Randomized Phase II oncology trial endpoints for decision making include both progression-free survival (PFS) and change in tumor burden as measured by the sum of longest diameters (SLD) of the target lesions. In addition to observed SLD changes, tumor shrinkage and growth parameters can be estimated from the patient-specific SLD profile over time. The ability of these SLD analyses to identify ...

We show that for integers k ≥ 2 and n ≥ 3, the diameter of the Cayley graph of SLn(Z/kZ) associated to a standard two-element generating set, is at most a constant times n 2 ln k. This answers a question of A. Lubotzky concerning SLn(Fp) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing eleme...

We derive a new upper bound for the diameter of a k-regular graphG as a function of the eigenvalues of the adjacency matrix. Namely, supposethe adjacency matrix of G has eigenvalues AI , A2 .••.• An with lAd:::: IA21 ::::... :::: IAnl where AI = k, A = IA21. Then the diameter D(G) must satisfy D(G) :::; rlog(n 1)f1og(k/A)l. We wilJ consider families of graphs whose eigenvalues can b...

We study the relation between the diameter, the first positive eigenvalue of the discrete p-Laplacian and the `p-distortion of a finite graph. We prove an inequality relating these three quantities and apply it to families of Cayley and Schreier graphs. We also show that the `p-distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain estimates for the...

The relationship between the Tibetan prelate Tāranātha (1575-1634) and his major patrons, the various sDe pa of gTsang is a most complex one. In studying it I am increasingly aware that the wealth of detail to be gleaned from the various relevant texts is not just limited to the narrow study of the lives of just a few people, in this case those of Tāranātha and the various rulers of gTsang. Ind...

It has been demonstrated that the diameters of porous particles are underestimated by Coulter measurements. This phenomenon has also been observed in hydrogel particles, but not characterized. Since the Coulter principle uses the displacement of electrolyte to determine particle size, electrolyte contained within the swelled hydrogel microparticles results in an underestimate of actual particle...