title: Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. II. Numerical simulations, spectral entropy, and correlation times

authors: Steyn-Ross, D. Alistair

subjects: numerical simulations

abstract: In our two recent papers [M.L. Steyn-Ross et al., Phys. Rev. E 60, 7299 (1999); 64, 011917 (2001)] we presented clinical evidence for a general anesthetic-induced phase change in the cerebral cortex, and showed how the significant features of the cortical phase change (biphasic power surge, spectral energy redistribution, “heat capacity” divergence), could be explained using a stochastic single-macrocolumn model of the cortex. The model predictions were based on rather strong “adiabatic” assumptions which assert that the mean-field excitatory and inhibitory macrocolumn voltages are “slow” variables whose equilibration times are much longer than those of the input “currents” that drive the macrocolumn. In the present paper we test the adiabatic assumption by running numerical simulations of the stochastic differential equations. These simulations confirm the number and nature of the steady-state solutions, the growth of fluctuation power at transition, and the redistribution of spectral energy towards lower frequencies. We use spectral entropy to quantify these changes in the power spectral density, and to show that the spectral entropy should decrease markedly at the point of transition. This prediction agrees with recent clinical findings by Viertiö-Oja and colleagues [J. Clinical Monitoring Computing 16, 60 (2000)]. Our modeling work shows that there is an inverse relationship between spectral entropy H and correlation time T of the soma-voltage fluctuations: H∝- (ln T). In a theoretical analysis we prove that this proportionality becomes exact for an ideal Lorentzian process. These findings suggest that by monitoring the changes in EEG correlation time, it should be possible to track changes in the state of patient consciousness.

text: Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. II. Numerical simulations, spectral entropy, and correlation times In our two recent papers [M.L. Steyn-Ross et al., Phys. Rev. E 60, 7299 (1999); 64, 011917 (2001)] we presented clinical evidence for a general anesthetic-induced phase change in the cerebral cortex, and showed how the significant features of the cortical phase change (biphasic power surge, spectral energy redistribution, “heat capacity” divergence), could be explained using a stochastic single-macrocolumn model of the cortex. The model predictions were based on rather strong “adiabatic” assumptions which assert that the mean-field excitatory and inhibitory macrocolumn voltages are “slow” variables whose equilibration times are much longer than those of the input “currents” that drive the macrocolumn. In the present paper we test the adiabatic assumption by running numerical simulations of the stochastic differential equations. These simulations confirm the number and nature of the steady-state solutions, the growth of fluctuation power at transition, and the redistribution of spectral energy towards lower frequencies. We use spectral entropy to quantify these changes in the power spectral density, and to show that the spectral entropy should decrease markedly at the point of transition. This prediction agrees with recent clinical findings by Viertiö-Oja and colleagues [J. Clinical Monitoring Computing 16, 60 (2000)]. Our modeling work shows that there is an inverse relationship between spectral entropy H and correlation time T of the soma-voltage fluctuations: H∝- (ln T). In a theoretical analysis we prove that this proportionality becomes exact for an ideal Lorentzian process. These findings suggest that by monitoring the changes in EEG correlation time, it should be possible to track changes in the state of patient consciousness.

year: 2001

title: Spectral analysis of seasonality in tourism demand

authors: Chan, Felix

subjects: Fast Fourier Transform

abstract: This paper aims to analyse the seasonality in New Zealand tourism demand from Australia and the USA using spectral analysis. Tourism demand is divided into four different categories depending on the tourists’ visiting purposes as registered in the customs cards upon their arrivals in New Zealand. Spectral analysis based on the sample from January 1980 to December 2007 revealed that different travel purposes share similar cyclical components but their contributions to the total variation in tourism demand differ between travel purposes and markets. More importantly, the results show that analysing aggregated data is often not sufficient to reveal the underlying seasonal patterns of tourist arrivals and policy makers would benefit greatly by analysing disaggregated data rather than relying on the analysis of aggregated data alone.

text: Spectral analysis of seasonality in tourism demand This paper aims to analyse the seasonality in New Zealand tourism demand from Australia and the USA using spectral analysis. Tourism demand is divided into four different categories depending on the tourists’ visiting purposes as registered in the customs cards upon their arrivals in New Zealand. Spectral analysis based on the sample from January 1980 to December 2007 revealed that different travel purposes share similar cyclical components but their contributions to the total variation in tourism demand differ between travel purposes and markets. More importantly, the results show that analysing aggregated data is often not sufficient to reveal the underlying seasonal patterns of tourist arrivals and policy makers would benefit greatly by analysing disaggregated data rather than relying on the analysis of aggregated data alone.

year: 2010

title: The southern initiative: How indigenous values inspire social innovation and impact

authors: Niu, Xiaoliang

abstract: Indigenous values are increasingly recognised in helping organisations contribute to wellbeing within and beyond the workplace. Adopting the theoretical lens of Māori economies of wellbeing, this case study examines how The Southern Initiative (TSI), a unit within Auckland Council, incorporates Māori values to co-create place-based solutions and foster whānau (family) wellbeing. Through kōrero (conversations) with three people, a wānanga (collaborative discussion) with TSI members, and analysis of organisational literature, we identified how TSI's organising approach synthesises social innovation and bureaucracy. We found that indigeneity-embedded intrapreneurship, distributed leadership, and whānau-centred design support TSI's innovations. Mana (prestige) emerged as a primary organising principle, sustaining TSI's approach to achieving systemic change. By bridging Indigenous paradigms and conventional managerial practice, this case study demonstrates how Māori values can transform public sector management, elevate social justice, and encourage community resilience. These findings highlight culturally grounded frameworks for delivering social impact and shaping equitable outcomes.

text: The southern initiative: How indigenous values inspire social innovation and impact Indigenous values are increasingly recognised in helping organisations contribute to wellbeing within and beyond the workplace. Adopting the theoretical lens of Māori economies of wellbeing, this case study examines how The Southern Initiative (TSI), a unit within Auckland Council, incorporates Māori values to co-create place-based solutions and foster whānau (family) wellbeing. Through kōrero (conversations) with three people, a wānanga (collaborative discussion) with TSI members, and analysis of organisational literature, we identified how TSI's organising approach synthesises social innovation and bureaucracy. We found that indigeneity-embedded intrapreneurship, distributed leadership, and whānau-centred design support TSI's innovations. Mana (prestige) emerged as a primary organising principle, sustaining TSI's approach to achieving systemic change. By bridging Indigenous paradigms and conventional managerial practice, this case study demonstrates how Māori values can transform public sector management, elevate social justice, and encourage community resilience. These findings highlight culturally grounded frameworks for delivering social impact and shaping equitable outcomes.

year: 2025