A simple renewal process is a stochastic process {Xn} taking values in {0,1} where the lengths of the runs of 1's between successive zeros are independent and identically distributed. After observing X0,X1,…Xn one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution of the time to renewal.
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an h0 with probability one and whose cardinality grows at most at exponential rate h0.
The study relating to the history of ethnology assesses the importance of a significant memory institution, the Masaryk University Archives in Brno, for the investigations aimed at the research into ethnographical activities developed within 1945-1989 in Moravia, especially in Brno. The essay submits an overview of particular collections which offer a plenty of noteworthy documents about the department of ethnography at the Faculty of Arts at Brno University, its history, educational and research work, leading personalities and study of numerous graduates. Special attention is paid to the personal estate of Professor Antonín Václavík, the larger part of which is stored there.