Open Access

In the accompanying paper [1] the authors study a model of concurrent programs in terms of events and a dependence relation, i.e., a set of arrows, between them. There also two simplifying interface models are presented; they abstract in different ways from the intricate network of internal points and arrows of program components. This report supplements [1] by presenting full proofs for the properties of the interface models, in particular, that both models exhibit homomorphic behaviour w.r.t. sequential and concurrent composition. [1] B. Möller, C.A.R. Hoare, M.E. Müller, G. Struth: A discrete geometric model of concurrent program execution. In H. Zhu, J. Bowen: Proc. UTP 16. LNCS 10134. Springer 2017, 1-25

This article is the posthumous publication of a fundamental work of the late genius M.U. Newtral. Little is known of his life, upbringing, education and his golf handicap. Whether he enjoyed flyfishing is still a matter of scientific controversy. From his style of writing and the locations where his manuscripts were discovered one might conclude that he spent a reasonable time of his life in India and the United Kingdom, where he presumably worked under the influence of many such famous people as Luke Withstone, Rudinch Kipling, Morten Haydagger and, last but not least, Petula Farnsbath-Wellworth, 31 Rosebud Drive, Eightashgreen, Devonshire (ring and knock thrice to be admitted). Newtral disappeared under nebulous circumstances somewhere in South-America. Some of his belongings were discovered by Leumas Reltub on the Island of Erewhon, and the here partially reprinted manuscript was not discovered by a nihilist. Yet, the editors wish to keep the exact location of the original a secret. Newtral probably received the impetus for writing his treatise upon the following occasion. In his 2011 paper on "Constructions Around Partialities" Gunther Schmidt discussed a partiality of quite unique character. It is known as the smallest part or piece of a whole, and it is unique in the way that it seems there is only exactly one instance and interpretation of it: nothing. When the editors became involved in the production of a Festschrift for Gunther Schmidt they decided to finally publish Newtral's work, which happened to have been in their hands for quite some time without them knowing what to do with it, as a tribute to Gunther in the hope that it will further or at least subtract nothing from the growth of relational mathematics. The original manuscript (partially handwritten) has been typeset with greatest care; so for all the mistakes, only M.U. Newtral himself is to blame. Helpful comments by R. Berghammer, P. Höfner and M. Winter are gratefully acknowledged.

Opening of the endothelial barrier and targeted infiltration of leukocytes into the affected tissue are hallmarks of the inflammatory response. The molecular mechanisms regulating these processes are still widely elusive. In this study, we elucidate a novel regulatory network, in which miR-125a acts as a central hub that regulates and synchronizes both endothelial barrier permeability and monocyte migration. We found that inflammatory stimulation of endothelial cells induces miR-125a expression, which consecutively inhibits a regulatory network consisting of the two adhesion molecules VE-Cadherin (CDH5) and Claudin-5 (CLDN5), two regulatory tyrosine phosphatases (PTPN1, PPP1CA) and the transcription factor ETS1 eventually leading to the opening of the endothelial barrier. Moreover, under the influence of miR-125a, endothelial expression of the chemokine CCL2, the most predominant ligand for the monocytic chemokine receptor CCR2, was strongly enhanced. In monocytes, on the other hand, we detected markedly repressed expression levels of miR-125a upon inflammatory stimulation. This induced a forced expression of its direct target gene CCR2, entailing a strongly enhanced monocyte chemotaxis. Collectively, cell-type-specific differential expression of miR-125a forms a synergistic functional network controlling monocyte trafficking across the endothelial barrier towards the site of inflammation. In addition to the known mechanism of miRNAs being shuttled between cells via extracellular vesicles, our study uncovers a novel dimension of miRNA function: One miRNA, although disparately regulated in the cells involved, directs a biologic process in a synergistic and mutually reinforcing manner. These findings provide important new insights into the regulation of the inflammatory cascade and may be of great use for future clinical applications.