$ of `optimal agents focusing our analysis on three cases: MGs with market impact correction, grand-canonical MGs and MGs with heterogeneous comfort levels.
