Topological analysis of population activity in visual cortex

Singh, G., Memoli, F., Ishkhanov, T., Sapiro, G., Carlsson, G., & Ringach, D. L. (2008). Topological analysis of population activity in visual cortex. Journal of Vision, 8(8):11, 1–18,, doi:10.1167/8.8.11

From sparsely sampled data, we can attempt to estimate some of topological structure of the data.

Toplogical structure is here represented by Betti numbers. The paper explains this best:

Consider a world where objects are made of elastic rubber. Two objects are considered equivalent if they can be deformed into each other without tearing the material. If such a transformation between X and Y exists, we say they are topologically equivalent……it is evident that a possible reason for two objects not to be equivalent is that they differ in the number of holes. Thus, simply counting holes can provide a signature for the object at hand. Holes can exist in different dimensions. A one-dimensional hole is exposed when a one-dimensional loop (a closed curve) on the object cannot be deformed into a single point without tearing the loop. If two such loops can be deformed into one another they define the same hole, which should be counted only once. Analogous definitions can be invoked in higher dimensions. For example, a two-dimensional hole is revealed when a closed two-dimensional oriented surface on the object cannot be deformed into a single point.

This notion of counting holes of different dimensions is formalized by the definition of Betti numbers. The Betti numbers of an object X can be arranged in a sequence, b ( X )=( b 0 , b 1 , b 2 , I ), where b 0 represents the number of connected components, b 1 represents the number of one- dimensional holes, b 2 the number of two-dimensional holes, and so forth. An important property of Betti sequences is that if two objects are topologically equiv- alent (they can be deformed into each other) they share the same Betti sequence. One must note, as we will shortly illustrate, that the reverse is not always true: two objects can be different but have the same Betti sequence.

A technique is presented for estimating the Betti numbers of sampled data using “Rips complexes” and “barcodes”. To put this technique to use on neural data, the spiking of 5 cells (mostly “complex cells in the superficial layers”) with high spontaineous rate in V1 in Macaques were recorded from. The spikes were binned and a point cloud in 5D was constructed (so i think the coordinates of the point cloud representing the spike rate in each of the 5 dimensions).

This was done in two experimental conditions, when a stimulus was being presented, and when the eyes were occluded. In both cases, the topological structure varied between a circle and a sphere, although the circle structure was found with higher probability in the stimulus condition. The authors present a model of circular structure generated “if cortical activity is dominated by neuronal responses to stimulus orientation”, and a model of toroidal structure generated “A toroidal representation may arise from a neuronal population responding to two circular variables, such as orientation and color hue”. Note that a torus wasn’t actually observed in the data; a circle and a sphere was. In the conclusions the authors speculate what could have caused the sphere.

The authors conclude that the topology of spiking patterns for “both the data for spontaneous and driven conditions have similar topological structures, with the signatures of the circle and the sphere dominating the results”.

Local sleep in awake rats

this experiment claims to show that

(1) when rats are sleep-deprived, small populations of rat brain neurons can fall asleep while the rest of the rat is awake, and
(2) this may correspond to performance degradation



i haven’t read the actual article yet…

IBM Cat Brain Simulation Scuffle: Symbolic?

You’ve probably read by now about the announcement by IBM’s Cognitive Computing group that they had created a “computer system that simulates and emulates the brain’s abilities for sensation, perception, action, interaction and cognition” at the “scale of a cat cortex”.    For their work, the IBM team led by Dharmendra Modha was awarded the ACM Gordon Bell prize, which recognizes “outstanding achievement in high-performance computing”.

A few days later, Henry Markram, leader of the Blue Brain Project at EPFL, sent off an e-mail to IBM CTO Bernard Meyerson harshly criticizing the IBM press release, and cc’ed several reporters. This brought a spate of shock media into the usually placid arena of computational neuroscience reporting, with headlines such as “IBM’s cat-brain sim a ‘scam,’ says Swiss boffin: Neuroscientist hairs on end”, and “Meow! IBM cat brain simulation dissed as ‘hoax’ by rival scientist”.  One reporter chose to highlight the rivalry as cat versus rat, using the different animal model choice of the two researchers as a theme.  Since then, additional criticisms from Markram have appeared online.

Find out more after the jump.

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Henry Markram on TED – video online

We had read that Dr. Henry Markram of the Blue Brain project had given a talk at TED (technology, entertainment, design), but the video wasn’t released until this month.  This talk is geared towards a general audience, rather than getting into the specific details of the Blue Brain project, as he has before.  It is engaging and includes many suggestions towards the future of neuroscience and AI.

Watch it online at the TED website.

Transcriptomics of the fetal human brain

A cutting-edge application of the Affy total human exome GeneChip (4X coverage per exon, 40X coverage per gene): Functional and Evolutionary Insights into Human Brain Development through Global Transcriptome Analysis.

From the News and Views, I was intrigued to learn that previous transcriptome analyses of adult human brains found very little difference in gene expression between brain areas:

[…] this suggests that it is the gene expression during development that largely determines higher brain functions by specifying the complexity of neural connections. Numerically, the most important genes relating to cognitive differences between species may be genes that specify how the machinery is put together. In support of this hypothesis, many of the identified differentially expressed genes in this study are related to processes involved in connection formation, such as axonal guidance and cell adhesion.

An impressive 76% of all human genes are expressed in the developing fetal brain. Of those, 33% are differentially expressed over brain regions (13 regions were examined) and 28% are alternatively spliced. The differentially expressed genes are also ones that seem to have evolved the most recently. Even in these early (midgestation) stages, left-right asymmetry was seen, such as the localization of the language-associated FOXP2 genes to Broca’s area.

Of interest to computational folks, they find that gene expression follows power-law scaling (as many other naturally occurring “small-worlds” networks do) with certain hub genes connected to many others and certain spoke genes with relatively few connections. Unsupervised hierarchical clustering is used in this analysis.