Q-Gaussian diffusion in stock markets

We analyze the Standard & Poor's 500 stock market index from the past 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong superdiffusion together with short-time correlations and the second one corresponds to weak superdiffusion with weak time correlations. Both regimes are well described by q-Gaussian distributions. The porous media equation-a special case of the Tsallis-Bukman equation-is used to derive the governing equation for these regimes and the Black-Scholes diffusion coefficient is explicitly obtained from the governing equation.

Self-referential basis of undecidable dynamics: From the Liar paradox and the halting problem to the edge of chaos

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.

The Association Between Social Network Factors with Depression and Anxiety at Different Life Stages

This study examines whether social network factors influence individual's depression and anxiety outcomes at different life stages. Data was drawn from the Household, Income and Labour Dynamics in Australia survey. Hierarchical regression modelling was applied to examine the effects within and across different life stages. The depression and anxiety measures were taken from the Kessler Psychological Distress Scale (K10) and the social network factors were taken from the self-completion questionnaire. With the exception of social trust in seniors, the social network factors were significant predictors of depression and anxiety. This has practical implications for the design of social policy initiatives.

Social network factors as mediators of mental health and psychological distress

BACKGROUND

Although mental health (MH) is overall strongly associated with psychological distress (PD), this association is very weak for the sample with high PD. This relationship remains understudied.

AIM

This study examines the association between MH and PD and whether this association is mediated by social network (SN) factors for individuals with high PD.

METHOD

Data were taken from the Household Income and Labour Dynamics in Australia study ( N = 756). MH was measured using the MH sub-scale of the general health survey (Short Form (SF)-36) and PD was measured using the Kessler Psychological Distress Scale (K10). The SN measures were derived from the self-completion questionnaire. Using bootstrap mediation analysis, we tested whether the association between MH and PD is mediated by SN factors.

RESULT

The correlation between MH and PD was r = -.410 ( p < .001). The mediational analysis results show that social isolation mediates the association between MH and PD with an indirect effect of β = -0.0070 (confidence interval (CI) = -0.0133 to -0.0023). Moreover, social connections also mediated the association between MH and PD with an indirect effect of β = -0.0073 (CI = -0.0141 to -0.0028).

CONCLUSION

This study has practical implications for the design of social policies that attempt to reduce social isolation and enhance social connectedness to protect MH.

Fisher transfer entropy: quantifying the gain in transient sensitivity

We introduce a novel measure, Fisher transfer entropy (FTE), which quantifies a gain in sensitivity to a control parameter of a state transition, in the context of another observable source. The new measure captures both transient and contextual qualities of transfer entropy and the sensitivity characteristics of Fisher information. FTE is exemplified for a ferromagnetic two-dimensional lattice Ising model with Glauber dynamics and is shown to diverge at the critical point.

The neural circuitry of expertise: perceptual learning and social cognition

Amongst the most significant questions we are confronted with today include the integration of the brain's micro-circuitry, our ability to build the complex social networks that underpin society and how our society impacts on our ecological environment. In trying to unravel these issues one place to begin is at the level of the individual: to consider how we accumulate information about our environment, how this information leads to decisions and how our individual decisions in turn create our social environment. While this is an enormous task, we may already have at hand many of the tools we need. This article is intended to review some of the recent results in neuro-cognitive research and show how they can be extended to two very specific and interrelated types of expertise: perceptual expertise and social cognition. These two cognitive skills span a vast range of our genetic heritage. Perceptual expertise developed very early in our evolutionary history and is a highly developed part of all mammals' cognitive ability. On the other hand social cognition is most highly developed in humans in that we are able to maintain larger and more stable long term social connections with more behaviorally diverse individuals than any other species. To illustrate these ideas I will discuss board games as a toy model of social interactions as they include many of the relevant concepts: perceptual learning, decision-making, long term planning and understanding the mental states of other people. Using techniques that have been developed in mathematical psychology, I show that we can represent some of the key features of expertise using stochastic differential equations (SDEs). Such models demonstrate how an expert's long exposure to a particular context influences the information they accumulate in order to make a decision.These processes are not confined to board games, we are all experts in our daily lives through long exposure to the many regularities of daily tasks and social contexts.

Information flow in a kinetic Ising model peaks in the disordered phase

There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition.

Hysteresis effects of changing the parameters of noncooperative games

We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hysteresis effects. In particular, we show that by gradually imposing individual-specific tax rates on the players of the game, and then gradually removing those taxes, the players move from a poor equilibrium to one that is better for all of them.