Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods of such synchronous solutions. Our results demonstrate that the presence of coupling delays in the network promotes synchronization. Numerical simulations are conducted to supplement and validate analytical results. We show the results carry over to a model for spindle sleep rhythms in thalamocortical networks, one of the biological systems which motivated our study. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms.Comment: 43 pages, 12 figure

Phase models and clustering in networks of oscillators with delayed coupling

We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to study the existence and stability of cluster solutions. Cluster solutions are phase locked solutions where the oscillators separate into groups. Oscillators within a group are synchronized while those in different groups are phase-locked. We give model independent existence and stability results for symmetric cluster solutions. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies

A hierarchy of personal agency for people with life-limiting illness

The purpose of the study was to discover how individuals diagnosed with a life-limiting illness experienced themselves as agents, even in the face of death. In this qualitative, multiple case study design four female outpatient hospice patients with terminal illnesses received humanistic counselling to explore their experiences of themselves and their illness. A graded set of 8 levels of personal agency emerged from analyses of the texts of their sessions, ranging from a passive, objectified Non-agentic mode to an active, autonomous Fully Agentic mode, with multiple subcategories representing further gradations within levels. Our results are consistent with guidelines for supportive and palliative care with advanced cancer, which specify that dying patients’ needs be assessed and that they be involved in decisions about their care

One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE) approximation for the marginal voltage density under a first order moment closure for coupled networks of integrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than the mean-field system, and provides a great deal more information, at the cost of analytical tractability. The convergence properties of the mean-field system in the low noise limit are elucidated. A novel method for the analysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlike previous attempts at stability analysis with these network types, information about the marginal densities of the adaptation variables is used. This method can in principle be applied to other systems with nonlinear partial differential equations.Comment: 26 Pages, 6 Figure

Hearing the student voice : promoting and encouraging the effective use of the student voice to enhance professional development in learning, teaching and assessment within higher education

This is an ESCalate development project led by Fiona Campbell of Napier University that was completed in 2007. The Hearing the Student Voice project aimed to promote and encourage the use of the student voice to enhance the effectiveness of academic professional development and ultimately the learning experience of students. Students can have a powerful impact on academic professional development aimed at enhancing learning, teaching and assessment practice. By providing qualitative insights about the nature of their learning experience, students can bring both valid and valuable viewpoints and motivate staff who are engaged by the students' perspective and often admire their perspicacity. This report records the progress and achievements of the Hearing the Student Voice project, funded by ESCalate to promote and encourage the use of the student voice to enhance the effectiveness of academic professional development in learning, teaching and assessment practice and ultimately the learning experience of students. The report has been written by the team representing the four universities who collaborated on the projec

The Strange and Surprising World of Curriculum Reform and Its Consequences for Eighteenth-Century Studies

Despite every conceivable obstacle, including innumerable departmental, college, and university committees seemingly created for the sole purpose of impeding change, both my university’s core curriculum and my department’s literature curriculum have in the span of the last two years been dramatically revised, or reformed as the university refers to the process, for the first time in thirty years. I have regarded this strange and surprising process with alternating wonder, anxiety, disorientation, and denial, much like Robinson Crusoe when he is first stranded on his island. Although neither savages nor wild beasts threatened me, I felt wholly isolated as our university’s only specialist in eighteenth-century British literature. Observing and to some degree participating in this process — though my involvement was limited to futile attempts to oppose the departmental changes — has made me realize how much my ability to teach my area of expertise to undergraduate students is circumscribed by curriculum