In certain physical situations, extensive interactions arise naturally in systems. We consider one such situation, namely, small-world couplings. We show that, for a fixed fraction of nonlocal couplings, synchronous chaos is always a stable attractor in the thermodynamic limit. We point out that randomness helps synchronization. We also show that there is a size dependent bifurcation in the collective behavior in such systems.

The nucleocapsid protein (N) of the severe acute respiratory syndrome coronavirus (SARS-CoV) packages the viral genomic RNA and is crucial for viability. However, the RNA-binding mechanism is poorly understood. We have shown previously that the N protein contains two structural domains—the N-terminal domain (NTD; residues 45 to 181) and the C-terminal dimerization domain (CTD; residues 248 to 365)—flanked by long stretches of disordered regions accounting for almost half of the entire sequence. Small-angle X-ray scattering data show that the protein is in an extended conformation and that the two structural domains of the SARS-CoV N protein are far apart. Both the NTD and the CTD have been shown to bind RNA. Here we show that all disordered regions are also capable of binding to RNA. Constructs containing multiple RNA-binding regions showed Hill coefficients greater than 1, suggesting that the N protein binds to RNA cooperatively. The effect can be explained by the “coupled-allostery” model, devised to explain the allosteric effect in a multidomain regulatory system. Although the N proteins of different coronaviruses share very low sequence homology, the physicochemical features described above may be conserved across different groups of Coronaviridae . The current results underscore the important roles of multisite nucleic acid binding and intrinsic disorder in N protein function and RNP packaging.

We present an exact solution of Eigen’s quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasispecies under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady-state solution shows a multicenter behavior.

Real network data is often incomplete and noisy, where link prediction algorithms and spurious link identification algorithms can be applied. Thus far, it lacks a general method to transform network organizing mechanisms to link prediction algorithms. Here we use an algorithmic framework where a network’s probability is calculated according to a predefined structural Hamiltonian that takes into account the network organizing principles and a non-observed link is scored by the conditional probability of adding the link to the observed network. Extensive numerical simulations show that the proposed algorithm has remarkably higher accuracy than the state-of-the-art methods in uncovering missing links and identifying spurious links in many complex biological and social networks. Such method also finds applications in exploring the underlying network evolutionary mechanisms.

The phase transition in the Ising model and the percolation transition in the lattice percolation model have many common characteristics which have motivated researchers to explore whether the former is a percolation transition of a correlated percolation model. Previous attempts to draw such a connection have been either unsuccessful or unsatisfactory. Considering each lattice site with an Ising spin occupied and the nearest-neighbor (NN) coupling between occupied sites as a bond with a bond probability $p$ depending on the NN coupling constant $J$ and the temperature $T$, we formally show that the partition function of the Ising model is the generating function of bond-correlated percolation model (BCPM) with a bond probability $p=1-\exp \left(\frac{-2J}{\mathrm{kT}}\right)$. The BCPM has the Ising critical temperature and exponents, including $\nu ,{\nu }^{\prime },\eta ,\beta ,\alpha ,{\alpha }^{\prime }$, and $\gamma$ (perhaps also ${\gamma }^{\prime }$). From the connection between the Ising model and the BCPM, we also derive and hence give a geometrical meaning of the finite-size scaling and broadening at first-order phase transitions of the Ising model. Our approach may easily be extended to many spin models and give geometrical meaning to other properties of spin models.

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class.