title: White-noise susceptibility and critical slowing in neurons near spiking threshold

authors: Steyn-Ross, D. Alistair

subjects: neuron

abstract: We present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon (“resonator”) and a human cortical neuron (“integrator”). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate voltage fluctuations that exhibit critical slowing down—that is, the voltage responsiveness to noisy input currents grows in amplitude while slowing in frequency—as the membrane approaches spiking threshold from below. We define threshold unambiguously as that dc current that renders a zero real eigenvalue for the Jacobian matrix for the integrator neuron, and, for the resonator neuron, as the dc current that gives a complex eigenvalue pair whose real part is zero. Using a linear Ornstein-Uhlenbeck analysis, we give exact small-noise expressions for the variance, power spectrum, and correlation function of the voltage fluctuations, and we derive the scaling laws for the divergence of susceptibility and correlation times for approach to threshold. We compare these predictions with numerical simulations of the nonlinear stochastic equations, and demonstrate that, provided the white-noise perturbations are kept sufficiently small, the linearized theory works well. These predictions should be testable in the laboratory using a current-clamped cell configuration. If confirmed, then the proximity of a neuron to its spike-transition point can be judged by measuring its subthreshold susceptibility to white-noise stimulation. We postulate that such temporally correlated fluctuations could provide a means of subthreshold signaling via gap-junction connections with neighboring neurons.

text: White-noise susceptibility and critical slowing in neurons near spiking threshold We present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon (“resonator”) and a human cortical neuron (“integrator”). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate voltage fluctuations that exhibit critical slowing down—that is, the voltage responsiveness to noisy input currents grows in amplitude while slowing in frequency—as the membrane approaches spiking threshold from below. We define threshold unambiguously as that dc current that renders a zero real eigenvalue for the Jacobian matrix for the integrator neuron, and, for the resonator neuron, as the dc current that gives a complex eigenvalue pair whose real part is zero. Using a linear Ornstein-Uhlenbeck analysis, we give exact small-noise expressions for the variance, power spectrum, and correlation function of the voltage fluctuations, and we derive the scaling laws for the divergence of susceptibility and correlation times for approach to threshold. We compare these predictions with numerical simulations of the nonlinear stochastic equations, and demonstrate that, provided the white-noise perturbations are kept sufficiently small, the linearized theory works well. These predictions should be testable in the laboratory using a current-clamped cell configuration. If confirmed, then the proximity of a neuron to its spike-transition point can be judged by measuring its subthreshold susceptibility to white-noise stimulation. We postulate that such temporally correlated fluctuations could provide a means of subthreshold signaling via gap-junction connections with neighboring neurons.

year: 2006

title: Sappers of the south: the origins and impact of the Corps of the Royal New Zealand Engineers

authors: Berry, Peter Edwin

subjects: New Zealand engineers

abstract: This thesis traces the growth, leadership, changes in role, and strategic employments of the Royal New Zealand Engineers from their formation in 1902 until the present day. The writer has deliberately chosen to make his major concern the Corps development since the Second World War. However, because there was a military engineer presence in New Zealand prior to the Corps formation, indeed from the establishment of the first 'Redcoats' fighting force in New Zealand in the1840’s, a preliminary study has been done of the British and Volunteer New Zealand Sappers of the period prior to 1902.
This thesis is intended as a contribution to New Zealand's sparse military history. Concentration on the post-war World War two period has seemed fitting in that, it is in this period that the Corps of the Royal New Zealand Engineers has provided specialist service, in diverse roles through the new regions of New Zealand’s strategic interest – South East Asia, the pacific and Antarctica.

text: Sappers of the south: the origins and impact of the Corps of the Royal New Zealand Engineers This thesis traces the growth, leadership, changes in role, and strategic employments of the Royal New Zealand Engineers from their formation in 1902 until the present day. The writer has deliberately chosen to make his major concern the Corps development since the Second World War. However, because there was a military engineer presence in New Zealand prior to the Corps formation, indeed from the establishment of the first 'Redcoats' fighting force in New Zealand in the1840’s, a preliminary study has been done of the British and Volunteer New Zealand Sappers of the period prior to 1902.
This thesis is intended as a contribution to New Zealand's sparse military history. Concentration on the post-war World War two period has seemed fitting in that, it is in this period that the Corps of the Royal New Zealand Engineers has provided specialist service, in diverse roles through the new regions of New Zealand’s strategic interest – South East Asia, the pacific and Antarctica.

year: 1984

title: Effective teaching for indigenous and minoritized students

authors: Bishop, Russell

subjects: effective teaching profile

abstract: Te Kotahitanga is a kaupapa Māori research and professional development project currently operating in 33 mainstream secondary schools. This project was developed in response to the ongoing problem of educational disparities for Māori students, one of New Zealand's most pressing educational issues. From initial conversations with Maori students, their families, their principals and their teachers about what constituted effective teaching understandings and practice for Maori students, we developed an Effective Teaching Profile. This Profile is central to the professional development work that has been implemented in Te Kotahitanga schools with notable increases in a range of outcomes for Maori students.

text: Effective teaching for indigenous and minoritized students Te Kotahitanga is a kaupapa Māori research and professional development project currently operating in 33 mainstream secondary schools. This project was developed in response to the ongoing problem of educational disparities for Māori students, one of New Zealand's most pressing educational issues. From initial conversations with Maori students, their families, their principals and their teachers about what constituted effective teaching understandings and practice for Maori students, we developed an Effective Teaching Profile. This Profile is central to the professional development work that has been implemented in Te Kotahitanga schools with notable increases in a range of outcomes for Maori students.

year: 2010