Accurate computation of low-temperature thermodynamics for quantum spin chains

We apply the biorthonormal transfer-matrix renormalization group (BTMRG) [Phys. Rev. E 83, 036702 (2011)] to study low-temperature properties of quantum spin chains. Simulation on isotropic Heisenberg spin-1/2 chain demonstrates that the BTMRG outperforms the conventional transfer-matrix renormalization group (TMRG) by successfully accessing far lower temperature unreachable by conventional TMRG, while retaining the same level of accuracy. The power of the method is further illustrated by the calculation of the low-temperature specific heat for a frustrated spin chain.Comment: 5 pages, 4 figure

Long-time dynamics of quantum chains: transfer-matrix renormalization group and entanglement of the maximal eigenvector

By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recent proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012)]

Evolutionary hypergame dynamics

A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and political systems, diversity in the knowledge, experience, and background among the individuals can be expected. Games in which the players do not have an identical strategy set are hypergames. Studies of hypergame dynamics have been scarce, especially those on networks. We investigate evolutionary hypergame dynamics on regular lattices using a prototypical model of three available strategies, in which the strategy set of each player contains two of the three strategies. Our computations reveal that more complex dynamical phases emerge from the system than those from the traditional evolutionary game dynamics with full knowledge of the complete set of available strategies, which include single-strategy absorption phases, a cyclic competition (`rock-paper-scissors') type of phase, and an uncertain phase in which the dominant strategy adopted by the population is unpredictable. Exploiting the pair interaction and mean field approximations, we obtain a qualitative understanding of the emergence of the single strategy and uncertain phases. We find the striking phenomenon of strategy revival associated with the cyclic competition phase and provide a qualitative explanation.Our work demonstrates that the diversity in the individuals' strategy set can play an important role in the evolution of strategy distribution in the system. From the point of view of control, the emergence of the complex phases offers the possibility for harnessing evolutionary game dynamics through small changes in individuals' probability of strategy adoption.Comment: 11 pages, 10 figure

Spatiotemporal patterns and predictability of cyberattacks

A relatively unexplored issue in cybersecurity science and engineering is whether there exist intrinsic patterns of cyberattacks. Conventional wisdom favors absence of such patterns due to the overwhelming complexity of the modern cyberspace. Surprisingly, through a detailed analysis of an extensive data set that records the time-dependent frequencies of attacks over a relatively wide range of consecutive IP addresses, we successfully uncover intrinsic spatiotemporal patterns underlying cyberattacks, where the term "spatio" refers to the IP address space. In particular, we focus on analyzing {\em macroscopic} properties of the attack traffic flows and identify two main patterns with distinct spatiotemporal characteristics: deterministic and stochastic. Strikingly, there are very few sets of major attackers committing almost all the attacks, since their attack "fingerprints" and target selection scheme can be unequivocally identified according to the very limited number of unique spatiotemporal characteristics, each of which only exists on a consecutive IP region and differs significantly from the others. We utilize a number of quantitative measures, including the flux-fluctuation law, the Markov state transition probability matrix, and predictability measures, to characterize the attack patterns in a comprehensive manner. A general finding is that the attack patterns possess high degrees of predictability, potentially paving the way to anticipating and, consequently, mitigating or even preventing large-scale cyberattacks using macroscopic approaches