Efficient and flexible representation of higher-dimensional cognitive variables with grid cells

Robust and efficient coding with grid cells

The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach t...

Sparse Higher Order Functions of Discrete Variables — Representation and Optimization

Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing such functions. We observed that higher order functions encountered in computer vision are very oft...

Sparse grid methods for higher dimensional approximation

Tubular Splines Using A Higher Dimensional Representation

Tubular splines are like the usual spline curves, but have thickness, i.e. locally look like circular cones. They are constructed with pieces of indefinitely differentiable surfaces whose profiles are circles, which are joined together with a prescribed degree of smoothness. We consider splines constructed joining together pieces of canal surfaces bounded by circles. A canal surface is determin...

gridlib: Flexible and Efficient Grid Management for Simulation and Visualization

This paper describes the gridlib project, a unified grid management framework for simulation and visualization. Both, adaptive PDE-solvers and interactive visualization toolkits, have to manage dynamic grids. The gridlib meets the similar but not identical demands on grid management from the two sides, visualization and simulation. One immediate advantage of working on a common grid is the fact...