Iterated sums of arithmetic progressions

Using generating functions we obtain a closed form expression involving two binomial coefficients for the iterated or k-fold summation of an arbitrary arithmetic progression of real numbers. As a contrast we obtain the same closed form expression using an elementary method based on an examination of Pascal's triangle. Some combinatorial interpretations of the iterated sums are also provided

A counting function for the sequence of perfect powers

Not availabl

A summation formula for sequences involving floor and ceiling functions

A closed form expression for the Nth partial sum of the pth powers of ||Sqrt(n)|| is obtained, where || · || denotes the nearest integer function. As a consequence, a necessary and sufficient condition for the divisibility of n by ||Sqrt(n)|| is derived together with a closed form expression for the least nonnegative residue of n modulo ||Sqrt(n)||. In addition an identity involving the zeta function ζ(s) and the infinite series SUM_(n=1)^(∞) 1/ ||Sqrt(n)|| ^(s+1) for real s > 1 is also obtained. Formatted abstract is available at http://rmmc.asu.edu/abstracts/rmj/vol36-5/nyblpag1.pdf

Safe Concurrency Introduction through Slicing

Traditional refactoring is about modifying the structure of existing code without changing its behaviour, but with the aim of making code easier to understand, modify, or reuse. In this paper, we introduce three novel refactorings for retrofitting concurrency to Erlang applications, and demonstrate how the use of program slicing makes the automation of these refactorings possible

Identification of fragments binding to SARS-CoV-2 nsp10 reveals ligand-binding sites in conserved interfaces between nsp10 and nsp14/nsp16

Since the emergence of SARS-CoV-2 in 2019, Covid-19 has developed into a serious threat to our health, social and economic systems. Although vaccines have been developed in a tour-de-force and are now increasingly available, repurposing of existing drugs has been less successful. There is a clear need to develop new drugs against SARS-CoV-2 that can also be used against future coronavirus infections. Non-structural protein 10 (nsp10) is a conserved stimulator of two enzymes crucial for viral replication, nsp14 and nsp16, exhibiting exoribonuclease and methyltransferase activities. Interfering with RNA proofreading or RNA cap formation represents intervention strategies to inhibit replication. We applied fragment-based screening using nano differential scanning fluorometry and X-ray crystallography to identify ligands targeting SARS-CoV-2 nsp10. We identified four fragments located in two distinct sites: one can be modelled to where it would be located in the nsp14–nsp10 complex interface and the other in the nsp16–nsp10 complex interface. Microscale thermophoresis (MST) experiments were used to quantify fragment affinities for nsp10. Additionally, we showed by MST that the interaction by nsp14 and 10 is weak and thereby that complex formation could be disrupted by small molecules. The fragments will serve as starting points for the development of more potent analogues using fragment growing techniques and structure-based drug design

Strain-level bacterial typing directly from patient samples using optical DNA mapping

For bacterial infections, it is important to rapidly and accurately identify and characterize the type of bacteria involved so that optimal antibiotic treatment can be given quickly to the patient. However, current diagnostic methods are sometimes slow and cannot be used for mixtures of bacteria. We have, therefore, developed a method to identify bacteria directly from patient samples. The method was tested on two common species of disease-causing bacteria - Escherichia coli and Klebsiella pneumoniae - and it could correctly identify the bacterial strain or subtype in both urine samples and mixtures. Hence, the method has the potential to provide fast diagnostic information for choosing the most suited antibiotic, thereby reducing the risk of death and suffering. Nyblom, Johnning et al. develop an optical DNA mapping approach for bacterial strain typing of patient samples. They demonstrate rapid identification of clinically relevant E. coli and K. pneumoniae strains, without the need for cultivation. BackgroundIdentification of pathogens is crucial to efficiently treat and prevent bacterial infections. However, existing diagnostic techniques are slow or have a too low resolution for well-informed clinical decisions.MethodsIn this study, we have developed an optical DNA mapping-based method for strain-level bacterial typing and simultaneous plasmid characterisation. For the typing, different taxonomical resolutions were examined and cultivated pure Escherichia coli and Klebsiella pneumoniae samples were used for parameter optimization. Finally, the method was applied to mixed bacterial samples and uncultured urine samples from patients with urinary tract infections.ResultsWe demonstrate that optical DNA mapping of single DNA molecules can identify Escherichia coli and Klebsiella pneumoniae at the strain level directly from patient samples. At a taxonomic resolution corresponding to E. coli sequence type 131 and K. pneumoniae clonal complex 258 forming distinct groups, the average true positive prediction rates are 94% and 89%, respectively. The single-molecule aspect of the method enables us to identify multiple E. coli strains in polymicrobial samples. Furthermore, by targeting plasmid-borne antibiotic resistance genes with Cas9 restriction, we simultaneously identify the strain or subtype and characterize the corresponding plasmids.ConclusionThe optical DNA mapping method is accurate and directly applicable to polymicrobial and clinical samples without cultivation. Hence, it has the potential to rapidly provide comprehensive diagnostics information, thereby optimizing early antibiotic treatment and opening up for future precision medicine management

Regulation of the Cardiac Na+/K+ ATPase by Phospholemman

Hansraj Dhayan, Rajender Kumar, Andreas Kukol, ‘Regulation of the Cardiac Na+/K+ ATPase by Phospholemman’, in Sajal Chakraborti, Naranjan Dhalla, eds., Regulation of Membrane Na+-K+ ATPase, (Switzerland: Springer, 2016), ISBN 978-3-319-24748-9, eISBN 978-3-319-24750-2.Peer reviewe

Proceedings of EADPH Pre -Congress Workshop held on Wednesday, 11 September 2019 at Het Pand, University of Ghent, Belgium. Best practices in dental curricula development – a follow-up to the 2018 EADPH Pre-Congress Workshop

This document reports the proceedings of a workshop held in Ghent on 11 September 2019, the day before the annual congress of the European Association of Dental Public Health. It is taken directly from the transcription of an audio recording. The workshop consisted of eight short presentations which described curriculum changes and examples of inter-professional education and practice involving dental public health in European countries. The presentations were followed by discussions in four small working groups and reports from each group which highlighted achievements, barriers and challenge