- Richard H. Randedit
Research Interests:
Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are... more
Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are incommensurable, and domain-specific language poses an obstacle to integration. Still, conceptual integration is a form of understanding that provides intuition and consolidation, without which progress remains unguided. This paper is concerned with the integration of deterministic and stochastic processes within an information theoretic framework, linking information entropy and free energy to mechanisms of emergent dynamics and self-organization in brain networks. We identify basic properties of neuronal populations leading to an equivariant matrix in a network, in which complex behaviors can naturally be represented through structured flows on manifolds establishing the internal model relevant to theories of brain function. We propose a neural mechanism for the generation of internal models from symmetry breaking in the connectivity of brain networks. The emergent perspective illustrates how free energy can be linked to internal models and how they arise from the neural substrate.
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Abstract We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to... more
Abstract We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to resonance where the spinning top is locked in a state of relative equilibrium: precessing with an angular speed equal to that of the turntable while maintaining a constant nutation angle. Bifurcation diagrams are presented to depict how the stability of these relative equilibria, along with the corresponding value of the nutation angle, depends on the two parameters: the initial spin angular momentum and Ω. We discuss the classical spinning top, that is, the Ω = 0 case, and address the relation of the “sleeping top” state to the aforementioned relative equilibria. We also relate the dynamics to that of a spherical pendulum on a rotary arm and show that the latter can be viewed as a special case of the system at hand. Finally, we illustrate how the relative equilibria can be exploited for the attitude control of the top through resonance capture while slowly varying the turnable angular speed, Ω.
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We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption... more
We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonli...
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Healthy aging is accompanied by heterogeneous decline of cognitive abilities among individuals, especially during senescence. The mechanisms of this variability are not understood, but have been associated with the reorganization of white... more
Healthy aging is accompanied by heterogeneous decline of cognitive abilities among individuals, especially during senescence. The mechanisms of this variability are not understood, but have been associated with the reorganization of white matter fiber tracts and the functional co-activations of brain regions. Here, we built a causal inference framework to provide mechanistic insight into the link between structural connectivity and brain function, informed by brain imaging data and network modeling. By applying various degrees of interhemispheric degradation of structural connectivity, we were not only able to reproduce the age-related decline in interhemispheric functional communication and the associated dynamical flexibility, but we obtained an increase of global modulation of structural connectivity over the brain function during senescence. Notably, the increase in modulation between structural connectivity and brian function was higher in magnitude and steeper in its increase ...
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Summary. An autonomous system of three coupled nonlinear oscillators with widely separated frequencies is investigated using the method of direct partition of motion (DPM). Approximate expressions for two of the limit cycle oscillations... more
Summary. An autonomous system of three coupled nonlinear oscillators with widely separated frequencies is investigated using the method of direct partition of motion (DPM). Approximate expressions for two of the limit cycle oscillations are presented in terms of Jacobi elliptic functions whose amplitude and frequency depend on the coupling parameters. Critical values for the coupling parameters were found, above which the oscillations of one of the limit cycles are quenched.
Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are... more
Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are incommensurable, and domain-specific language poses an obstacle to integration. Still, conceptual integration is a form of understanding that provides intuition and consolidation, without which progress remains unguided. This paper is concerned with the integration of deterministic and stochastic processes within an information theoretic framework, linking information entropy and free energy to mechanisms of emergent dynamics and self-organization in brain networks. We identify basic properties of neuronal populations leading to an equivariant matrix in a network, in which complex behaviors can naturally be represented through structured flows on manifolds establishing the internal model relevant to theories of brain function. We propose a neural mechanism for th...
Abstract. We investigate the dynamics of a simple pendulum coupled to a horizontal mass-spring system. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass-spring oscillator, when... more
Abstract. We investigate the dynamics of a simple pendulum coupled to a horizontal mass-spring system. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass-spring oscillator, when un-coupled from the pendulum, is an order of magnitude larger than that of the oscillations of the pendulum. The leading order dynamics of the autonomous coupled system is studied using the method of Direct Partition of Motion(DPM), in conjunction with a rescaling of fast time in a manner that is inspired by theWKB method. We particularly study the motions in which the amplitude of the motion of the harmonic oscillator is an order of magnitude smaller than that of the pendulum. In this regime, a pitchfork bifurcation of periodic orbits is found to occur for energy values larger that a critical value. The bifurcation gives rise to non-local periodic and quasi-periodic orbits in which the pendulum oscillates about an angle between zero and pi/2 from the down ...
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Spontaneously fluctuating brain activity patterns emerge at rest and relate to brain functional networks involved in task conditions. Despite detailed descriptions of the spatio-temporal brain patterns, our understanding of their... more
Spontaneously fluctuating brain activity patterns emerge at rest and relate to brain functional networks involved in task conditions. Despite detailed descriptions of the spatio-temporal brain patterns, our understanding of their generative mechanism is still incomplete. Using a combination of computational modeling and dynamical systems analysis we provide a complete mechanistic description in terms of the constituent entities and the productive relation of their causal activities leading to the formation of a resting state manifold via the network connectivity. We demonstrate that the symmetry breaking by the connectivity creates a characteristic flow on the manifold, which produces the major empirical data features including spontaneous high amplitude co-activations, neuronal cascades, spectral cortical gradients, multistability and characteristic functional connectivity dynamics. The understanding of the brain’s resting state manifold is fundamental for the construction of task-...
We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to... more
We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to resonance where the spinning top is locked in a state of relative equilibrium: precessing with an angular speed equal to that of the turntable while maintaining a constant nutation angle. Bifurcation diagrams are presented to depict how the stability of these relative equilibria, along with the corresponding value of the nutation angle, depends on the two parameters: the initial spin angular momentum and Ω. We discuss the classical spinning top, that is, the Ω = 0 case, and address the relation of the “sleeping top” state to the aforementioned relative equilibria. We also relate the dynamics to that of a spherical pendulum on a rotary arm and show that the latter can be viewed as a special case of the system at hand. Finally, we illustrate how the relative ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
In the past several decades, there has been numerous experimental and modeling efforts to study ephaptic interactions in neuronal systems. While studies on the matter have looked at either axons of the peripheral nervous system or... more
In the past several decades, there has been numerous experimental and modeling efforts to study ephaptic interactions in neuronal systems. While studies on the matter have looked at either axons of the peripheral nervous system or cortical neuronal structures, no attention has be given to the possibility of ephaptic interactions in the white matter tracts of the brain. Inspired by the highly organized and tightly packed geometry of axons in neuronal fiber pathways, we aim to theoretically investigate the potential effects of ephaptic interactions along these structures that are resilient to experimental probing. For that end, we use axonal cable theory to derive a minimal model of a sheet of N ephaptically coupled axons. We numerically solve the equations and explore the dynamics of the system as the ephaptic coupling parameter is varied. We demonstrate that ephaptic interactions can lead to local phase locking between impulses traveling along adjacent axons. As ephaptic coupling is...