Spatiotemporal consistency of neural responses to repeatedly presented video stimuli accounts for population preferences.

Population preferences for video advertisements vary across short video clips. What underlies these differences? Repeatedly watching a video clip may produce a consistent spatiotemporal pattern of neural activity that is dependent on the individual and the stimulus. Moreover, such consistency may be associated with the degree of engagement and memory of individual viewers. Since the population preferences are associated with the engagement and memory of the individual viewers, the consistency observed in a smaller group of viewers can be a predictor of population preferences. To test the hypothesis, we measured the degree of inter-trial consistency in participants' electroencephalographic (EEG) responses to repeatedly presented television commercials. We observed consistency in the neural activity patterns across repetitive views and found that the similarity in the spatiotemporal patterns of neural responses while viewing popular television commercials predicts population preferences obtained from a large audience. Moreover, a regression model that used two datasets, including two separate groups of participants viewing different stimulus sets, showed good predictive performance in a leave-one-out cross-validation. These findings suggest that universal spatiotemporal patterns in EEG responses can account for population-level human behaviours.

Non-Markov-Type Analysis and Diffusion Map Analysis for Molecular Dynamics Trajectory of Chignolin at a High Temperature.

We apply the non-Markov-type analysis of state-to-state transitions to nearly microsecond molecular dynamics (MD) simulation data at a folding temperature of a small artificial protein, chignolin, and we found that the time scales obtained are consistent with our previous result using the weighted ensemble simulations, which is a general path-sampling method to extract the kinetic properties of molecules. Previously, we also applied diffusion map (DM) analysis, which is one of a manifold of learning techniques, to the same trajectory of chignolin in order to cluster the conformational states and found that DM and relaxation mode analysis give similar results for the eigenvectors. In this paper, we divide the same trajectory into shorter pieces and further apply DM to such short-length trajectories to investigate how the obtained eigenvectors are useful to characterize the conformational change of chignolin.

A manifold learning approach to mapping individuality of human brain oscillations through beta-divergence.

This paper proposes an approach for visualizing individuality and inter-individual variations of human brain oscillations measured as multichannel electroencephalographic (EEG) signals in a low-dimensional space based on manifold learning. Using a unified divergence measure between spectral densities termed the "beta-divergence", we introduce an appropriate dissimilarity measure between multichannel EEG signals. Then, t-distributed stochastic neighbor embedding (t-SNE; a state-of-the-art algorithm for manifold learning) together with the beta-divergence based distance was applied to resting state EEG signals recorded from 100 healthy subjects. We were able to obtain a fine low-dimensional visualization that enabled each subject to be identified as an isolated point cloud and that represented inter-individual variations as the relationships between such point clouds. Furthermore, we also discuss how the performance of the low-dimensional visualization depends on the beta-divergence parameter and the t-SNE hyper parameter. Finally, borrowing from the concept of locally linear embedding (LLE), we propose a method for projecting the test sample to the t-SNE space obtained from the training samples and investigate that availability.

Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates.

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates.

Manifold learning approach for chaos in the dripping faucet.

Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of intervals τn between drop separations becomes a subject of analysis. Even if the mass mn of a drop at the onset of the nth separation, which is difficult to observe experimentally, exhibits perfectly deterministic dynamics, it may be difficult to obtain the same information about the underlying dynamics from the time series τn. This is because the return plot τn-1 vs. τn may become a multivalued relation (i.e., it doesn't represent a function describing deterministic dynamics). In this paper, we propose a method to construct a nonlinear coordinate which provides a "surrogate" of the internal state mn from the time series of τn. Here, a key of the proposed approach is to use isomap, which is a well-known method of manifold learning. We first apply it to the time series of τn generated from the numerical simulation of a phenomenological mass-spring model for the dripping faucet system. It is shown that a clear one-dimensional map is obtained by the proposed approach, whose characteristic quantities such as the Lyapunov exponent, the topological entropy, and the time correlation function coincide with the original dripping faucet system. Furthermore, we also analyze data obtained from real dripping faucet experiments, which also provide promising results.

Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force.

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1:1 phase locking between a single spike and one period of the force and 1:l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.

Bifurcation analysis of solitary and synchronized pulses and formation of reentrant waves in laterally coupled excitable fibers.

We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.

Noise-induced enhancement of fluctuation and spurious synchronization in uncoupled type-I intermittent chaotic systems.

We study the dynamics of a pair of two uncoupled identical type-I intermittent chaotic systems driven by common random forcing. We first observe that the degree of the fluctuation of the local expansion rate of orbits to perturbations of a single system as a function of the noise intensity shows a convex curve and takes its maximum value at a certain noise intensity, whereas the Liapunov exponent itself monotonically increases in this range. Furthermore, it is numerically demonstrated that this nontrivial enhancement of fluctuation causes that two orbits with different initial conditions may synchronize each other after a finite interval of time. As pointed out by Pikovsky [Phys. Lett. A 165, 33 (1992)], since the Liapunov exponent of the present system is positive, the synchronization that we observed is a numerical artifact due to the finite precision of calculations. The spurious noise-induced synchronization in an ensemble of uncoupled type-I intermittent chaotic systems are numerically characterized and the relations between these features and the fluctuation properties of the local expansion rate are also discussed.

Singularities in the fluctuation of on-off intermittency.

For a two-dimensional piecewise linear map exhibiting on-off intermittency, the scaling property of fluctuation, i.e., the large deviation property is investigated. It is shown that there are three phases of fluctuation and the q-weighted average of an observed quantity has singularities such as jumps or a plateau due to transitions between the phases. At the onset of on-off intermittency, the width of the plateau vanishes due to the disappearance of one of the three phases and the singularity becomes weaker but more probable. The singularity at the onset of on-off intermittency is also examined on the coupled logistic map.

Multifractal structure of a riddled basin.

For a two-dimensional piecewise linear map with a riddled basin, a multifractal spectrum f(gamma), which characterizes the "skeletons" of the riddled basin, is introduced. With f(gamma), the uncertainty exponent is obtained by a variational principle, which enables us to introduce a concept of a "boundary" for the riddled basin. A conjecture on the relation between f(gamma) and the "stable sets" of various ergodic measures, which coexist with the natural invariant measure on the chaotic attractor, is also proposed. (c) 2001 American Institute of Physics.