Theory of the Three-Group Evolutionary Minority Game

Based on the adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier[1], we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from segregation (into opposing groups) to clustering (towards cautious behaviors). Particular to the three-group EMG, the strategy switching in the "extreme" group does not occur at every losing step and is strongly intermittent. This leads to an correction to the critical value of the number of agents at the transition, $N_c$. Our expression for $N_c$ is in agreement with the results obtained from our numerical simulations.Comment: 4 pages and 2 figure

Supramolecular drug inclusion complex constructed from cucurbit[7]uril and the hepatitis B drug Adefovir

The interaction between cucuribit[7]uril (Q[7]) and Adefovir (ADV) has been studied in aqueous solution by 1H NMR spectroscopy, electronic absorption spectroscopy, Isothermal Titration Calorimetry and mass spectrometry. The results revealed that an inclusion complex was formed via encapsulation of the purine rings of the guest ADV, while the phosphonomethoxyethyl group was prevented from entering the cavity. ITC data revealed that the formation of this 1:1 inclusion complex is mainly driven by favourable enthalpy changes. Studies investigating the release of ADV from the inclusion complex revealed enhanced rates under acidic conditions, although the rates were slower than observed for the free guest under the same conditions. Thermal stability studies indicated that the included form of ADV was more stable that the free form

A hemicyanine and cucurbit[n]uril inclusion complex: competitive guest binding of cucurbit[7]uril and cucurbit[8]uril

The interaction between the hemicyanine indole derivative H and the cucubit[n]urils Q[7] and Q[8] has been studied using 1H NMR and UV spectroscopy as well as by fluorescence experiments. Competitive studies on the inclusion of H by Q[7] and Q[8] have also been conducted, and reveal that on changing the size of the Q[n] cavity, the binding behaviour can be very different

Theory of Phase Transition in the Evolutionary Minority Game

We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis of a simplified EMG involving three groups of agents: two groups of opposing agents and one group of cautious agents. Two key factors affect the population distribution of the agents. One is the market impact (the self-interaction), which has been identified previously. The other is the market inefficiency due to the short-time imbalance in the number of agents using opposite strategies. Large market impact favors "extreme" players who choose fixed strategies, while large market inefficiency favors cautious players. The phase transition depends on the number of agents ($N$), the reward-to-fine ratio ($R$), as well as the wealth reduction threshold ($d$) for switching strategy. When the rate for switching strategy is large, there is strong clustering of cautious agents. On the other hand, when $N$ is small, the market impact becomes large, and the extreme behavior is favored.Comment: 5 pages and 3 figure