Self-avoiding walks crossing a square

We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \times [0, L]$ on the square lattice ${\mathbb Z}^2$. The number of distinct walks is known to grow as $\lambda^{L^2+o(L^2)}$. We estimate $\lambda = 1.744550 \pm 0.000005$ as well as obtaining strict upper and lower bounds, $1.628 < \lambda < 1.782.$ We give exact results for the number of SAW of length $2L + 2K$ for $K = 0, 1, 2$ and asymptotic results for $K = o(L^{1/3})$. We also consider the model in which a weight or {\em fugacity} $x$ is associated with each step of the walk. This gives rise to a canonical model of a phase transition. For $x < 1/\mu$ the average length of a SAW grows as $L$, while for $x > 1/\mu$ it grows as $L^2$. Here $\mu$ is the growth constant of unconstrained SAW in ${\mathbb Z}^2$. For $x = 1/\mu$ we provide numerical evidence, but no proof, that the average walk length grows as $L^{4/3}$. We also consider Hamiltonian walks under the same restriction. They are known to grow as $\tau^{L^2+o(L^2)}$ on the same $L \times L$ lattice. We give precise estimates for $\tau$ as well as upper and lower bounds, and prove that $\tau < \lambda.$Comment: 27 pages, 9 figures. Paper updated and reorganised following refereein

Comparative efficacy and tolerability of first-generation and newer-generation antidepressant medications for depressive disorders in children and adolescents: Study protocol for a systematic review and network meta-analysis

Introduction: Depressive disorders are among the most common psychiatric disorders in children and adolescents, and have adverse effects on their psychosocial functioning. Questions concerning the efficacy and safety of antidepressant medications in the treatment of depression in children and adolescents, led us to integrate the direct and indirect evidence using network meta-analysis to create hierarchies of these drugs. Methods and analysis: Seven databases with PubMed, EMBASE, the Cochrane Library, Web of Science, CINAHL, LiLACS and PsycINFO will be searched from 1966 to December 2013 (updated to May, 2015). There are no restrictions on language or type of publication. Randomised clinical trials assessing first-generation and newer-generation antidepressant medications against active comparator or placebo as acute treatment for depressive disorders in children and adolescents (under 18 years of age) will be included. The primary outcome for efficacy will be mean improvement in depressive symptoms, as measured by the mean change score of a depression rating scale from baseline to post-treatment. The tolerability of treatment will be defined as side effect discontinuation, as defined by the proportion of patients who discontinued treatment due to adverse events during the trial. We will also assess the secondary outcome for efficacy (response rate), acceptability (all-cause discontinuation) and suiciderelated outcomes. We will perform the Bayesian network meta-analyses for all relative outcome measures. Subgroup analyses and sensitivity analyses will be conducted to assess the robustness of the findings. Dissemination: The network meta-analysis will provide useful information on antidepressant treatment for child and adolescent depression. The results will be disseminated through peer-reviewed publication or conference presentations

Practitioner accounts and knowledge production: an analysis of three marketing discourses

Responding to repeated calls for marketing academicians to connect with marketing actors, we offer an empirically-sourced discourse analysis of the ways in which managers portray their practices. Focusing on the micro-discourses and narratives that marketing actors draw upon to represent their work we argue that dominant representations of marketing knowledge production present a number of critical concerns for marketing theory and marketing education. We also evidence that the often promoted idea of a need to close the gap between theory - as a dominant discourse - and practice, as a way of doing marketing, is problematic to pursue. We suggest that a more fruitful agenda resides in the development of a range of polyphonic and creative micro-discourses of management, promoting context, difference and individual meaning in marketing knowledge production

Comparative efficacy and acceptability of psychotherapies for acute anxiety disorders in children and adolescents: Study protocol for a network metaanalysis

