I am a scientist, author, grandfather, husband and good friend that has been around long enough to know that wisdom is more important than knowledge and then there is everything else.
We study a two-state statistical process with a non-Poisson distribution of sojourn times. In acc... more We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck ͓J. Stat. Phys. 104, 489 ͑2001͔͒. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.
Canadian journal of rural medicine: the official journal of the Society of Rural Physicians of Canada = Journal canadien de la medecine rurale: le journal officiel de la Societe de medecine rurale du Canada
This case study describes the priority-setting process undertaken by health care providers in the... more This case study describes the priority-setting process undertaken by health care providers in the Municipal District of Taber, Alta., to improve and integrate chronic disease services within a fixed budget. Providers first reviewed the current chronic disease management system, then considered alternatives based on program priorities and costs and benefits of potential changes. Despite reaching consensus that a chronic disease clinic was the top priority for funding, providers were unable to redesign services accordingly. Redesign efforts were hampered by the groups' difficulty in identifying services that should receive fewer resources in order to fund priority areas, inexperience with priority-setting frameworks, group composition, the belief that many programs were already at "bare bone" funding levels, and perceptions of limited budget control. In the end, recommendations were made to use attrition to release resources, establish multi-disciplinary teams and group visits, where appropriate, and relocate providers to a centralized location. Upon review of study outcomes, Taber providers were granted more decision-making authority. Overall, the use of a systematic priority-setting process, culminating in recommendations for action, has moved Taber providers closer to an integrated model of service delivery. It is recommended that formal priority-setting frameworks continue to be used in Taber for primary care renewal or at any level where consideration of existing evidence and projected costs is required.
Physica A: Statistical Mechanics and its Applications, 1999
It is argued that the evolution of complex phenomena ought to be described by fractional, differe... more It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion.
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation t... more We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order beta truncation in both the consolidated perturbation expansions and in the "mass operator" of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation.
Frontiers in Bioengineering and Biotechnology, 2015
The recent article discusses the emergence of intelligence via criticality as a consequence of lo... more The recent article discusses the emergence of intelligence via criticality as a consequence of locality breakdown. Herein, we use criticality for the foundation of a novel generation of game theory making the local interaction between players yield long-range effects. We first establish that criticality is not confined to the Ising-like structure of the sociological model of , called the decision making model (DMM), through the study of the emergence of altruism using the altruismselfishness model (ASM). Both models generate criticality, one by imitation of opinion (DMM) and the other by imitation of behavior (ASM). The dynamics of a sociological network S influences the behavioral network F through two game theoretic paradigms: (i) the value of altruism; (ii) the benefit of rapid consensus. In (i), the network S debates the moral issue of altruism by means of the DMM, while at the level F the individuals operate according to the ASM. The individuals of the level S, through a weak influence on the individuals of the level F, exert a societal control on F, fitting the principle of complexity management and complexity matching. In (ii), the benefit to society is the rapid attainment of consensus in the S level. The agents of the level F operate according to the prisoner's dilemma prescription, with the defectors acting as DMM contrarians at the level S. The contrarians, acting as the inhibitory links of neural networks, exert on society the same beneficial effect of maintaining the criticality-induced resilience that they generate in neural networks. The conflict between personal and social benefit makes the networks evolve toward criticality. Finally, we show that the theory of this article is compatible with recent discoveries in the burgeoning field of social neuroscience.
Many adaptive evolutionary systems display spatial and temporal features, such as long-range corr... more Many adaptive evolutionary systems display spatial and temporal features, such as long-range correlations, typically associated with the critical point of a phase transition in statistical physics. Empirical and theoretical studies suggest that operating near criticality enhances the functionality of biological networks, such as brain and gene networks, in terms for instance of information processing, robustness, and evolvability. While previous studies have explained criticality with specific system features, we still lack a general theory of critical behavior in biological systems. Here we look at this problem from the complex systems perspective, since in principle all critical biological circuits have in common the fact that their internal organization can be described as a complex network. An important question is how self-similar structure influences self-similar dynamics. Modularity and heterogeneity, for instance, affect the location of critical points and can be used to tune the system toward criticality. We review and discuss recent studies on the criticality of neuronal and genetic networks, and discuss the implications of network theory when assessing the evolutionary features of criticality.
Journal of neuroengineering and rehabilitation, 2005
The stride interval in healthy human gait fluctuates from step to step in a random manner and sca... more The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control ...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
We present a nonlinear dynamical model of the human gait control system in a variety of gait regi... more We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.
Journal of The Chemical Society, Chemical Communications, 1981
Sumvnary Reaction of some ctp-unsaturated ketones with palladium(I1) chloride and sodium carbonat... more Sumvnary Reaction of some ctp-unsaturated ketones with palladium(I1) chloride and sodium carbonate in tetrahydrofuran (THF) gives acetylacetonate complexes ; use of 180-enriched carbonate shows that the reaction involves a highly unusual transfer of oxygen from carbonate ion to the organic ligand.
Herein we present a calculation of the mean first-passage time for a bistable one-dimensional sys... more Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time τ c . We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree ...
Journal of the Chemical Society, Dalton Transactions, 1977
Page 1. 1478 JCS Dalton An Electron Spin Resonance Study of the Oxygenation of a Quadridentate Th... more Page 1. 1478 JCS Dalton An Electron Spin Resonance Study of the Oxygenation of a Quadridentate Thiosalicylideneimine Cobalt(ii) Chelate By Michael F. Corrigan, Keith S. Murray, and Bruce 0. West," Chemistry Department, Monash University, ...
