Tag Archives: blue brain project

The 11 Dimensional Brain

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Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks

Posted on June 12, 2017 in Neuroscience

Using mathematics in a novel way in neuroscience, the Blue Brain Project shows that the brain operates on many dimensions, not just the three dimensions that we are accustomed to.

For most people, it is a stretch of the imagination to understand the world in four dimensions but a new study has discovered structures in the brain with up to eleven dimensions – ground-breaking work that is beginning to reveal the brain’s deepest architectural secrets.

Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.

The research, published today in Frontiers in Computational Neuroscience, shows that these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object.

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Topology in neuroscience: The image attempts to illustrate something that can not be imaged – a universe of multi-dimensional structures and spaces. On the left is a digital copy of a part of the neocortex, the most evolved part of the brain. On the right are shapes of different sizes and geometries in an attempt to represent structures ranging from 1D to 7D and beyond. The “black-hole” in the middle is used to symbolise a complex x of multi-dimensional spaces, or cavities. Courtesy of the Blue Brain Project

“We found a world that we had never imagined,” says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, and co-founder and Editor-in-Chief of Frontiers, “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.”

Markram suggests this may explain why it has been so hard to understand the brain. “The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly.”

If 4D worlds stretch our imagination, worlds with 5, 6 or more dimensions are too complex for most of us to comprehend. This is where algebraic topology comes in: a branch of mathematics that can describe systems with any number of dimensions. The mathematicians who brought algebraic topology to the study of brain networks in the Blue Brain Project were Kathryn Hess from EPFL and Ran Levi from Aberdeen University.

“Algebraic topology is like a telescope and microscope at the same time. It can zoom into networks to find hidden structures – the trees in the forest – and see the empty spaces – the clearings – all at the same time,” explains Hess.

In 2015, Blue Brain published the first digital copy of a piece of the neocortex — the most evolved part of the brain and the seat of our sensations, actions, and consciousness. In this latest research, using algebraic topology, multiple tests were performed on the virtual brain tissue to show that the multi-dimensional brain structures discovered could never be produced by chance. Experiments were then performed on real brain tissue in the Blue Brain’s wet lab in Lausanne confirming that the earlier discoveries in the virtual tissue are biologically relevant and also suggesting that the brain constantly rewires during development to build a network with as many high-dimensional structures as possible.

When the researchers presented the virtual brain tissue with a stimulus, cliques of progressively higher dimensions assembled momentarily to enclose high-dimensional holes, that the researchers refer to as cavities. “The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner,” says Levi. “It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates.”

The big question these researchers are asking now is whether the intricacy of tasks we can perform depends on the complexity of the multi-dimensional “sandcastles” the brain can build. Neuroscience has also been struggling to find where the brain stores its memories. “They may be ‘hiding’ in high-dimensional cavities,” Markram speculates.

Original research article: Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function

Citation: Reimann MW, Nolte M, Scolamiero M, Turner K, Perin R, Chindemi G, Dłotko P, Levi R, Hess K and Markram H (2017) Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function. Front. Comput. Neurosci. 11:48. doi: 10.3389/fncom.2017.00048

This research was funded by: ETH Domain for the Blue Brain Project (BBP) and the Laboratory of Neural Microcircuitry (LNMC); The Blue Brain Project’s IBM BlueGene/Q system, BlueBrain IV, funded by ETH Board and hosted at the Swiss National Supercomputing Center (CSCS); NCCR Synapsy grant of the Swiss National Science Foundation; GUDHI project, supported by an Advanced Investigator Grant of the European Research Council and hosted by INRIA.

from:     https://blog.frontiersin.org/2017/06/12/blue-brain-team-discovers-a-multi-dimensional-universe-in-brain-networks/

What’s Inside Your Head?

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The multi-dimensional universe hiding inside your head

A model from the Blue Brain Project describes the brain as being made up of ‘multi-dimensional’ geometrical structures and spaces

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A fabric of complex structures in our brain could be the key to understanding how the organ works, according to a new study. It could even provide an answer to mysteries like where our memories are stored.

The human brain is one of the most complex structures in nature, and we are still a long way from fully understanding how it works. Now, a group of researchers from the Blue Brain Project is bringing us closer to this goal using complex computer models.

Its latest model describes the brain as being made up of ‘multi-dimensional’ geometrical structures and spaces.

“We found a world that we had never imagined,” said neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland.

“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 structures form when a group of neurons – cells that transmit signals in the brain – forms something called a clique. Each neuron connects to every other neuron in the group in a specific way, to form a new object.

The more neurons there are in a clique, the higher the ‘dimension’ of the object.

It is important to understand these structures do not exist in more than three dimensions in space. Only the mathematics used to describe them uses more than three dimensions.

“Outside of physics, high-dimensional spaces are frequently used to describe complex data structures or conditions of systems, for instance, the state of a dynamical system in state space,” professor Cees van Leeuwen, from KU Leuven, Belgium and reviewer of the paper, told WIRED.

“The space is simply the union of all the degrees of freedom the system has, and its state describes the values these degrees of freedom are actually assuming.”

“When you take a complex network like the brain, you try to associate some familiar objects with it so that you can try to understand what it does,” Ran Levi from Aberdeen University, who worked on the paper, told WIRED. “Without it, all you see is a mess of ‘trees’ i.e. neurons firing at what appears to be random patterns.

“What we did is we took the complex structure of the brain network and mapped it to this universe. thus picking up very precisely defined high dimensional objects that give us a key to understanding structure and function.”

The team used a mathematical branch called algebraic topology to model these structures within a virtual brain, generated using a computer. Experiments were then carried out on real brain tissue, to test the results.

When the researchers added a stimulus into the virtual brain tissue, cliques of progressively higher dimensions assembled. In between these cliques were holes, or cavities.

“The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organised manner,” said Levi.

“It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materialises out of the sand and then disintegrates.”

The next step will be to see what practical role these structures play in the brain. For example, neuroscience has also been struggling to find where the brain stores its memories, and the holes could be a solution.

“They may be ‘hiding’ in high-dimensional cavities,” Markram speculates.

The research is published in Frontiers in Computational Neuroscience.

from:    https://www.wired.co.uk/article/neurons-multi-dimensional-network-brains