Despite more than thirty years of intensive research efforts, textual passwords are still enveloped in mysterious veils. In this work, we make a substantial step forward in understanding the underlying distributions of passwords. By conducting linear regressions on a corpus of 97.2 million passwords (a mass of chaotic data), we for the first time show that Zipf ’s law perfectly exists in user-g...

As we set up last week, let M n = [X ij ] n i,j=1 be a symmetric n × n matrix with Random entries such that • X i.j = X j,i • X i,j s are iid for all i < j, and X jj are iid for all j with E[X 2 ij ] = 1, E[X i j] = 0 • All moments exists for each entries. We considered the eigenvector of this random matrix; λ 1 ≤ λ 2 ≤ · · · ≤ λ n which turns out to be random elements depending continuously on...

Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as Benford’s Law (BL) or, in a special case, as the First Digit Law. The invariance properties that characterize BL are developed in detail. Special attention is gi...

0

The articles [8], [19], [2], [10], [12], [18], [20], [1], [15], [5], [21], [11], [3], [9], [7], [6], [17], [4], [16], [14], and [13] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: Ω, I are non empty sets, F is a σ-field of subsets of Ω, P is a probability on F , D, E, F are families of subsets of Ω, A, B, s are non empty subsets of F , b ...

BY MICHAEL W. PEREGRINE AND JAMES R. SCHWARTZ T he year 2009 witnessed an extraordinary series of developments in nonprofit corporate and charitable trust law as they affect the governance and operation of hospitals and health care systems. This is consistent with a decade-long trend that has made corporate law and governance key legal feasibility considerations for nonprofit organizations. The...

We have applied the Zipf method to extract the ζ ′ exponent for seven financial indices (DAX, FTSE; DJIA, NASDAQ, S&P500; Hang-Seng and Nikkei 225), after having translated the signals into a text based on two letters. We follow considerations based on the signal Hurst exponent and the notion of a time dependent Zipf law and exponent in order to implement two simple investment strategies for su...

It is argued that the fundamental theory of X-ray diffraction is based on a flawed model of wave interference. This is because the macroscopic distances between the crystalline sample on the one hand, and the X-ray source and the detector on the other, cannot be defined to the accuracy of a fractional wave-length. Thus, the inherent ‘graininess’ of the detector surface does not support the idea...