Related papers: Torus Graphs for Multivariate Phase Coupling Analy…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
There are many methods for projecting spherical maps onto the plane. Interactive versions of these projections allow the user to centre the region of interest. However, the effects of such interaction have not previously been evaluated. In…
We investigate the relative merit of phase-based methods---mean phase coherence, unweighted and weighted phase lag index---for estimating the strength of interactions between dynamical systems from empirical time series which are affected…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…
We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most…
Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled…
This work revisits the Euclidean Dynamical Triangulation (DT) approach to non-perturbative quantum gravity in three dimensions. Inspired by a recent combinatorial study by T. Budd and L. Lionni of a subclass of 3-sphere triangulations…
The various human brain tasks are performed at different locations and time scales. Yet, we discovered the existence of time-invariant (above an essential time scale) partitioning of the brain activity into personal state-specific frequency…
We present a comparative study on Explosive Synchronization (ES) in temporal networks consisting of phase oscillators. The temporal nature of the networks is modeled with two configurations: (1) oscillators are allowed to move in a closed…
We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely…
Ranked data is commonly used in research across many fields of study including medicine, biology, psychology, and economics. One common statistic used for analyzing ranked data is Kendall's {\tau} coefficient, a non-parametric measure of…
Loss of cortical integration and changes in the dynamics of electrophysiological brain signals characterize the transition from wakefulness towards unconsciousness. The common mechanism underlying these observations remains unknown. In this…
We propose Moebius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally…
Our paper gives bounds for the rate of convergence for a class of random walks on the d-dimensional torus generated by a set of n vectors in R^d/Z^d. We give bounds on the discrepancy distance from Haar measure; our lower bound holds for…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…