Irregular behaviour of class numbers and Euler-Kronecker constants of cyclotomic fields: the log log log devil at play

Kummer (1851) and, many years later, Ihara (2005) both posed conjectures on invariants related to the cyclotomic field $\mathbb Q(\zeta_q)$ with $q$ a prime. Kummer's conjecture concerns the asymptotic behaviour of the first factor of the class number of $\mathbb Q(\zeta_q)$ and Ihara's the positivity of the Euler-Kronecker constant of $\mathbb Q(\zeta_q)$ (the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_{\mathbb Q(\zeta_q)}(s)$ at $s=1$). If certain standard conjectures in analytic number theory hold true, then one can show that both conjectures are true for a set of primes of natural density 1, but false in general. Responsible for this are irregularities in the distribution of the primes. With this survey we hope to convince the reader that the apparently dissimilar mathematical objects studied by Kummer and Ihara actually display a very similar behaviour.Comment: 20 pages, 1 figure, survey, to appear in `Irregularities in the Distribution of Prime Numbers - Research Inspired by Maier's Matrix Method', Eds. J. Pintz and M. Th. Rassia

Breeding schemes: what are they, how to formalize them, and how to improve them?

Open Access Journal; Published online: 21 Jan 2022Formalized breeding schemes are a key component of breeding program design and a gateway to conducting plant breeding as a quantitative process. Unfortunately, breeding schemes are rarely defined, expressed in a quantifiable format, or stored in a database. Furthermore, the continuous review and improvement of breeding schemes is not routinely conducted in many breeding programs. Given the rapid development of novel breeding methodologies, it is important to adopt a philosophy of continuous improvement regarding breeding scheme design. Here, we discuss terms and definitions that are relevant to formalizing breeding pipelines, market segments and breeding schemes, and we present a software tool, Breeding Pipeline Manager, that can be used to formalize and continuously improve breeding schemes. In addition, we detail the use of continuous improvement methods and tools such as genetic simulation through a case study in the International Institute of Tropical Agriculture (IITA) Cassava east-Africa pipeline. We successfully deploy these tools and methods to optimize the program size as well as allocation of resources to the number of parents used, number of crosses made, and number of progeny produced. We propose a structured approach to improve breeding schemes which will help to sustain the rates of response to selection and help to deliver better products to farmers and consumers

Short term non-invasive ventilation post-surgery improves arterial blood-gases in obese subjects compared to supplemental oxygen delivery - a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>In the immediate postoperative period, obese patients are more likely to exhibit hypoxaemia due to atelectasis and impaired respiratory mechanics, changes which can be attenuated by non-invasive ventilation (NIV). The aim of the study was to evaluate the duration of any effects of early initiation of short term pressure support NIV vs. traditional oxygen delivery via venturi mask in obese patients during their stay in the PACU.</p> <p>Methods</p> <p>After ethics committee approval and informed consent, we prospectively studied 60 obese patients (BMI 30-45) undergoing minor peripheral surgery. Half were randomly assigned to receive short term NIV during their PACU stay, while the others received routine treatment (supplemental oxygen via venturi mask). Premedication, general anaesthesia and respiratory settings were standardized. We measured arterial oxygen saturation by pulse oximetry and blood gas analysis on air breathing. Inspiratory and expiratory lung function was measured preoperatively (baseline) and at 10 min, 1 h, 2 h, 6 h and 24 h after extubation, with the patient supine, in a 30 degrees head-up position. The two groups were compared using repeated-measure analysis of variance (ANOVA) and t-test analysis. Statistical significance was considered to be P < 0.05.</p> <p>Results</p> <p>There were no differences at the first assessment. During the PACU stay, pulmonary function in the NIV group was significantly better than in the controls (p < 0.0001). Blood gases and the alveolar to arterial oxygen partial pressure difference were also better (p < 0.03), but with the addition that overall improvements are of questionable clinical relevance. These effects persisted for at least 24 hours after surgery (p < 0.05).</p> <p>Conclusion</p> <p>Early initiation of short term NIV during in the PACU promotes more rapid recovery of postoperative lung function and oxygenation in the obese. The effect lasted 24 hours after discontinuation of NIV. Patient selection is necessary in order to establish clinically relevant improvements.</p> <p>Trial Registration#</p> <p>DRKS00000751; <url>http://www.germanctr.de</url></p

What Glues a Homodimer Together Systematic Analysis of the Stabilizing Effect of an Aromatic Hot Spot in the Protein Protein Interface of the tRNA Modifying Enzyme Tgt

Shigella bacteria constitute the causative agent of bacillary dysentery, an acute inflammatory disease causing the death of more than one million humans per year. A null mutation in the tgt gene encoding the tRNA modifying enzyme tRNA guanine transglycosylase Tgt was found to drastically decrease the pathogenicity of Shigella bacteria, suggesting the use of Tgt as putative target for selective antibiotics. The enzyme is only functionally active as a homodimer; thus, interference with the formation of its protein protein interface is an attractive opportunity for therapeutic intervention. To better understand the driving forces responsible for the assembly, stability, and formation of the homodimer, we studied the properties of the residues that establish the dimer interface in detail. We performed site directed mutagenesis and controlled shifts in the monomer dimer equilibrium ratio in solution in a concentration dependent manner by native mass spectrometry and used crystal structure analysis to elucidate the geometrical modulations resulting from mutational variations. The wild type enzyme exhibits nearly exclusive dimer geometry. A patch of four aromatic amino acids, embedded into a ring of hydrophobic residues and further stabilized by a network of H bonds, is essential for the stability of the dimer s contact. Accordingly, any perturbance in the constitution of this aromatic patch by nonaromatic residues reduces dimer stability significantly, with some of these exchanges resulting in a nearly exclusively monomeric state. Apart from the aromatic hot spot, the interface comprises an extended loop helix motif that exhibits remarkable flexibility. In the destabilized mutated variants, the loop helix motif adopts deviating conformations in the interface region, and a number of water molecules, penetrating into the interface, are observe