Friday, October 31, 2014

Topographic Maps in Neuroanatomy

A topographic map is the ordered projection of a sensory surface, like the retina or the skin, or an effector system, like the musculature, to one or more structures of the central nervous system. Topographic maps can be found in all sensory systems and in many motor systems. 




“Topographically” mapped visual cortical areas,such as primary visual cortex map Cartesian X-­Y positions in visual space using an approximate log conformal mapping (From The Conscious Grid).


Images of concentric circles of radii between  and  around the origin under the (conformal) map . Large circles are mapped into parallel lines with increasing real parts. (Courtesy: http://functions.wolfram.com/ElementaryFunctions/Log/visualizations/4/)

The maps are not a strict isomorphic representation of XY space. Also, neurons in such maps do not stand for “pixels” of XY space.

Kohonen Maps are relevant as a first step in understanding such topographic maps.



More here on: Wikipedia

Tuesday, October 28, 2014

Kohonen Self Organizing Map

Kohonen Self Organization Map 

To map a 2D triangle (set of vectors) to a 1-D vector:

Input to the Kohonen Map:





Simulation - Ordering and beginning of Convergence:




Final output (below) - end of Convergence phase:
From a project done in Complex Adaptive Systems course 'Neural Networks' at the Chalmers University of Technology, Gothenburg, Sweden, 2014.

Tuesday, October 21, 2014

On Complexity

Any entity in the world around us, such as an individual human being, owes its existence not only to the simple fundamental law of physics and the boundary condition on the early universe but also to the outcomes of an inconceivably long sequence of probabilistic events, each of which could have turned out differently. - Murray Gell Mann

Saturday, October 04, 2014

Real-time updates and schedules - Public Transport System in Sweden

Was speaking to a personnel setting up a schedule display at the tram station opposite Chalmers Univ (Gothenburg, Sweden). There is actually a sensor on the tram/bus and one on the track and cables run throughout the tracks in order to display data in the stations. So exact timings about departure and arrival of different buses and trams gets tracked in real-time.  The displays have a modem inside and also send out data for the mobile apps and the website.