title: Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles

authors: Steyn-Ross, D. Alistair

subjects: subthreshold oscillation

abstract: The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement.

text: Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement.

year: 2010

title: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

text: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

year: 1996-12

title: Behind the label: Complexities of identifying Māori whānau in an away from home hospital transfer

authors: Masters-Awatere, Bridgette

subjects: Māori whānau

abstract: This paper highlights two methodological issues that arose for a group of Māori researchers during the first few months of a Māori CoRE funded project. The issues were in relation to defining 1) the evolving construction of Māori whānau in New Zealand, and 2) an away from home hospital transfer. Through the process of reflexive practice about our knowledge constructs the research team highlight some of the complexities that we as indigenous researchers had to navigate when working within a cultural context. We describe the details of the Hospital Transfers project and reflect on the learning experienced during the pilot interview phase of a three year project.

text: Behind the label: Complexities of identifying Māori whānau in an away from home hospital transfer This paper highlights two methodological issues that arose for a group of Māori researchers during the first few months of a Māori CoRE funded project. The issues were in relation to defining 1) the evolving construction of Māori whānau in New Zealand, and 2) an away from home hospital transfer. Through the process of reflexive practice about our knowledge constructs the research team highlight some of the complexities that we as indigenous researchers had to navigate when working within a cultural context. We describe the details of the Hospital Transfers project and reflect on the learning experienced during the pilot interview phase of a three year project.

year: 2017