title: Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

authors: Steyn-Ross, Moira L.

subjects: biological physics

abstract: Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning.

text: Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning.

year: 2013

title: Measurement of natural convection heat transfer in an attic shaped enclosure

authors: Anderson, Timothy Nicholas

subjects: solar

abstract: Heat transfer by natural convection in triangular enclosures is an area of significant importance in applications such as the design of greenhouses, attics and solar water heaters. However, given its significance to these areas it has not been widely examined. In this study, the natural convection heat transfer coefficients for air in an attic shaped enclosure were determined for Grashof Numbers over the range of 10⁷ to 10⁹. It was found that the measured heat transfer coefficients could be predicted to within 5% by Ridouane and Campo’ (2005) equation (Eqn. 1) for natural convection in a triangular enclosure previously developed for Grashof Numbers in the range 10⁵ and 10⁶. 
Nu= 0.286A⁻⁰•²⁸⁶ Gr¼    (1)
As such, it is suggested that this equation may be suitable for predicting the natural convection heat transfer coefficients in full scale attic enclosures.

text: Measurement of natural convection heat transfer in an attic shaped enclosure Heat transfer by natural convection in triangular enclosures is an area of significant importance in applications such as the design of greenhouses, attics and solar water heaters. However, given its significance to these areas it has not been widely examined. In this study, the natural convection heat transfer coefficients for air in an attic shaped enclosure were determined for Grashof Numbers over the range of 10⁷ to 10⁹. It was found that the measured heat transfer coefficients could be predicted to within 5% by Ridouane and Campo’ (2005) equation (Eqn. 1) for natural convection in a triangular enclosure previously developed for Grashof Numbers in the range 10⁵ and 10⁶. 
Nu= 0.286A⁻⁰•²⁸⁶ Gr¼    (1)
As such, it is suggested that this equation may be suitable for predicting the natural convection heat transfer coefficients in full scale attic enclosures.

year: 2008

title: Maori & Psychology Research Unit annual report 2005

authors: Rua, Mohi

subjects: Maori and Psychology Research Unit

abstract: Annual report of the Maori and Psychology Research Unit (MPRU) 2005. The unit was established in August of 1997. The unit is designed to provide a catalyst and support network for enhancing research concerning the psychological needs, aspirations, and priorities of Maori people. The MPRU is well situated to draw together skilled and experienced interdisciplinary research groups by networking and establishing working relationships with staff and students within the Faculty of Arts and Social Sciences, the University, and the wider community.

text: Maori & Psychology Research Unit annual report 2005 Annual report of the Maori and Psychology Research Unit (MPRU) 2005. The unit was established in August of 1997. The unit is designed to provide a catalyst and support network for enhancing research concerning the psychological needs, aspirations, and priorities of Maori people. The MPRU is well situated to draw together skilled and experienced interdisciplinary research groups by networking and establishing working relationships with staff and students within the Faculty of Arts and Social Sciences, the University, and the wider community.

year: 2005