Brain tissue tessellation shows absence of canonical microcircuits

A model of individualized canonical microcircuits supporting cognitive operations

Major cognitive functions such as language, memory, and decision-making are thought to rely on distributed networks of a large number of basic elements, called canonical microcircuits. In this theoretical study we propose a novel canonical microcircuit model and find that it supports two basic computational operations: a gating mechanism and working memory. By means of bifurcation analysis we systematically investigate the dynamical behavior of the canonical microcircuit with respect to parameters that govern the local network balance, that is, the relationship between excitation and inhibition, and key intrinsic feedback architectures of canonical microcircuits. We relate the local behavior of the canonical microcircuit to cognitive processing and demonstrate how a network of interacting canonical microcircuits enables the establishment of spatiotemporal sequences in the context of syntax parsing during sentence comprehension. This study provides a framework for using individualized canonical microcircuits for the construction of biologically realistic networks supporting cognitive operations.

From abstract topology to real thermodynamic brain activity

Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Changes in thermodynamic parameters and dimensions occur in the brain during symmetry breakings and transitions from one functional state to another. Based on topological results and string-like trajectories into nervous energy landscapes, we provide a novel method for the evaluation of energetic features and constraints in different brain functional activities. We show how abstract approaches, namely the Borsuk-Ulam theorem and its variants, may display real, energetic physical counterparts. When topology meets the physics of the brain, we arrive at a general model of neuronal activity, in terms of multidimensional manifolds and computational geometry, that has the potential to be operationalized.

The human brain from above: an increase in complexity from environmental stimuli to abstractions

Contrary to common belief, the brain appears to increase the complexity from the perceived object to the idea of it. Topological models predict indeed that: (a) increases in anatomical/functional dimensions and symmetries occur in the transition from the environment to the higher activities of the brain, and (b) informational entropy in the primary sensory areas is lower than in the higher associative ones. To demonstrate this novel hypothesis, we introduce a straightforward approach to measuring island information levels in fMRI neuroimages, via Rényi entropy derived from tessellated fMRI images. This approach facilitates objective detection of entropy and corresponding information levels in zones of fMRI images generally not taken into account. We found that the Rényi entropy is higher in associative cortices than in the visual primary ones. This suggests that the brain lies in dimensions higher than the environment and that it does not concentrate, but rather dilutes messages coming from external inputs.

Topodynamics of metastable brains

The brain displays both the anatomical features of a vast amount of interconnected topological mappings as well as the functional features of a nonlinear, metastable system at the edge of chaos, equipped with a phase space where mental random walks tend towards lower energetic basins. Nevertheless, with the exception of some advanced neuro-anatomic descriptions and present-day connectomic research, very few studies have been addressing the topological path of a brain embedded or embodied in its external and internal environment. Herein, by using new formal tools derived from algebraic topology, we provide an account of the metastable brain, based on the neuro-scientific model of Operational Architectonics of brain-mind functioning. We introduce a "topodynamic" description that shows how the relationships among the countless intertwined spatio-temporal levels of brain functioning can be assessed in terms of projections and mappings that take place on abstract structures, equipped with different dimensions, curvatures and energetic constraints. Such a topodynamical approach, apart from providing a biologically plausible model of brain function that can be operationalized, is also able to tackle the issue of a long-standing dichotomy: it throws indeed a bridge between the subjective, immediate datum of the naïve complex of sensations and mentations and the objective, quantitative, data extracted from experimental neuro-scientific procedures. Importantly, it opens the door to a series of new predictions and future directions of advancement for neuroscientific research.

Bold-Independent Computational Entropy Assesses Functional Donut-Like Structures in Brain fMRI Images

We introduce a novel method for the measurement of information level in fMRI (functional Magnetic Resonance Imaging) neural data sets, based on image subdivision in small polygons equipped with different entropic content. We show how this method, called maximal nucleus clustering (MNC), is a novel, fast and inexpensive image-analysis technique, independent from the standard blood-oxygen-level dependent signals. MNC facilitates the objective detection of hidden temporal patterns of entropy/information in zones of fMRI images generally not taken into account by the subjective standpoint of the observer. This approach befits the geometric character of fMRIs. The main purpose of this study is to provide a computable framework for fMRI that not only facilitates analyses, but also provides an easily decipherable visualization of structures. This framework commands attention because it is easily implemented using conventional software systems. In order to evaluate the potential applications of MNC, we looked for the presence of a fourth dimension's distinctive hallmarks in a temporal sequence of 2D images taken during spontaneous brain activity. Indeed, recent findings suggest that several brain activities, such as mind-wandering and memory retrieval, might take place in the functional space of a four dimensional hypersphere, which is a double donut-like structure undetectable in the usual three dimensions. We found that the Rényi entropy is higher in MNC areas than in the surrounding ones, and that these temporal patterns closely resemble the trajectories predicted by the possible presence of a hypersphere in the brain.