Non-hexagonal neural dynamics in vowel space

Are the grid cells discovered in rodents relevant to human cognition? Following up on two seminal studies by others, we aimed to check whether an approximate 6-fold, grid-like symmetry shows up in the cortical activity of humans who "navigate" between vowels, given that vowel space can be approximated with a continuous trapezoidal 2D manifold, spanned by the first and second formant frequencies. We created 30 vowel trajectories in the assumedly flat central portion of the trapezoid. Each of these trajectories had a duration of 240 milliseconds, with a steady start and end point on the perimeter of a "wheel". We hypothesized that if the neural representation of this "box" is similar to that of rodent grid units, there should be an at least partial hexagonal (6-fold) symmetry in the EEG response of participants who navigate it. We have not found any dominant n-fold symmetry, however, but instead, using PCAs, we find indications that the vowel representation may reflect phonetic features, as positioned on the vowel manifold. The suggestion, therefore, is that vowels are encoded in relation to their salient sensory-perceptual variables, and are not assigned to arbitrary gridlike abstract maps. Finally, we explored the relationship between the first PCA eigenvector and putative vowel attractors for native Italian speakers, who served as the subjects in our study

Free association transitions in models of cortical latching dynamics

Potts networks, in certain conditions, hop spontaneously from one discrete attractor state to another, a process we have called latching dynamics. When continuing indefinitely, latching can serve as a model of infinite recursion, which is nontrivial if the matrix of transition probabilities presents a structure, i.e. a rudimentary grammar. We show here, with computer simulations, that latching transitions cluster in a number of distinct classes: effectively random transitions between weakly correlated attractors; structured, history-dependent transitions between attractors with intermediate correlations; and oscillations between pairs of closely overlapping attractors. Each type can be described by a reduced set of equations of motion, which, once numerically integrated, matches simulations results. We propose that the analysis of such equations may offer clues on how to embed meaningful grammatical structures into more realistic models of specific recursive processes

A modular latching chain

Many cognitive tasks involve transitions between distinct mental processes, which may range from discrete states to complex strategies. The ability of cortical networks to combine discrete jumps with continuous glides along ever changing trajectories, dubbed latching dynamics, may be essential for the emergence of the unique cognitive capacities of modern humans. Novel trajectories have to be followed in the multidimensional space of cortical activity for novel behaviours to be produced; yet, not everything changes: several lines of evidence point at recurring patterns in the sequence of activation of cortical areas in a variety of behaviours. To extend a mathematical model of latching dynamics beyond the simple unstructured auto-associative Potts network previously analysed, we introduce delayed structured connectivity and hetero-associative connection weights, and we explore their effects on the dynamics. A modular model in the small-world regime is considered, with modules arranged on a ring. The synaptic weights include a standard auto-associative component, stabilizing distinct patterns of activity, and a hetero-associative component, favoring transitions from one pattern, expressed in one module, to the next, in the next module. We then study, through simulations, how structural parameters, like those regulating rewiring probability, noise and feedback connections, determine sequential association dynamics. \ua9 2013 Springer Science+Business Media Dordrecht

The challenge of taming a latching network near criticality

This book offers a timely overview of theories and methods developed by an authoritative group of researchers to understand the link between criticality and brain functioning. Cortical information processing in particular and brain function in general rely heavily on the collective dynamics of neurons and networks distributed over many brain areas. A key concept for characterizing and understanding brain dynamics is the idea that networks operate near a critical state, which offers several potential benefits for computation and information processing. However, there is still a large gap between research on criticality and understanding brain function. For example, cortical networks are not homogeneous but highly structured, they are not in a state of spontaneous activation but strongly driven by changing external stimuli, and they process information with respect to behavioral goals. So far the questions relating to how critical dynamics may support computation in this complex setting, and whether they can outperform other information processing schemes remain open. Based on the workshop \u201cDynamical Network States, Criticality and Cortical Function", held in March 2017 at the Hanse Institute for Advanced Studies (HWK) in Delmenhorst, Germany, the book provides readers with extensive information on these topics, as well as tools and ideas to answer the above-mentioned questions. It is meant for physicists, computational and systems neuroscientists, and biologists

Grid alignment in entorhinal cortex

The spatial responses of many of the cells recorded in all layers of rodent medial entorhinal cortex (mEC) show mutually aligned grid patterns. Recent experimental findings have shown that grids can often be better described as elliptical rather than purely circular and that, beyond the mutual alignment of their grid axes, ellipses tend to also orient their long axis along preferred directions. Are grid alignment and ellipse orientation aspects of the same phenomenon? Does the grid alignment result from single-unit mechanisms or does it require network interactions? We address these issues by refining a single-unit adaptation model of grid formation, to describe specifically the spontaneous emergence of conjunctive grid-by-head-direction cells in layers III, V, and VI of mEC. We find that tight alignment can be produced by recurrent collateral interactions, but this requires head-direction (HD) modulation. Through a competitive learning process driven by spatial inputs, grid fields then form already aligned, and with randomly distributed spatial phases. In addition, we find that the self-organization process is influenced by any anisotropy in the behavior of the simulated rat. The common grid alignment often orients along preferred running directions (RDs), as induced in a square environment. When speed anisotropy is present in exploration behavior, the shape of individual grids is distorted toward an ellipsoid arrangement. Speed anisotropy orients the long ellipse axis along the fast direction. Speed anisotropy on its own also tends to align grids, even without collaterals, but the alignment is seen to be loose. Finally, the alignment of spatial grid fields in multiple environments shows that the network expresses the same set of grid fields across environments, modulo a coherent rotation and translation. Thus, an efficient metric encoding of space may emerge through spontaneous pattern formation at the single-unit level, but it is coherent, hence context-invariant, if aided by collateral interactions