The Advanced Encryption Standard (AES) is widely recognized as the most important block cipher in common use nowadays. This high assurance in AES is given by its resistance to ten years of extensive cryptanalysis, that has shown no weakness, not even any deviation from the statistical behaviour expected from a random permutation. Only reduced versions of the ciphers have been broken, but they a...

Elections with small margins of victory represent an important form of electoral competition and, increasingly, an opportunity for causal inference. Scholars using regression discontinuity designs (RDD) have interpreted the winners of close elections as randomly separated from the losers, using marginal election results as an experimental assignment of office-holding to one candidate versus the...

Given an undirected graph G, let us randomly orient G by tossing independent (possibly biased) coins, one for each edge of G. Writing a→ b for the event that there exists a directed path from a vertex a to a vertex b in such a random orientation, we prove that for any three vertices s, a and b of G, we have P(s→ a ∩ s→ b) ≥ P(s→ a)P(s→ b).

In 2 experiments, the authors examined whether and to what degree young adults can learn to produce random planar motion of the index finger or fingers. Three different types of information feedback were provided to the participants (N = 8 in each experiment) over up to 5 days of practice across the 2 experiments. The results from both experiments revealed that the participants produced a relat...

Many real-world optimization problems in, e. g., engineering or biology have the property that not much is known about the function to be optimized. This excludes the application of problem-specific algorithms. Simple randomized search heuristics are then used with surprisingly good results. In order to understand the working principles behind such heuristics, they are analyzed on combinatorial...

A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributio...

M. Mendoza, ∗ S. Succi, † and H. J. Herrmann 3, ‡ ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstrasse 6, HIF, CH-8093 Zürich (Switzerland) Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19 00185, Rome (Italy), and Freiburg Institute for Advanced Studies, Albertstrasse, 19, D-79104, Freiburg, (Germany) Departamento de...

As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

A discrete stochastic process involving random amplification with additive noise is studied analytically. If the non-negative random amplification factor b is such that =1, where beta is any positive noninteger, then the steady state probability density function for the process will have power law tails of the form p(x) approximately 1/x(beta+1). This is a generalization of recent resu...