The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Citizenship Education and Liberalism: A State of the Debate Analysis 1990–2010

What kind of citizenship education, if any, should schools in liberal societies promote? And what ends is such education supposed to serve? Over the last decades a respectable body of literature has emerged to address these and related issues. In this state of the debate analysis we examine a sample of journal articles dealing with these very issues spanning a twenty-year period with the aim to analyse debate patterns and developments in the research field. We first carry out a qualitative analysis where we design a two-dimensional theoretical framework in order to systematise the various liberal debate positions, and make us able to study their justifications, internal tensions and engagements with other positions. In the ensuing quantitative leg of the study we carry out a quantitative bibliometric analysis where we weigh the importance of specific scholars. We finally discuss possible merits and flaws in the research field, as evidenced in and by the analysis

The Resource Curse and Rentier States in the Caspian Region : A Need for Context Analysis

Although much attention is paid to the Caspian region with regard to energy issues, the domestic consequences of the region’s resource production have so far constituted a neglected field of research. A systematic survey of the latest research trends in the economic and political causalities of the resource curse and of rentier states reveals that there is a need for context analysis. In reference to this, the paper traces any shortcomings and promising approaches in the existent body of literature on the Caspian region. Following on from this, the paper then proposes a new approach; specifically, one in which any differences and similarities in the context conditions are captured. This enables a more precise exploration of the exact ways in which they form contemporary post-Soviet Caspian rentier states.Obwohl der Region am Kaspischen Meer im Zuge von Energiediskursen große Aufmerksamkeit zuteil wird, stellen die innerstaatlichen Folgen der Ressourcenproduktion in der Region ein bislang vernachlässigtes Forschungsfeld dar. Ein systematischer Überblick über die jüngsten Forschungstrends zu wirtschaftlichen und politischen Kausalzusammenhängen des Ressourcenfluchs und zu Rentierstaaten offenbart die Notwendigkeit von Kontextanalysen. Hierauf Bezug nehmend, analysiert der Aufsatz sowohl die Mängel als auch viel versprechende Ansätze in der betreffenden Literatur zur Region am Kaspischen Meer. Der Aufsatz stellt letztendlich einen neuen Ansatz vor, der Unterschiede und Gemeinsamkeiten in den Kontextbedingungen erfasst, um zu erforschen, wie diese die gegenwärtigen post-sowjetischen Rentierstaaten in der Region am Kaspischen Meer tatsächlich prägen

Attachment to mother and father at transition to middle childhood

The present study investigated concordance between representations of attachment to mother and attachment to father, and convergence between two narrative-based methods addressing these representations in middle childhood: the Manchester Child Attachment Story Task (MCAST) and the Secure Base Script Test (SBST). One hundred and twenty 6-year-old children were assessed by separate administrations of the MCAST for mother and father, respectively, and results showed concordance of representations of attachment to mother and attachment to father at age 6.5 years. 75 children were additionally tested about 12 months later, with the SBST, which assesses scripted knowledge of secure base (and safe haven), not differentiating between mother and father attachment rela- tionships. Concerning attachment to father, dichotomous classifications (MCAST) and a continuous dimension cap- turing scripted secure base knowledge (MCAST) converged with secure base scriptedness (SBST), yet we could not show the same pattern of convergence concerning attach- ment to mother. Results suggest some convergence between the two narrative methods of assessment of secure base script but also highlight complications when using the MCAST for measuring attachment to father in middle childhood