Numerical studies of planar closed random walks

Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\approx 1.77$.Comment: 15 pages, 15 figure

Off-Critical SLE(2) and SLE(4): a Field Theory Approach

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the off-critical statistics of the source in the Loewner equation describing the two dimensional interfaces. In these two cases we show that ratios of massive by massless partition functions, expressible as ratios of regularised determinants of massive and massless Laplacians, are (local) martingales for the massless interfaces. The off-critical drifts in the stochastic source of the Loewner equation are proportional to the logarithmic derivative of these ratios. We also show that massive correlation functions are (local) martingales for the massive interfaces. In the case of massive SLE(4), we use this property to prove a factorisation of the free boson measure.Comment: 30 pages, 1 figures, Published versio

Note on SLE and logarithmic CFT

It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable highest-weight module of the Virasoro algebra, the representation theory of the logarithmic conformal field theory is related to entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe

Conformal loop ensembles and the stress-energy tensor

We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c <= 1, and including all CFT minimal models). We provide a quick introduction to CLE, a mathematical theory for random loops in simply connected domains with properties of conformal invariance, developed by Sheffield and Werner (2006). We consider its extension to more general regions of definition, and make various hypotheses that are needed for our construction and expected to hold for CLE in the dilute regime. Using this, we identify the stress-energy tensor in the context of CLE. This is done by deriving its associated conformal Ward identities for single insertions in CLE probability functions, along with the appropriate boundary conditions on simply connected domains; its properties under conformal maps, involving the Schwarzian derivative; and its one-point average in terms of the "relative partition function." Part of the construction is in the same spirit as, but widely generalizes, that found in the context of SLE_{8/3} by the author, Riva and Cardy (2006), which only dealt with the case of zero central charge in simply connected hyperbolic regions. We do not use the explicit construction of the CLE probability measure, but only its defining and expected general properties.Comment: 49 pages, 3 figures. This is a concatenated, reduced and simplified version of arXiv:0903.0372 and (especially) arXiv:0908.151

The effects of the spontaneous presence of a spouse/partner and others on cardiovascular reactions to an acute psychological challenge

The presence of supportive others has been associated with attenuated cardiovascular reactivity in the laboratory. The effects of the presence of a spouse and others in a more naturalistic setting have received little attention. Blood pressure and heart rate reactions to mental stress were recorded at home in 1028 married/partnered individuals. For 112 participants, their spouse/partner was present; for 78, at least one other person was present. Women tested with a spouse/partner present showed lower magnitude systolic blood pressure and heart rate reactivity than those tested without. Individuals tested with at least one nonspousal other present also displayed attenuated reactivity. This extends the results of laboratory studies and indicates that the spontaneous presence of others is associated with a reduction in cardiovascular reactivity in an everyday environment; spouse/partner presence would appear to be especially effective for women.\ud \u

TEAMwork: Testing Emotional Attunement and Mutuality During Parent-Adolescent fMRI.

The parent-child relationship and family context influence the development of emotion regulation (ER) brain circuitry and related skills in children and adolescents. Although both parents' and children's ER neurocircuitry simultaneously affect how they interact with one another, neuroimaging studies of parent-child relationships typically include only one member of the dyad in brain imaging procedures. The current study examined brain activation related to parenting and ER in parent-adolescent dyads during concurrent fMRI scanning with a novel task - the Testing Emotional Attunement and Mutuality (TEAM) task. The TEAM task includes feedback trials indicating the other dyad member made an error, resulting in a monetary loss for both participants. Results indicate that positive parenting practices as reported by the adolescent were positively correlated with parents' hemodynamic activation of the ventromedial prefrontal cortex, a region related to empathy, during these error trials. Additionally, during feedback conditions both parents and adolescents exhibited fMRI activation in ER-related regions, including the dorsolateral prefrontal cortex, anterior insula, fusiform gyrus, thalamus, caudate, precuneus, and superior parietal lobule. Adolescents had higher left amygdala activation than parents during the feedback condition. These findings demonstrate the utility of dyadic fMRI scanning for investigating relational processes, particularly in the parent-child relationship

Ignition of thermally sensitive explosives between a contact surface and a shock

The dynamics of ignition between a contact surface and a shock wave is investigated using a one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing and contrasting the solutions with those of the ignition process between a piston and a shock, considered previously. The large activation energy asymptotic solutions are found to be qualitatively different from the piston driven shock case, in that thermal runaway first occurs ahead of the contact surface, and both forward and backward moving reaction waves emerge. These waves take the form of quasi-steady weak detonations that may later transition into strong detonation waves. For the finite activation energies considered in the numerical simulations, the results are qualitatively different to the asymptotic predictions in that no backward weak detonation wave forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance of the contact surface. The above conclusions are relevant to gas phase equation of state models. However, when a large polytropic index more representative of condensed phase explosives is used, the large activation energy asymptotic and finite activation energy numerical results are found to be in quantitative agreement

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

Always on my mind: Cross-brain associations of mental health symptoms during simultaneous parent-child scanning.

How parents manifest symptoms of anxiety or depression may affect how children learn to modulate their own distress, thereby influencing the children's risk for developing an anxiety or mood disorder. Conversely, children's mental health symptoms may impact parents' experiences of negative emotions. Therefore, mental health symptoms can have bidirectional effects in parent-child relationships, particularly during moments of distress or frustration (e.g., when a parent or child makes a costly mistake). The present study used simultaneous functional magnetic resonance imaging (fMRI) of parent-adolescent dyads to examine how brain activity when responding to each other's costly errors (i.e., dyadic error processing) may be associated with symptoms of anxiety and depression. While undergoing simultaneous fMRI scans, healthy dyads completed a task involving feigned errors that indicated their family member made a costly mistake. Inter-brain, random-effects multivariate modeling revealed that parents who exhibited decreased medial prefrontal cortex and posterior cingulate cortex activation when viewing their child's costly error response had children with more symptoms of depression and anxiety. Adolescents with increased anterior insula activation when viewing a costly error made by their parent had more anxious parents. These results reveal cross-brain associations between mental health symptomatology and brain activity during parent-child dyadic error processing

Quantifying the impact of climate change on drought regimes using the Standardised Precipitation Index

The study presents a methodology to characterise short- or long-term drought events, designed to aid understanding of how climate change may affect future risk. An indicator of drought magnitude, combining parameters of duration, spatial extent and intensity, is presented based on the Standardised Precipitation Index (SPI). The SPI is applied to observed (1955–2003) and projected (2003–2050) precipitation data from the Community Integrated Assessment System (CIAS). Potential consequences of climate change on drought regimes in Australia, Brazil, China, Ethiopia, India, Spain, Portugal and the USA are quantified. Uncertainty is assessed by emulating a range of global circulation models to project climate change. Further uncertainty is addressed through the use of a high-emission scenario and a low stabilisation scenario representing a stringent mitigation policy. Climate change was shown to have a larger effect on the duration and magnitude of long-term droughts, and Australia, Brazil, Spain, Portugal and the USA were highlighted as being particularly vulnerable to multi-year drought events, with the potential for drought magnitude to exceed historical experience. The study highlights the characteristics of drought which may be more sensitive under climate change. For example, on average, short-term droughts in the USA do not become more intense but are projected to increase in duration. Importantly, the stringent mitigation scenario had limited effect on drought regimes in the first half of the twenty-first century, showing that adaptation to drought risk will be vital in these regions