Contextuality in the Integrated Information Theory

Integrated Information Theory (IIT) is one of the most influential theories of consciousness, mainly due to its claim of mathematically formalizing consciousness in a measurable way. However, the theory, as it is formulated, does not account for contextual observations that are crucial for understanding consciousness. Here we put forth three possible difficulties for its current version, which could be interpreted as a trilemma. Either consciousness is contextual or not. If contextual, either IIT needs revisions to its axioms to include contextuality, or it is inconsistent. If consciousness is not contextual, then IIT faces an empirical challenge. Therefore, we argue that IIT in its current version is inadequate

Mathematical Analysis and Simulations of the Neural Circuit for Locomotion in Lamprey

We analyze the dynamics of the neural circuit of the lamprey central pattern generator (CPG). This analysis provides insights into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behaviour regimes (characterized by phase and amplitude relationships between oscillators) of forward/backward swimming, and turning, can be controlled using the neural connection strengths and external inputs.Comment: 4 pages, accepted for publication in Physical Review Letter

Mathematical analysis and simulations of the neural circuit for locomotion in lamprey

We analyze the dynamics of the neural circuit of the lamprey central pattern generator. This analysis provides insight into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behavior regimes (characterized by phase and amplitude relationships between oscillators) of forward or backward swimming, and turning, can be controlled using the neural connection strengths and external inputs

A variational method for analyzing stochastic limit cycle oscillators

We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations (SDEs) for the amplitude and phase of the solution, which are accurate over times over order $\exp\big(Cb\epsilon^{-1}\big)$, where $\epsilon$ is the amplitude of the noise and $b$ the magnitude of decay of transverse fluctuations. Within the variational framework, different choices of the amplitude-phase decomposition correspond to different choices of the inner product space $\mathbb{R}^d$. For concreteness, we take a weighted Euclidean norm, so that the minimization scheme determines the phase by projecting the full solution on to the limit cycle using Floquet vectors. Since there is coupling between the amplitude and phase equations, even in the weak noise limit, there is a small but non-zero probability of a rare event in which the stochastic trajectory makes a large excursion away from a neighborhood of the limit cycle. We use the amplitude and phase equations to bound the probability of it doing this: finding that the typical time the system takes to leave a neighborhood of the oscillator scales as $\exp\big(Cb\epsilon^{-1}\big)$

Collective modes of coupled phase oscillators with delayed coupling

We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelength. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.Comment: 5 pages, 2 figure

Geometrical Properties of Coupled Oscillators at Synchronization

We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At synchronization, we find two distinct quantities which characterize four of the oscillators, two pairs of nearest neighbors, which are at the border of the clusters before total synchronization occurs. These oscillators are responsible for the saddle node bifurcation, of which only two of them have a phase-lock of phase difference equals $\pm$$\pi$/2. Using these properties we build a technique based on geometric properties and numerical observations to arrive to an exact analytic expression for the coupling strength at full synchronization and determine the two oscillators that have a phase-lock condition of $\pm$$\pi$/2.Comment: accepted for publication in "Communications in Nonlinear Science and Numerical Simulations

Neuro-mechanical entrainment in a bipedal robotic walking platform

In this study, we investigated the use of van der Pol oscillators in a 4-dof embodied bipedal robotic platform for the purposes of planar walking. The oscillator controlled the hip and knee joints of the robot and was capable of generating waveforms with the correct frequency and phase so as to entrain with the mechanical system. Lowering its oscillation frequency resulted in an increase to the walking pace, indicating exploitation of the global natural dynamics. This is verified by its operation in absence of entrainment, where faster limb motion results in a slower overall walking pace

Neuro-mechanical entrainment in a bipedal robotic walking platform

In this study, we investigated the use of van der Pol oscillators in a 4-dof embodied bipedal robotic platform for the purposes of planar walking. The oscillator controlled the hip and knee joints of the robot and was capable of generating waveforms with the correct frequency and phase so as to entrain with the mechanical system. Lowering its oscillation frequency resulted in an increase to the walking pace, indicating exploitation of the global natural dynamics. This is verified by its operation in absence of entrainment, where faster limb motion results in a slower overall walking pace

Proprioceptive perception of phase variability

Previous work has established that judgments of relative phase variability of 2 visually presented oscillators covary with mean relative phase. Ninety degrees is judged to be more variable than 0° or 180°, independently of the actual level of phase variability. Judged levels of variability also increase at 180°. This pattern of judgments matches the pattern of movement coordination results. Here, participants judged the phase variability of their own finger movements, which they generated by actively tracking a manipulandum moving at 0°, 90°, or 180°, and with 1 of 4 levels of Phase Variability. Judgments covaried as an inverted U-shaped function of mean relative phase. With an increase in frequency, 180° was judged more variable whereas 0° was not. Higher frequency also reduced discrimination of the levels of Phase Variability. This matching of the proprioceptive and visual results, and of both to movement results, supports the hypothesized role of online perception in the coupling of limb movements. Differences in the 2 cases are discussed as due primarily to the different sensitivities of the systems to the information

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example