Dimensionality of charge space

Geometry of Time and Dimensionality of Space

On the dimensionality of odor space

There is great interest in understanding human olfactory experience from a principled and quantitative standpoint. The comparison is often made to color vision, where a solid framework with a three-dimensional perceptual space enabled a rigorous search for the underlying neural pathways, and the technological development of lifelike color display devices. A recent, highly publicized report clai...

The Global Dimensionality of Face Space

Low-dimensional representations of sensory signals are key to solving many of the computational problems encountered in high-level vision. Principal Component Analysis (PCA) has been used in the past to derive such compact representations for the object class of human faces. Here, with an interpretation of PCA as a probabilistic model, we employ two objective criteria to study its generalizatio...

Fractal Theory Space: Spacetime of Noninteger Dimensionality

We construct matter field theories in “theory space” that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant “compactific...

On the dimensionality of olfactory space

We recently presented an estimate of the number of mutually discriminable olfactory stimuli at one trillion (1). Subjects were asked to sniff mixtures of molecules with increasing component overlap selected from a panel of 128 isointense structurally and perceptually diverse monomolecular odorants (2). We considered stimulus pairs discriminable when the majority of subjects could significantly ...