We show that a-parabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called-Gaussian estimates for the transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume property, and the fact that the mean exit time in any ball of radius R is of the order R. The latter condition can be replaced by a cert...

We resolve the local semistable reduction problem for overconvergent F -isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree 0). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-adic...

This note briefly reviews the Mirror Principle as developed in the series of papers [19][20][21][22][23]. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting holomorphic disks and annuli. This note has been submitted for the proceedings of the Workshop on Strings, Duality and Geometry the C.R.M. in Montreal of March 2000.

We characterize the error distribution of BATSE GRB locations by modeling the distribution of separations between BATSE locations and IPN annuli. We determine error model parameters by maximizing likelihood and rank the models by their Bayesian odds ratios. The best models have several systematic error terms. The simplest good model has a 1.9 degree systematic error with probability 73% and 5.4...

Viewing of annuli modulated in color in a sawtooth fashion in time results in differential threshold elevations for the detection of color changes of inscribed disks. The elevations are of nearly the same magnitude as those resulting from viewing modulated disks. However, the differential effects on thresholds for complimentary colors are reversed. The differential effects, thus, are correlated...