A multiplicative random cascade refers to a positive T -martingale in the sense of Kahane on the ultrametric space T = {0, 1, . . . , b− 1}. A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are ...

In November, 2014, 65 prostate cancer pathology experts, along with 17 clinicians including urologists, radiation oncologists, and medical oncologists from 19 different countries gathered in a consensus conference to update the grading of prostate cancer, last revised in 2005. The major conclusions were: (1) Cribriform glands should be assigned a Gleason pattern 4, regardless of morphology; (2)...

Prior studies of radical prostatectomies have reported a small percentage of men with biochemical progression after radical prostatectomy showing organ-confined, Gleason Score 6. One might predict that this should virtually never occur. We identified 2551 (1983-2005) radical prostatectomies coded by the urologists at our institution as pathologically organ-confined, Gleason score 6 cancer with ...

conclusions psa, psa density, and gleason score should be considered together in order to more accurately predict the adverse pathologic features of prostate cancer. methods we conducted a cross-sectional study of 105 patients with localized prostate cancer who underwent radical prostatectomy between 2006 and 2013. we recorded gleason scores and psa levels, in addition to the results of patholo...

preoperative gleason score (gs) obtained from trans rectal ultra sonography (trus) is the most common grading system to evaluate the appropriate treatment for patients with clinically localized prostate cancer. but this method showed upgraded and downgraded results in comparison to gleason score obtained from radical prostatectomy. the current study aimed to determine clinical or pathological v...

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have power decay Fourier transform at infinity. In homogeneous case, when contraction ratios are equal, this is essentially due to Erdős and Kahane. non-homogeneous case difficulty we overcome apparent lack convolution structure.