A theory of cross-spaces

The Brain Maps Out Ideas and Memories Like Spaces
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The tug of gravity

Until his death more than half a century later, H. At the very least, the hippocampus seemed like a promising place to start looking for hints of such maps.

That work eventually led a then-married pair of scientists at the Norwegian University of Science and Technology, May-Britt Moser and Edvard Moser , to direct their attention to the entorhinal cortex, located just next door to the hippocampus. There, the researchers found what they called grid cells, which experts now think may be the most compelling candidate for cognitive mapmaker.

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Unlike the place cells, grid cells do not represent particular locations. Each grid cell fires at regularly spaced positions, which form a hexagonal pattern. Imagine the floor of your bedroom is tiled with regular hexagons, all the same size, and each hexagon is divided into six equilateral triangles. As you walk across the room, one of your grid cells fires every time you reach a vertex of any of those triangles.

Different sets of grid cells form different grids: grids with larger or smaller hexagons, grids oriented in other directions, grids offset from one another.

An Expanding Role for Grid Cells

This kind of grid network, or code, constructs a more intrinsic sense of space than the place cells do. While place cells provide a good means of navigating where there are landmarks and other meaningful locations to provide spatial information, grid cells provide a good means of navigating in the absence of such external cues. And not just that: Since the grid network is based on relative relations, it could, at least in theory, represent not only a lot of information but a lot of different types of information, too.

Since researchers usually could not take direct measurements of individual neurons in their test subjects, they had to get clever with their methodology.

Einstein's Theory of General Relativity

In , for instance, neuroscientists figured out a certain kind of signal to look for in functional magnetic resonance imaging fMRI scans of the brain as an indirect signature of grid cell activity. As it turns out, it also characterizes other tasks, some spatial, some not so much. One of the earliest examples came with behavior that fell somewhere between the two: the navigation of visual space. When monkeys, with their heads fixed in place, tracked images with just their eyes, researchers found evidence of grid cell activity in the entorhinal cortex.

More recent work in humans has uncovered the same hexadirectional signature, and some experiments have even pinpointed other, more direct properties of the grid code already observed in physical navigation tasks.

What Are the Van Allen Belts? And How Can We Get Past Them?

Similar principles may also guide how the brain encodes time. Rats would run through a maze, in which one section involved trotting in place on a wheel or treadmill for some predetermined number of seconds before continuing onwards. During the interval when the rats ran in place, their actual location held constant, cells fired in their hippocampus to track their temporal progression: Some neurons were active for the first few seconds, others for the next few and so on.

More recently, work published in Nature last summer turned up evidence for a coding system that uniquely represents time in the context of memories or experiences. A team of researchers, led by the Mosers, uncovered a coding scheme for time that spanned multiple scales, from seconds to hours. Although no explicit link has yet been drawn between temporal organization and grid cells, scientists have seen hints of a connection: Grid cells signal elapsed time in rats running on treadmills, for instance.

A theory of cross-spaces (Annals of mathematics studies series;no.26)

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University of Oxford Libraries. Science Museum Library. University of Sheffield Library. In he was appointed to an assistant professorship at University of Vermont. In , he went to Kansas University , first as extraordinary professor until and then as ordinary professor until In he became professor at Hunter College , where he stayed until his death.

Bulletin of the American Mathematical Society

More information about this seller Contact this seller 6. Although instruments can neither see nor measure space-time, several of the phenomena predicted by its warping have been confirmed. About this Item: Princeton: Princeton Univ. A western shop Programming Flex 2: The Comprehensive Guide to Creating Rich Internet Applications with Adobe Flex of materials about the download of checkout in library and the back at unpublished. We received that ebook Keynes's Philosophical Development said unexpectedly survey us Spectral, particular, or active.

Schatten widely studied tensor products of Banach spaces. In functional analysis, he is the namesake of the Schatten norm and the Schatten class operators. His doctoral students included Elliott Ward Cheney, Jr.