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”.

ConnectomeViewer – Multi-Modal Multi-Level Network and Neuroimaging Visualization and Analysis

Two neat tools concerned with the “connectome” (i.e. the pattern of connections in the nervous system):

Semantic wiki:

Desktop viewer: “Multi-Modal Multi-Level Network and Neuroimaging Visualization and Analysis” (screencasts)

Over time, distribution of shot lengths in movies has moved closer to pink noise

The statistics of shot durations in 150 films from 1935 to 2005 were analyzed. From about 1970 to the present, the power spectrum of shot durations in individual films has tended to become more like pink noise (power ~= 1/f). Also, autocorrelation shows that the lengths of nearby shots has become more and more correlated.

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Dead salmon in fMRI machine shows signs of thought (not really)

This poster, by Bennett, Baird, Miller, and Wolford, provides a memorable reminder that you have to do a statistical correction for multiple comparisons when you datamine a large number of things for correlation.

“The task administered to the salmon involved completing an open-ended mentalizing task. The salmon was shown a series of photographs depicting human individuals in social situations with a specified emotional valence. The salmon was asked to determine what emotion the individual in the photo must have been experiencing.”

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Frontiers in Neuroscience Journal

The journal, Frontiers in Neuroscience, edited by Idan Segev, has made it Volume 3, issue 1.  Launching last year at the Society for Neuroscience conference, its probably the newest Neuroscience-related journal.

I’m a fan of it because it is an open-access journal featuring a “tiered system” and more.  From their website:

The Frontiers Journal Series is not just another journal. It is a new approach to scientific publishing. As service to scientists, it is driven by researchers for researchers but it also serves the interests of the general public. Frontiers disseminates research in a tiered system that begins with original articles submitted to Specialty Journals. It evaluates research truly democratically and objectively based on the reading activity of the scientific communities and the public. And it drives the most outstanding and relevant research up to the next tier journals, the Field Journals.

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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.