Schulman Replies

This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896 (2000)) on PRL 83, 5419 (1999). The suitability of the particlar two-time boundary value problem used in the earlier PRL is argued

Opposite Thermodynamic Arrows of Time

A model in which two weakly coupled systems maintain opposite running thermodynamic arrows of time is exhibited. Each experiences its own retarded electromagnetic interaction and can be seen by the other. The possibility of opposite-arrow systems at stellar distances is explored and a relation to dark matter suggested.Comment: To appear in Phys. Rev. Let

Redundant variables and Granger causality

We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under-estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.Comment: 4 pages, 5 figures. Accepted for publication in Physical Review

Transfer Entropy as a Log-likelihood Ratio

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic chi-squared distribution is established for the transfer entropy estimator. The result generalises the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

Conceptualizing cultures of violence and cultural change

The historiography of violence has undergone a distinct cultural turn as attention has shifted from examining violence as a clearly defined (and countable) social problem to analysing its historically defined 'social meaning'. Nevertheless, the precise nature of the relationship between 'violence' and 'culture' is still being established. How are 'cultures of violence' formed? What impact do they have on violent behaviour? How do they change? This essay examines some of the conceptual aspects of the relationship between culture and violence. It brings together empirical research into nineteenth-century England with recent research results from other European contexts to examine three aspects of the relationship between culture and violence. These are organised under the labels 'seeing violence', 'identifying the violent' and 'changing violence'. Within a particular society, narratives regarding particular kinds of behaviour shape cultural attitudes. The notion 'violence' is thus defined in relation to physically aggressive acts as well as by being connected to other kinds of attitudes and contexts. As a result, the boundaries between physical aggression which is legitimate and that which is illegitimate (and thus 'violence') are set. Once 'violence' is defined, particular cultures form ideas about who is responsible for it: reactions to violence become associated with social arrangements such as class and gender as well as to attitudes toward the self. Finally, cultures of violence make efforts to tame or eradicate illegitimate forms of physical aggression. This process is not only connected to the development of new forms of power (e.g., new policing or punishment strategies) but also to less tangible cultural influences which aim at changing the behaviour defined as violence (in particular among the social groups identified as violent). Even if successful, this three-tiered process of seeing violence, identifying the violent and changing violence continues anew, emphasising the ways that cultures of violence develop through a continuous process of reevaluation and reinvention

Noise-induced dynamics in bistable systems with delay

Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. In this two-state approximation, we found analytical formulae for the autocorrelation function, the power spectrum, and the linear response to a periodic perturbation. They show very good agreement with direct numerical simulations of the original Langevin equation. The power spectrum has a pronounced peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

A model of caregiver paediatric HIV disclosure decision-making

Many of the over 3 million HIV-positive children will only be told of their status as adolescents. Knowing one’s status may increase treatment adherence, reduce onward HIV transmission, increase trust in caregivers, and maximise available support. Yet deciding whether, what, how, and when to tell HIV-positive children about their condition, is challenging for caregivers. We systematically review HIV disclosure theories before presenting a process model of caregiver paediatric HIV disclosure decision-making. The model, consisting of both a pre-intention and a post-intention stage, integrates individual and contextual determinants. It aims to be situationally-specific, broadly applicable, and consistent with the empirical literature. Research and practice implications are discussed