We study a two-state statistical process with a non-Poisson distribution of sojourn times. In acc... more We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck ͓J. Stat. Phys. 104, 489 ͑2001͔͒. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.
Canadian journal of rural medicine: the official journal of the Society of Rural Physicians of Canada = Journal canadien de la medecine rurale: le journal officiel de la Societe de medecine rurale du Canada
This case study describes the priority-setting process undertaken by health care providers in the... more This case study describes the priority-setting process undertaken by health care providers in the Municipal District of Taber, Alta., to improve and integrate chronic disease services within a fixed budget. Providers first reviewed the current chronic disease management system, then considered alternatives based on program priorities and costs and benefits of potential changes. Despite reaching consensus that a chronic disease clinic was the top priority for funding, providers were unable to redesign services accordingly. Redesign efforts were hampered by the groups' difficulty in identifying services that should receive fewer resources in order to fund priority areas, inexperience with priority-setting frameworks, group composition, the belief that many programs were already at "bare bone" funding levels, and perceptions of limited budget control. In the end, recommendations were made to use attrition to release resources, establish multi-disciplinary teams and group visits, where appropriate, and relocate providers to a centralized location. Upon review of study outcomes, Taber providers were granted more decision-making authority. Overall, the use of a systematic priority-setting process, culminating in recommendations for action, has moved Taber providers closer to an integrated model of service delivery. It is recommended that formal priority-setting frameworks continue to be used in Taber for primary care renewal or at any level where consideration of existing evidence and projected costs is required.
Physica A: Statistical Mechanics and its Applications, 1999
It is argued that the evolution of complex phenomena ought to be described by fractional, differe... more It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion.
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation t... more We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order beta truncation in both the consolidated perturbation expansions and in the "mass operator" of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation.
Frontiers in Bioengineering and Biotechnology, 2015
The recent article discusses the emergence of intelligence via criticality as a consequence of lo... more The recent article discusses the emergence of intelligence via criticality as a consequence of locality breakdown. Herein, we use criticality for the foundation of a novel generation of game theory making the local interaction between players yield long-range effects. We first establish that criticality is not confined to the Ising-like structure of the sociological model of , called the decision making model (DMM), through the study of the emergence of altruism using the altruismselfishness model (ASM). Both models generate criticality, one by imitation of opinion (DMM) and the other by imitation of behavior (ASM). The dynamics of a sociological network S influences the behavioral network F through two game theoretic paradigms: (i) the value of altruism; (ii) the benefit of rapid consensus. In (i), the network S debates the moral issue of altruism by means of the DMM, while at the level F the individuals operate according to the ASM. The individuals of the level S, through a weak influence on the individuals of the level F, exert a societal control on F, fitting the principle of complexity management and complexity matching. In (ii), the benefit to society is the rapid attainment of consensus in the S level. The agents of the level F operate according to the prisoner's dilemma prescription, with the defectors acting as DMM contrarians at the level S. The contrarians, acting as the inhibitory links of neural networks, exert on society the same beneficial effect of maintaining the criticality-induced resilience that they generate in neural networks. The conflict between personal and social benefit makes the networks evolve toward criticality. Finally, we show that the theory of this article is compatible with recent discoveries in the burgeoning field of social neuroscience.
Many adaptive evolutionary systems display spatial and temporal features, such as long-range corr... more Many adaptive evolutionary systems display spatial and temporal features, such as long-range correlations, typically associated with the critical point of a phase transition in statistical physics. Empirical and theoretical studies suggest that operating near criticality enhances the functionality of biological networks, such as brain and gene networks, in terms for instance of information processing, robustness, and evolvability. While previous studies have explained criticality with specific system features, we still lack a general theory of critical behavior in biological systems. Here we look at this problem from the complex systems perspective, since in principle all critical biological circuits have in common the fact that their internal organization can be described as a complex network. An important question is how self-similar structure influences self-similar dynamics. Modularity and heterogeneity, for instance, affect the location of critical points and can be used to tune the system toward criticality. We review and discuss recent studies on the criticality of neuronal and genetic networks, and discuss the implications of network theory when assessing the evolutionary features of criticality.
Journal of neuroengineering and rehabilitation, 2005
The stride interval in healthy human gait fluctuates from step to step in a random manner and sca... more The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control ...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
We present a nonlinear dynamical model of the human gait control system in a variety of gait regi... more We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.
Journal of The Chemical Society, Chemical Communications, 1981
Sumvnary Reaction of some ctp-unsaturated ketones with palladium(I1) chloride and sodium carbonat... more Sumvnary Reaction of some ctp-unsaturated ketones with palladium(I1) chloride and sodium carbonate in tetrahydrofuran (THF) gives acetylacetonate complexes ; use of 180-enriched carbonate shows that the reaction involves a highly unusual transfer of oxygen from carbonate ion to the organic ligand.
Herein we present a calculation of the mean first-passage time for a bistable one-dimensional sys... more Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time τ c . We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree ...
Journal of the Chemical Society, Dalton Transactions, 1977
Page 1. 1478 JCS Dalton An Electron Spin Resonance Study of the Oxygenation of a Quadridentate Th... more Page 1. 1478 JCS Dalton An Electron Spin Resonance Study of the Oxygenation of a Quadridentate Thiosalicylideneimine Cobalt(ii) Chelate By Michael F. Corrigan, Keith S. Murray, and Bruce 0. West," Chemistry Department, Monash University, ...
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