Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Rehabilitation of Childs Park, Delaware Water Gap National Recreation Area (NRA) : environmental assessment, public scoping meetings, July 11 & 12, 2006 /

Shows recommended changes at the Childs Park recreation area within the N.R.A. on the Pa. side of the Delaware River.

Delaware Water Gap National Recreation Area, Pennsylvania and New Jersey, river guide /

Shows boating, camping, and canoe rental facilities.

Delaware Water Gap National Recreation Area, New Jersey and Pennsylvania /

Relief shown by shading and spot heights.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.

Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network.

Mind the gap! An exploration of the role of lifelong learning in promoting co-production and citizenship within social care for older people

Contemporary themes in public policy have emphasised co-productive approaches within both the access and provision of support services to older people. This paper provides a cross disciplinary exploration from its respective authors perspectives on social work and educational gerontology to examine the potential for lifelong learning and learning interventions from which co-production with those using social care services in later life might be better facilitated. Using an example from the UK, we specifically elicit how co-produced care can enhance the horizon of learning and learning research. The synthesis of ideas across these two disciplines could enrich understanding and provide essential levers for moving towards empowerment and emancipation by engaging with a more co-productive approach in social care for older people. (DIPF/Orig.)

Chaos decomposition and gap renormalization of brownian self-intersection local times

We study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards model.