The human body is truly a marvelous thing and our brains are far more important than we tend to realize. The complexities that make up our physical form is something even now we do not truly grasp and with good reason.

I recently came across a study published by the Blue Brain Project in the journal Frontiers of Computational Neuroscience and it blew me away. This study goes over a model that really delves into a side of our brains we have not seen before. It reveals that the scientists working for the Blue Brain Project have uncovered that the brain is full of multi-dimensional geometrical structures. These structures operating in up to eleven dimensions which is seemingly unheard of, to say the least.

The lead researcher on this study Henry Markram from the EPFL in Switzerland said as follows on the topic in a press release:

“We found a world that we had never imagined, there are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions.”

“The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly.”

According to Markram in the past, their mathematical approaches struggled to really make sense of the activity being generated by the neurons within and so mapping them out became quite frustrating until moving forth into high dimensional geometries. This kind of thing really puts a lot into perspective and reveals just how abundant the information that we have yet to find in this world truly is. ACTU. EPFL wrote on their website that these findings suggest the brain is constantly rewiring itself as it processes information. That in itself shows just how complex the network within each of us truly is.

The introduction of this study goes as follows:

“The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission into account, constructing graphs of a network that reflect the direction of information flow, and analyzing these directed graphs using algebraic topology. Applying this approach to a local network of neurons in the neocortex revealed a remarkably intricate and previously unseen topology of synaptic connectivity.

The synaptic network contains an abundance of cliques of neurons bound into cavities that guide the emergence of correlated activity. In response to stimuli, correlated activity binds synaptically connected neurons into functional cliques and cavities that evolve in a stereotypical sequence toward peak complexity. We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities.

How the structure of a network determines its function is not well understood. For neural networks specifically, we lack a unifying mathematical framework to unambiguously describe the emergent behavior of the network in terms of its underlying structure (Bassett and Sporns, 2017). While graph theory has been used to analyze network topology with some success (Bullmore and Sporns, 2009), current methods are usually constrained to analyzing how local connectivity influences local activity (Pajevic and Plenz, 2012; Chambers and MacLean, 2016) or global network dynamics (Hu et al., 2014), or how global network properties like connectivity and balance of excitatory and inhibitory neurons influence network dynamics (Renart et al., 2010; Rosenbaum et al., 2017). One such global network property is small-worldness. While it has been shown that small-worldness optimizes information exchange (Latora and Marchiori, 2001), and that adaptive rewiring during chaotic activity leads to small world networks (Gong and Leeuwen, 2004), the degree of small-worldness cannot describe most local network properties, such as the different roles of individual neurons.

Algebraic topology (Munkres, 1984) offers the unique advantage of providing methods to describe quantitatively both local network properties and the global network properties that emerge from local structure, thus unifying both levels. More recently, algebraic topology has been applied to functional networks between brain regions using fMRI (Petri et al., 2014) and between neurons using neural activity (Giusti et al., 2015), but the underlying synaptic connections (structural network) were unknown. Furthermore, all formal topological analyses have overlooked the direction of information flow, since they analyzed only undirected graphs.

Algebraic topology (Munkres, 1984) offers the unique advantage of providing methods to describe quantitatively both local network properties and the global network properties that emerge from local structure, thus unifying both levels. More recently, algebraic topology has been applied to functional networks between brain regions using fMRI (Petri et al., 2014) and between neurons using neural activity (Giusti et al., 2015), but the underlying synaptic connections (structural network) were unknown. Furthermore, all formal topological analyses have overlooked the direction of information flow, since they analyzed only undirected graphs.”

To learn more on this topic please feel free to click here or take a look at the video below. While it might not seem like much right now as time passes this could lead to marvelous finds. What do you think about the dimensions within? I for one am truly fascinated.