Process convergence for the complexity of Radix Selection on Markov sources

A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its complexity is measured by the number of symbols that have to be read. In this paper the model of independent data identically generated from a Markov chain is considered.The complexity is studied as a stochastic process indexed by the set of infinite strings over the given alphabet. The orders of mean and variance of the complexity and, after normalization, a limit theorem with a centered Gaussian process as limit are derived. This implies an analysis for two standard models for the ranks: uniformly chosen ranks, also called grand averages, and the worst case rank complexities which are of interest in computer science.For uniform data and the asymmetric Bernoulli model (i.e. memoryless sources), we also find weak convergence for the normalized process of complexities when indexed by the ranks while for more general Markov sources these processes are not tight under the standard normalizations.     

Blocking the Hype‐Hypocrisy‐Falsification‐Fakery Pathway is Needed to Safeguard Science

In chemistry and other sciences, hype has become commonplace, compounded by the hypocrisy of those who tolerate or encourage it while disapproving of the consequences. This reduces the credibility and trust upon which all science depends for support. Hype and hypocrisy are but first steps down a slippery slope towards falsification of results and dissemination of fake science. Systemic drivers in the contemporary structure of the science establishment encourage exaggeration and may lure the individual into further steps along the hype‐hypocrisy‐falsification‐fakery continuum. Collective, concerted intervention is required to effectively discourage entry to this dangerous pathway and to restore and protect the probity and reputation of the science system. Chemists must play and active role in this effort.     

Biuret—A Crucial Reaction Intermediate for Understanding Urea Pyrolysis To Form Carbon Nitrides: Crystal-Structure Elucidation and In Situ Diffractometric,Vibrational and Thermal Characterisation

The crystal structure of biuret was elucidated by means of XRD analysis of single crystals grown through slow evaporation from a solution in ethanol. It crystallises in its own structure type in space group C2/c (a=15.4135(8) Å, b=6.6042(3) Å, c=9.3055(4) Å, Z=8). Biuret decomposition was studied in situ by means of temperature-programmed powder XRD and FTIR spectroscopy, to identify a co-crystalline biuret–cyanuric acid phase as a previously unrecognised reaction intermediate. Extensive thermogravimetric studies of varying crucible geometry, heating rate and initial sample mass reveal that the concentration of reactive gases at the interface to the condensed sample residues is a crucial parameter for the prevailing decomposition pathway. Taking these findings into consideration, a study on the optimisation of carbon nitride synthesis from urea on the gram scale, with standard solid-state laboratory techniques, is presented. Finally, a serendipitously encountered self-coating of the crucible inner walls by graphite during repeated synthetic cycles, which prove to be highly beneficial for the obtained yields, is reported.     

Freitod in Dahlem (1915): Unveröffentlichte Briefe von Edith Hahn und Lise Meitner über Dr. Clara Haber geb. Immerwahr

The present contribution contains previously unpublished letters by Clara Haber's contemporaries Edith Hahn and Lise Meitner that were written within two weeks of Clara Haber′s tragic suicide. It also contains a commentary about the circumstances of obtaining these letters as well as notes concerning their interpretation.