Introduction: Anxiety disorders are associated with significant public health burden in young individuals. Cognitive-behavioural therapy (CBT) is the most commonly used psychotherapy for anxiety disorders in children and adolescents, but previous reviews were hindered by a limited number of trials with direct comparisons between different psychotherapies and their deliveries. Consequently, the main aim of this research was to investigate the comparative efficacy and acceptability of various types and deliveries of psychotherapies for anxiety disorders in children and adolescents. Methods and analysis: We will systematically search PubMed, EMBASE, Cochrane, Web of Science, PsycINFO, CINAHL, ProQuest Dissertations and LiLACS for randomised controlled trials, regardless of whether participants received blinding or not, published from 1 January 1966 to 30 January 2015 (updated to 1 July 2015), that compared any psychotherapy with either a control condition or an active comparator with different types and/or different delivery formats for the acute treatment of anxiety disorders in children and adolescents. Data extraction, risk of bias and quality assessments will be independently extracted by two reviewers. The primary outcome for efficacy will be mean overall change scores in anxiety symptoms (self-rated or assessor-rated) from baseline to post-treatment between two groups. The acceptability of treatment will be measured as the proportion of patients who discontinued treatment during the acute phase of treatment. We will assess efficacy, based on the standardised mean difference (SMD), and acceptability, based on the OR, using a random-effects network meta-analysis within a Bayesian framework. Subgroup and sensitivity analyses will be conducted to assess the robustness of the findings. Ethics and dissemination: No ethical issues are foreseen. The results will be published in a peer-reviewed journal and will be disseminated electronically and in print. The meta-analysis may be updated to inform and guide management of anxiety in children and adolescents

On directed interacting animals and directed percolation

We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n=17. The crossover region in the vicinity of the collapse transition is analyzed in detail and the crossover exponent $\phi$ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that $\phi$ is equal to the Fisher exponent $\sigma$ governing the size distribution of large directed percolation clusters.Comment: 23 pages, 3 figures; J. Phys. A 35 (2002) 272

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Securing Water, Sustaining Growth: Report of the GWP/OECD Task Force on Water Security and Sustainable Growth

Peer Revie

Resilience of a tropical sport fish population to a severe cold event varies across five estuaries in southern Florida

For species that are closely managed, understanding population resilience to environmental and anthropogenic disturbances (i.e., recovery trajectories across broad spatial areas) can guide which suite of management actions are available to mitigate any impacts. During January 2010, an extreme cold event in south Florida caused widespread mortality of common snook, Centropomus undecimalis, a popular sport fish. Interpretation of trends using fishery-independent monitoring data in five south Florida estuaries showed that changes in catch rates of adult snook (\u3e500 mm standard length) varied between no effects postevent to large effects and 4-yr recoveries. The reasons for the variation across estuaries are unknown, but are likely related to differences in estuary geomorphology and habitat availability (e.g., extent of deep rivers and canals) and differences in the proportions of behavior contingents (i.e., segments of the population that use divergent movement tactics) that place snook in different areas of the estuary during winter. Emerging awareness of the presence of behavior contingents, identification of overwintering sites, and improvements of abundance indices in remote nursery habitats should provide a better understanding of population resilience to disturbance events for snook. Given that changes in the frequency of short-lived, severe cold events are currently unknown, the findings and management actions described here for a tropical species living at the edge of its distribution should be useful to scientists forecasting the effects of climate change

Comparative efficacy and acceptability of psychotherapies for depression in children and adolescents: A systematic review and network meta-analysis

Previous meta-analyses of psychotherapies for child and adolescent depression were limited because of the small number of trials with direct comparisons between two treatments. A network meta-analysis, a novel approach that integrates direct and indirect evidence from randomized controlled studies, was undertaken to investigate the comparative efficacy and acceptability of psychotherapies for depression in children and adolescents. Systematic searches resulted in 52 studies (total N=3805) of nine psychotherapies and four control conditions. We assessed the efficacy at post-treatment and at follow-up, as well as the acceptability (all-cause discontinuation) of psychotherapies and control conditions. At post-treatment, only interpersonal therapy (IPT) and cognitive-behavioral therapy (CBT) were significantly more effective than most control conditions (standardized mean differences, SMDs ranged from -0.47 to -0.96). Also, IPT and CBT were more beneficial than play therapy. Only psychodynamic therapy and play therapy were not significantly superior to waitlist. At follow-up, IPT and CBT were significantly more effective than most control conditions (SMDs ranged from -0.26 to -1.05), although only IPT retained this superiority at both short-term and long-term follow-up. In addition, IPT and CBT were more beneficial than problem-solving therapy. Waitlist was significantly inferior to other control conditions. With regard to acceptability, IPT and problem-solving therapy had significantly fewer all-cause discontinuations than cognitive therapy and CBT (ORs ranged from 0.06 to 0.33). These data suggest that IPT and CBT should be considered as the best available psychotherapies for depression in children and adolescents. However, several alternative psychotherapies are understudied in this age group. Waitlist may inflate the effect of psychotherapies, so that psychological placebo or treatment-as-usual may be preferable as a control condition in psychotherapy trials