Reentrant phase transition in a predator-prey model.

We numerically investigate the six-species predator-prey game in complex networks as well as in d -dimensional regular hypercubic lattices with d=1,2,...,6 . The food-web topology of the six species contains two directed loops, each of which is composed of cyclically predating three species. As the mutation rate is lowered below the well-defined phase transition point, the Z2 symmetry related with the interchange in the two loops is spontaneously broken, and it has been known that the system develops the defensive alliance in which three cyclically predating species defend each other against the invasion of other species. In the Watts-Strogatz small-world network structure characterized by the rewiring probability alpha , the phase diagram shows the reentrant behavior as alpha is varied, indicating a twofold role of the shortcuts. In d -dimensional regular hypercubic lattices, the system also exhibits the reentrant phase transition as d is increased. We identify universality class of the phase transition and discuss the proper mean-field limit of the system.

Streptavidin-Decorated Algorithmic DNA Lattices Constructed by Substrate-Assisted Growth Method.

The ultimate goal of DNA computing is to store information at higher density and solve complex problems with less computational time and minimal error. Most algorithmic DNA lattices have been constructed using the free-solution growth (FSG) annealing method, and hairpin-embedded DNA rule tiles have been introduced in most algorithmic implementations to differentiate 0- and 1-bit information. Here, we developed streptavidin (SA)-decorated algorithmic COPY (produced line-like patterns with biotinylated 1-bit rule tiles) and XOR (triangle-like patterns) lattices constructed by a substrate-assisted growth (SAG) method and FSG. SA decoration in algorithmic lattices provides an efficient platform for visualizing bit information, and the SAG method in algorithmic assembly offers full coverage of algorithmic lattices on a substrate with a relatively lower DNA concentration than previous methods. The algorithmic COPY and XOR lattices assembled with various ratios of 0- and 1-bit rule tiles were verified by atomic force microscopy. We found that even asymmetric DNA patterns produced by certain algorithmic logic gates could be easily constructed by SAG. Finally, we evaluated sorting factors and error rates of algorithmic COPY and XOR lattices to determine the bit population and quality of the algorithmic assembly. Because of the catalytic effect of the substrate, the sorting factor of algorithmic DX-DNA lattices did not greatly influence the specific rules (i.e., COPY and XOR logic gates) annealed by SAG. Additionally, we found that the overall error rates of algorithmic DX-DNA lattices prepared by the FSG and SAG methods were low, within the range of 1-3%. Hence, the self-assembled algorithmic patterns generated with DNA molecules may serve as a scaffold for molecular demultiplexing circuits and computing.

Double resonance in the infinite-range quantum Ising model.

We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the z direction is performed at various transverse field strengths g. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of g, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.

Voter model on a directed network: role of bidirectional opinion exchanges.

The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability p . In order to discriminate the better and worse opinions, we break the Z2 symmetry (σ=±1) by giving a little more preference to the opinion σ=1 . It is found that as p becomes larger, introducing more complicated pattern of information flow channels, and as the network size N becomes larger, the system eventually evolves to the state in which more voters agree on the better opinion, even though the voter at the top of the hierarchy keeps the worse opinion. We also find that the pure hierarchical tree makes opinion agreement very fast, while the final absorbing state can easily be influenced by voters at the higher ranks. On the other hand, although the ordering occurs much slower, the existence of complicated pattern of bidirectional information flow allows the system to agree on the better opinion.