The Magic Number Problem for Subregular Language Families

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n). A number alpha not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Reproducibility of `COST Reference Microplasma Jets'

Atmospheric pressure plasmas have been ground-breaking for plasma science and technologies, due to their significant application potential in many fields, including medicinal, biological, and environmental applications. This is predominantly due to their efficient production and delivery of chemically reactive species under ambient conditions. One of the challenges in progressing the field is comparing plasma sources and results across the community and the literature. To address this a reference plasma source was established during the `Biomedical Applications of Atmospheric Pressure Plasmas' EU COST Action MP1101. It is crucial that reference sources are reproducible. Here, we present the reproducibility and variance across multiple sources through examining various characteristics, including: absolute atomic oxygen densities, absolute ozone densities, electrical characteristics, optical emission spectroscopy, temperature measurements, and bactericidal activity. The measurements demonstrate that the tested COST jets are mainly reproducible within the intrinsic uncertainty of each measurement technique

Recent visible light and metal free strategies in [2+2] and [4+2] photocycloadditions

When aiming to synthesize molecules with elevated molecular complexity starting from relatively simple starting materials, photochemical transformations represent an open avenue to circumvent analogous multistep procedures. Specifically, light-mediated cycloadditions remain as powerful tools to generate new bonds begotten from non-very intuitive disconnections, that alternative thermal protocols would not offer. In response to the current trend in both industrial and academic research pointing towards green and sustainable processes, several strategies that meet these requirements are currently available in the literature. This Minireview summarizes [2+2] and [4+2] photocycloadditions that do not require the use of metal photocatalysts by means of alternative strategies. It is segmented according to the cycloaddition type in order to give the reader a friendly approach and we primarily focus on the most recent developments in the field carried out using visible light, a general overview of the mechanism in each case is offered as wellFinancial support was provided by the European Research Council (ERC-CoG, Contract Number: 647550), the Spanish Government (RTI2018-095038-B-I00), the ‘Comunidad de Madrid’ and European Structural Funds (S2018/NMT-4367). R. I. R thanks Fundación Carolina for a graduate fellowshi

Advanced flavin catalysts elaborated with polymers

A variety of biological redox reactions are mediated by flavoenzymes due to the unique redox activity of isoalloxazine ring systems, which are found in flavin cofactors. In the field of synthetic organic chemistry, the term “flavin” is generally used for not only isoalloxazines but also related molecules including their isomers and some analogues, and those having catalytic activity are called flavin catalyst. Flavin catalysts are typically metal-free, and their catalytic activity can be readily accessed using mild terminal oxidants such as H2O2 and O2; therefore, redox reactions with these compounds have great promise as alternatives to reactions with conventional metal catalysts for the sustainable production of important chemicals. We recently became interested in using polymers for the development of flavin catalysts, especially to improve their practicality and advance the field of catalysis. Here, we summarize our recent research on such flavin-polymer collaborations including the development of facile preparation methods for flavin catalysts using polymers, readily reusable polymer-supported flavin catalysts, and flavin-peptide-polymer hybrids that can catalyze the first flavoenzyme-mimetic aerobic oxygenation reactions