A Translaminar Spacetime Code Supports Touch-Evoked Traveling Waves.

Linking sensory-evoked traveling waves to underlying circuit patterns is critical to understanding the neural basis of sensory perception. To form this link, we performed simultaneous electrophysiology and two-photon calcium imaging through transparent NeuroGrids and mapped touch-evoked cortical traveling waves and their underlying microcircuit dynamics. In awake mice, both passive and active whisker touch elicited traveling waves within and across barrels, with a fast early component followed by a variable late wave that lasted hundreds of milliseconds post-stimulus. Strikingly, late-wave dynamics were modulated by stimulus value and correlated with task performance. Mechanistically, the late wave component was i) modulated by motor feedback, ii) complemented by a sparse ensemble pattern across layer 2/3, which a balanced-state network model reconciled via inhibitory stabilization, and iii) aligned to regenerative Layer-5 apical dendritic Ca 2+ events. Our results reveal a translaminar spacetime pattern organized by cortical feedback in the sensory cortex that supports touch-evoked traveling waves. GRAPHICAL ABSTRACT AND HIGHLIGHTS: Whisker touch evokes both early- and late-traveling waves in the barrel cortex over 100's of millisecondsReward reinforcement modulates wave dynamics Late wave emergence coincides with network sparsity in L23 and time-locked L5 dendritic Ca 2+ spikes Experimental and computational results link motor feedback to distinct translaminar spacetime patterns.

Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators.

Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to investigate these networks, obtaining mathematical descriptions for the dynamics of multilayer and multiplex systems is still an open problem. Here, we combine ideas and concepts from linear algebra and graph theory with nonlinear dynamics to offer a novel approach to study multiplex networks of Kuramoto oscillators. Our approach allows us to study the dynamics of a large, multiplex network by decomposing it into two smaller systems: one representing the connection scheme within layers (intra-layer), and the other representing the connections between layers (inter-layer). Particularly, we use this approach to compose solutions for multiplex networks of Kuramoto oscillators. These solutions are given by a combination of solutions for the smaller systems given by the intra- and inter-layer systems, and in addition, our approach allows us to study the linear stability of these solutions.

Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks.

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.

Analytical Derivation of Nonlinear Spectral Effects and 1/f Scaling Artifact in Signal Processing of Real-World Data.

In estimating the frequency spectrum of real-world time series data, we must violate the assumption of infinite-length, orthogonal components in the Fourier basis. While it is widely known that care must be taken with discretely sampled data to avoid aliasing of high frequencies, less attention is given to the influence of low frequencies with period below the sampling time window. Here, we derive an analytic expression for the side-lobe attenuation of signal components in the frequency domain representation. This expression allows us to detail the influence of individual frequency components throughout the spectrum. The first consequence is that the presence of low-frequency components introduces a 1/f[Formula: see text] component across the power spectrum, with a scaling exponent of [Formula: see text]. This scaling artifact could be composed of diffuse low-frequency components, which can render it difficult to detect a priori. Further, treatment of the signal with standard digital signal processing techniques cannot easily remove this scaling component. While several theoretical models have been introduced to explain the ubiquitous 1/f[Formula: see text] scaling component in neuroscientific data, we conjecture here that some experimental observations could be the result of such data analysis procedures.

High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle.

Beta (ß)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units were classified as excitatory and inhibitory cells. We find that γ-oscillations in human and ß-oscillations in monkey are characterized by a strong implication of inhibitory neurons, both in terms of their firing rate and their phasic firing with the oscillation cycle. The ß- and γ-waves systematically propagate across the array, with similar velocities, during both wake and sleep. However, only in slow-wave sleep (SWS) ß- and γ-oscillations are associated with highly coherent and functional interactions across several millimeters of the neocortex. This interaction is specifically pronounced between inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of ß- and γ-oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain. The highest oscillation coherence found during SWS suggests that fast oscillations implement a highly coherent reactivation of wake patterns that may support memory consolidation during SWS.

Aspects of randomness in neural graph structures.

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions have been reported, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these "historical" graphs, both in their directed (original) and symmetrized (a common preprocessing step) forms, and provide a set of measures that can be consistently applied across graphs (directed or undirected, with or without self-loops). We focus on simple structural characterizations of network connectivity and find that in many measures, the networks studied are captured by simple random graph models. In a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in the networks studied is not well captured by existing abstract graph models in their first- and second-order connectivity.

Algebraic approach to small-world network models.

We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.