Entropy2015, 17(4), 1734-1754; doi:10.3390/e17041734 (registering DOI) - published 27 March 2015 Show/Hide Abstract
Abstract: We propose a new herd mechanism and embed it into an open financial market system, which allows traders to get in and out of the system based on some transition rates. Moreover, the novel mechanism can avoid the volatility disappearance when the population scale increases. There are three kinds of heterogeneous agents in the system: optimistic, pessimistic and fundamental. Interactions especially occur among three different groups of agents instead of two, which makes the artificial financial market more close to the real one. By the simulation results of this complex system, we can explain stylized facts like volatility clustering and find the key parameters of market bubbles and market collapses.
Entropy2015, 17(4), 1701-1733; doi:10.3390/e17041701 (registering DOI) - published 27 March 2015 Show/Hide Abstract
Abstract: The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related eventsmysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.
Entropy2015, 17(4), 1690-1700; doi:10.3390/e17041690 (registering DOI) - published 27 March 2015 Show/Hide Abstract
Abstract: Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (PME) give a solution to the obverse Majerník problem; and (2) isWagner correct when he claims that Jeffrey’s updating principle (JUP) contradicts PME? Majerník shows that PME provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether PME also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that in the special case introduced by Wagner PME does not contradict JUP, but elegantly generalizes it and offers a more integrated approach to probability updating.
Entropy2015, 17(4), 1673-1689; doi:10.3390/e17041673 (registering DOI) - published 27 March 2015 Show/Hide Abstract
Abstract: This study delves further into the analysis of genomic data by computing a variety of complexity measures. We analyze the effect of window size and evaluate the precision and recall of the prediction of gene zones, aided with a much larger dataset (full chromosomes). A technique based on the separation of two cases (gene-containing and non-gene-containing) has been developed as a basic gene predictor for automated DNA analysis. This predictor was tested on various sequences of human DNA obtained from public databases, in a set of three experiments. The first one covers window size and other parameters; the second one corresponds to an analysis of a full human chromosome (198 million nucleic acids); and the last one tests subject variability (with five different individual subjects). All three experiments have high-quality results, in terms of recall and precision, thus indicating the effectiveness of the predictor.
Entropy2015, 17(4), 1660-1672; doi:10.3390/e17041660 - published 26 March 2015 Show/Hide Abstract
Abstract: The voluntary prisoner’s dilemma (VPD) game has sparked interest from various fields since it was proposed as an effective mechanism to incentivize cooperative behavior. Current studies show that the inherent cyclic dominance of the strategies of the VPD game results in periodic oscillations in population. This paper investigated the influence of the level of individual rationality and the size of a population on the evolutionary dynamics of the VPD game. Different deterministic dynamics, such as the replicator dynamic, the Smith dynamic, the Brown-von Neumann-Nash (BNN) dynamic and the best response (BR) dynamic, for the evolutionary VPD game were modeled and simulated. The stochastic evolutionary dynamics based on quasi birth and death (QBD) process was proposed for the evolutionary VPD game and compared with deterministic dynamics. The results indicated that with the increase of the loners’ fixed payoff, the loner is more likely to remain in the stable state of a VPD game under any of the dynamics mentioned above. However, the different speeds of motion under the dynamics in the cycle dominance proved to be diverse under different evolutionary dynamics and also highly sensitive to the rationality of individuals in a population. Furthermore, in QBD stochastic dynamics, the size of the population has a remarkable effect on the possibility distribution. When the population size increases, the limited distribution of the QBD process will be in accordance with the results in the deterministic dynamics.
Entropy2015, 17(4), 1634-1659; doi:10.3390/e17041634 - published 26 March 2015 Show/Hide Abstract
Abstract: We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one-way information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All of these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.