We survey the literature on the eccentricity sequence of a connected graph and make the following contribution. The eccentricity sequence of a graph G is the list of its eccentricities in non-increasing order. Two graphs G1 and G2 are co-eccentric when they have the same eccentricity sequence. Then, we say that G1 and G2 are co-eccentric mates. We characterize the eccentricity sequence of almos...

Eccentricity-dependent resolution losses are sometimes compensated for in psychophysical experiments by magnifying (scaling) stimuli at each eccentricity. The use of either pre-selected scaling factors or unscaled stimuli sometimes leads to non-monotonic changes in performance as a function of eccentricity. We argue that such non-monotonic changes arise when performance is limited by more than ...

For any Borel probability measure on Rn, we may define a family of eccentricity tensors. This new notion, together with a tensorization trick, allows us to prove an energy minimization property for rotationally invariant probability measures. We use this theory to give a new proof of the Welch bounds, and to improve upon them for collections of real vectors. In addition, we are able to give ele...

Contrast thresholds of vertical Gabor patterns were measured as a function of their eccentricity, size, shape, and phase using a 2AFC method. The patterns were 4 c/deg and they were presented for 90 or 240 ms. Log thresholds increase linearly with eccentricity at a mean rate of 0.47 dB/wavelength. For patterns centered on the fovea, thresholds decrease as the area of the pattern increases over ...

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials Ar take the simple form (l/r) = 1 + e cos(mφ), where k = 2 − α > 0 and l and e are generalisations of the semilatus-rectum and the eccentricity. m is given as a function of ‘eccentricity’. For nearly circular orbits m is √ k, while the above orbit becomes exact at ...