The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

First aid guidelines for psychosis in Asian countries: A Delphi consensus study

BACKGROUND: Guidelines for how a member of the public should give first aid to a person who is becoming psychotic have been developed for English-speaking countries. However, these guidelines may not be appropriate for use in other cultures. A study was therefore carried out to examine whether it was possible to achieve consensus on guidelines that could apply in a range of Asian countries. METHODS: A Delphi consensus study was carried out with a panel of 28 Asian mental health clinicians drawn from Cambodia, China, Hong Kong, Indonesia, Japan, Malaysia, Mongolia, South Korea, Sri Lanka, Taiwan, Thailand and Vietnam. The panel was given a 211 item questionnaire about possible first aid actions and asked to rate whether they thought these should be included in guidelines. Panel members were invited to propose additional items. RESULTS: After three Delphi rounds, there were 128 items that were rated as "essential" or "important" by 80% or more of the panel members. These items covered: recognition of psychosis, encouraging and assisting the person to seek help, how to interact with the person, responding to acute psychosis, responding to aggression, and what to do if the person refuses to get professional help. CONCLUSION: Despite the diversity of the countries involved, there was consensus on a core set of first aid items that were considered as suitable for assisting a psychotic person. Future work is needed to develop guidelines for specific countries

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

Deformed strings in the Heisenberg model

We investigate solutions to the Bethe equations for the isotropic S = 1/2 Heisenberg chain involving complex, string-like rapidity configurations of arbitrary length. Going beyond the traditional string hypothesis of undeformed strings, we describe a general procedure to construct eigenstates including strings with generic deformations, discuss general features of these solutions, and provide a number of explicit examples including complete solutions for all wavefunctions of short chains. We finally investigate some singular cases and show from simple symmetry arguments that their contribution to zero-temperature correlation functions vanishes.Comment: 34 pages, 13 figure

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Mesoscopic description of reactions under anomalous diffusion: A case study

Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant concentrations separate. In the present work we discuss the possibilities of a generalization of reaction-diffusion equations to the case of anomalous diffusion described by continuous-time random walks with decoupled step length and waiting time probability densities, the first being Gaussian or Levy, the second one being an exponential or a power-law lacking the first moment. We consider a special case of an irreversible or reversible A ->B conversion and show that only in the Markovian case of an exponential waiting time distribution the diffusion- and the reaction-term can be decoupled. In all other cases, the properties of the reaction affect the transport operator, so that the form of the corresponding reaction-anomalous diffusion equations does not closely follow the form of the usual reaction-diffusion equations

Development of mental health first aid guidelines for suicidal ideation and behaviour: A Delphi study

<p>Abstract</p> <p>Background</p> <p>Suicide is a statistically rare event, but devastating to those left behind and one of the worst possible outcomes associated with mental illness. Although a friend, family member or co-worker may be the first person to notice that a person is highly distressed, few have the knowledge and skills required to assist. Simple guidelines may help such a person to encourage a suicidal individual to seek professional help or decide against suicide.</p> <p>Methods</p> <p>This research was conducted using the Delphi methodology, a method of reaching consensus in a panel of experts. Experts recruited to the panels included 22 professionals, 10 people who had been suicidal in the past and 6 carers of people who had been suicidal in the past. Statements about how to assist someone who is thinking about suicide were sourced through a systematic search of both professional and lay literature. The guidelines were written using the items most consistently endorsed by all three panels.</p> <p>Results</p> <p>Of 114 statements presented to the panels, 30 were accepted. These statements were used to develop the guidelines appended to this paper.</p> <p>Conclusion</p> <p>There are a number of actions which are considered to be useful for members of the public when they encounter someone who is experiencing suicidal thoughts or engaging in suicidal behaviour. These guidelines will be useful in revision of curricula of mental health first aid and suicide intervention training programs. They can also be used by members of the public who want immediate information about how to assist a suicidal person.</p

Null vectors, 3-point and 4-point functions in conformal field theory

We consider 3-point and 4-point correlation functions in a conformal field theory with a W-algebra symmetry. Whereas in a theory with only Virasoro symmetry the three point functions of descendants fields are uniquely determined by the three point function of the corresponding primary fields this is not the case for a theory with $W_3$ algebra symmetry. The generic 3-point functions of W-descendant fields have a countable degree of arbitrariness. We find, however, that if one of the fields belongs to a representation with null states that this has implications for the 3-point functions. In particular if one of the representations is doubly-degenerate then the 3-point function is determined up to an overall constant. We extend our analysis to 4-point functions and find that if two of the W-primary fields are doubly degenerate then the intermediate channels are limited to a finite set and that the corresponding chiral blocks are determined up to an overall constant. This corresponds to the existence of a linear differential equation for the chiral blocks with two completely degenerate fields as has been found in the work of Bajnok~et~al.Comment: 10 pages, LaTeX 2.09, DAMTP-93-4

Percolation and Conduction in Restricted Geometries

The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle algorithm. The percolation exponents, linked to the critical behaviour at corners, are in good agreement with the conformal results. The conductivity exponent, t', is found to be independent of the shape of the system. Its value is very close to recent estimates for the surface and bulk conductivity exponents.Comment: 10 pages, 7 figures, TeX, IOP macros include

Invariant Differential Operators and Characters of the AdS_4 Algebra

The aim of this paper is to apply systematically to AdS_4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS_4 algebra and group. We give explicitly all singular (null) vectors of the reducible AdS_4 Verma modules. These are used to obtain the AdS_4 invariant differential operators. Using this we display a new structure - a diagram involving four partially equivalent reducible representations one of which contains all finite-dimensional irreps of the AdS_4 algebra. We study in more detail the cases involving UIRs, in particular, the Di and the Rac singletons, and the massless UIRs. In the massless case we discover the structure of sets of 2s_0-1 conserved currents for each spin s_0 UIR, s_0=1,3/2,... All massless cases are contained in a one-parameter subfamily of the quartet diagrams mentioned above, the parameter being the spin s_0. Further we give the classification of the so(5,C) irreps presented in a diagramatic way which makes easy the derivation of all character formulae. The paper concludes with a speculation on the possible applications of the character formulae to integrable models.Comment: 30 pages, 4 figures, TEX-harvmac with input files: amssym.def, amssym.tex, epsf.tex; version 2 1 reference added; v3: minor corrections; v.4: minor corrections, v.5: minor corrections to conform with version in J. Phys. A: Math. Gen; v.6.: small correction and addition in subsections 4.1 & 4.