The "Initiative in Innovative Computing" at Harvard

[anhinga_drafts]

I've learned about a new organization (functioning since Summer 2006), which is doing various strange things, for example, "modifications to existing medical imaging programs that enable their use in astronomical research". "In particular, two software packages (3D Slicer and OsiriX) are being modified and used on data from the COMPLETE Survey of Star-Forming Regions, in order to characterize the physical nature of gas that forms new stars in our Galaxy."

http://iic.harvard.edu/

They are hiring new people too, with the emphasis on graphics/computer vision:

http://iic.harvard.edu/employment/index.html

Other than that, I am torturing myself trying to understand why for (pre)sheaves on a topology, it is not enough to take the topology itself as the set of logical values, but one needs to consider "sieves" aka "crib(b)les" (решета) over this topology to obtain the "classifier of subobjects"..

Comments

[anhinga-anhinga.livejournal.com]

> it is not enough to take the topology itself

ah, ok.. when one considers "points" of a sheaf (sections), e.g. partial functions, and defines something like a fuzzy equality between them, e.g. the degree of overlap, the topology itself is quite sufficient as the set of logical values..

but when one takes, say, two sheaves, one of them being a subsheaf of another, and wants to describe an equivalent of a characteristic function "classifying" the subsheaf, the question has to be answered on the level of each open set, so there is this whole structure associated with each open subset which is used to describe the "characteristic function" on the level of this subset..

so there is no paradox, it is just that the "internal logic of a sheaf" is simpler than the "internal logic of the category of such sheaves"..