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: The textual expression of critical thinking in PhD discussions in applied linguistics

authors: Bruce, Ian

abstract: The purpose of this study was to identify the textual resources used to express critical thinking in the Discussion chapters or chapter sections of PhD theses from the discipline of Applied Linguistics. Five Discussions were manually analysed using the social genre/cognitive genre model of the author (Bruce, 2008a) as the analytical framework. Three generic elements, used integratively, were found to express critical evaluations as part of constructing an overall argument in the Discussion chapters examined. The first element was the recursive use of an organizing content schema (move pattern), described as: Point, Support, Evaluation. The second was the use of key coherence relations to make critical statements in the ‘Evaluation’ part of this content schema. The third element was the embedding within the critical statements of the metadiscourse devices of hedging and attitude markers (Hyland, 2005). While not providing a prescriptive approach to expressing critical evaluation in this genre, the findings offer an analytical lens through which novice writers may examine and develop awareness of the types of textual resource used to develop this important element of Discussions

text: The textual expression of critical thinking in PhD discussions in applied linguistics The purpose of this study was to identify the textual resources used to express critical thinking in the Discussion chapters or chapter sections of PhD theses from the discipline of Applied Linguistics. Five Discussions were manually analysed using the social genre/cognitive genre model of the author (Bruce, 2008a) as the analytical framework. Three generic elements, used integratively, were found to express critical evaluations as part of constructing an overall argument in the Discussion chapters examined. The first element was the recursive use of an organizing content schema (move pattern), described as: Point, Support, Evaluation. The second was the use of key coherence relations to make critical statements in the ‘Evaluation’ part of this content schema. The third element was the embedding within the critical statements of the metadiscourse devices of hedging and attitude markers (Hyland, 2005). While not providing a prescriptive approach to expressing critical evaluation in this genre, the findings offer an analytical lens through which novice writers may examine and develop awareness of the types of textual resource used to develop this important element of Discussions

year: 2018

title: Joseph Harris Smallman

authors: Hart, Philip

abstract: Born to a mining agent and trained as a mining surveyor, in 1864, less than a year after the birth of his first child, Smallman left England for New Zealand to establish a ‘Mining business’, promising that his family would join him once it was successful. But they were never asked to join him, and after 1870 he ceased to write to his wife. 
The ‘Mining business’ never eventuated, but in 1865 he prospected at Thames, unsuccessfully seeking alluvial gold. Although criticized for living off Maori and doing little prospecting, with his partner he investigated several areas of the Hauraki Peninsula, again unsuccessfully. When the Thames goldfield was opened, with his encouragement, two years later, he mined there for some years, proving himself to be a competent miner but not making his fortune. After working elsewhere, by the mid-1870s he was living with another man’s ‘half-caste’ wife on her land near Te Aroha, having five children with her. Happy to be described as a Pakeha Maori and closely associated with the local hapu, he supported them over land dealings and the development of the district. Despite spending most of his time farming, he remained interested in prospecting, and made some explorations in districts closed to Pakeha. After gold was found at Te Aroha, for a short time he worked with Maori partners in unprofitable claims.
Either before or after his second wife had a child by another man in 1886, he left New Zealand to return to his English family; and remarkably, despite his first wife knowing that his liaison had produced children, she accepted him back after his long absence, and they remained together for the rest of their lives.

text: Joseph Harris Smallman Born to a mining agent and trained as a mining surveyor, in 1864, less than a year after the birth of his first child, Smallman left England for New Zealand to establish a ‘Mining business’, promising that his family would join him once it was successful. But they were never asked to join him, and after 1870 he ceased to write to his wife. 
The ‘Mining business’ never eventuated, but in 1865 he prospected at Thames, unsuccessfully seeking alluvial gold. Although criticized for living off Maori and doing little prospecting, with his partner he investigated several areas of the Hauraki Peninsula, again unsuccessfully. When the Thames goldfield was opened, with his encouragement, two years later, he mined there for some years, proving himself to be a competent miner but not making his fortune. After working elsewhere, by the mid-1870s he was living with another man’s ‘half-caste’ wife on her land near Te Aroha, having five children with her. Happy to be described as a Pakeha Maori and closely associated with the local hapu, he supported them over land dealings and the development of the district. Despite spending most of his time farming, he remained interested in prospecting, and made some explorations in districts closed to Pakeha. After gold was found at Te Aroha, for a short time he worked with Maori partners in unprofitable claims.
Either before or after his second wife had a child by another man in 1886, he left New Zealand to return to his English family; and remarkably, despite his first wife knowing that his liaison had produced children, she accepted him back after his long absence, and they remained together for the rest of their lives.

year: 2016