Dimensional analysis using toric ideals: Primitive invariants

© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1

Topological Modes in One Dimensional Solids and Photonic Crystals

This is the final version of the article. Available from American Physical Society via the DOI in this record.It is shown theoretically that a one-dimensional crystal with time reversal symmetry is characterized by a Z_{2} topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analogue in the microwave regime.We thank an anonymous referee for helpful comments. The authors acknowledge financial support from the EPSRC through the QUEST program grant (Grant No. EP/I034548/1), C.A.M.B. was supported by QinetiQ and the EPSRC through the Industrial CASE scheme (Grant No. 08000346). H.M. is supported by a grant from the U. S. Department of Energy to the Particle Astrophysics Theory group at CWRU. T.J.A. is funded by the Research Corporation for Science Advancement through a Cottrell Award

Association between Helicobacter pylori genotypes and severity of chronic gastritis, peptic ulcer disease and gastric mucosal interleukin-8 levels: evidence from a study in the Middle East

Background: The varied clinical presentations of Helicobacter pylori (H. pylori) infection are most likely due to differences in the virulence of individual strains, which determines its ability to induce production of interleukin-8 (IL-8) in the gastric mucosa. The aim of this study was to examine association between cagA, vacA-s1 and vacA-s2 genotypes of H. pylori and severity of chronic gastritis and presence of peptic ulcer disease (PUD), and to correlate these with IL-8 levels in the gastric mucosa. Methods: Gastric mucosal biopsies were obtained from patients during esophagogastroduodenoscopy. The severity of chronic gastritis was documented using the updated Sydney system. H. pylori cagA and vacA genotypes were detected by PCR. The IL-8 levels in the gastric mucosa were measured by ELISA. Results: H. pylori cagA and/or vacA genotypes were detected in 99 patients (mean age 38.4±12.9; 72 males), of whom 52.5% were positive for cagA, 44.4% for vacA-s1 and 39.4% for vacA-s2; and 70.7% patients had PUD. The severity of inflammation in gastric mucosa was increased with vacA-s1 (p=0.017) and decreased with vacA-s2 (p=0.025), while cagA had no association. The degree of neutrophil activity was not associated with either cagA or vacA-s1, while vacA-s2 was significantly associated with decreased neutrophil activity (p=0.027). PUD was significantly increased in patients with cagA (p=0.002) and vacA-s1 (p=0.031), and decreased in those with vacA-s2 (p=0.011). The level of IL-8 was significantly increased in patients with cagA (p=0.011) and vacA-s1 (p=0.024), and lower with vacA-s2 (p=0.004). Higher levels of IL-8 were also found in patients with a more severe chronic inflammation (p=0.001), neutrophil activity (p=0.007) and those with PUD (p=0.001). Conclusions: Presence of vacA-s1 genotype of H. pylori is associated with more severe chronic inflammation and higher levels of IL-8 in the gastric mucosa, as well as higher frequency of PUD. Patients with vacA-s2 have less severe gastritis, lower levels of IL-8, and lower rates of PUD. The presence of cagA genotype is not associated with the severity of gastritis or IL-8 induction in the gastric mucosa. The association of cagA with PUD may be a reflection of its presence with vacA-s1 genotype

Tubulin isoform composition tunes microtubule dynamics

Microtubules polymerize and depolymerize stochastically, a behavior essential for cell division, motility and differentiation. While many studies advanced our understanding of how microtubule-associated proteins tune microtubule dynamics in trans, we have yet to understand how tubulin genetic diversity regulates microtubule functions. The majority of in vitro dynamics studies are performed with tubulin purified from brain tissue. This preparation is not representative of tubulin found in many cell types. Here we report the 4.2Å cryo-EM structure and in vitro dynamics parameters of α1B/βI+βIVb microtubules assembled from tubulin purified from a human embryonic kidney cell line with isoform composition characteristic of fibroblasts and many immortalized cell lines. We find that these microtubules grow faster and transition to depolymerization less frequently compared to brain microtubules. Cryo-EM reveals that the dynamic ends of α1B/βI+βIVb microtubules are less tapered and that these tubulin heterodimers display lower curvatures. Interestingly, analysis of EB1 distributions at dynamic ends suggests no differences in GTP cap sizes. Lastly, we show that the addition of recombinant α1A/βIII tubulin, a neuronal isotype overexpressed in many tumors, proportionally tunes the dynamics of α1B/βI+βIVb microtubules. Our study is an important step towards understanding how tubulin isoform composition tunes microtubule dynamics

Metabolic phenotype of skeletal muscle in early critical illness

No commercial use is permitted unless otherwise expressly granted.ZAP was funded by the National Institute of Health Research (UK). Additional funding has been received from the European Society of Intensive Care Medicine, Guy’s & St Thomas’ and King’s College London NIHR Comprehensive Biomedical Research Centre (BRC) and the Whittington Hospital NHS Trust. SDH received support from the Research Councils UK. NH received funding from the NIHR Clinical Research Facility and BRC at Guy’s and St Thomas’ NHS Foundation Trust (GSTT) and King’s College London. HEM was funded by University College London and UCLH BRC. The Clinical Phenotyping Centre is supported by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Imperial College Healthcare NHS Trust and Imperial College London. MJWM is grateful to the Wellcome Trust for support in the form of a Postdoctoral Training Fellowship for part of this work. YP is grateful to Merz Pharmaceuticals for support in the form of a training fellowship award

Atrioventricular and interventricular delay optimization in cardiac resynchronization therapy: physiological principles and overview of available methods

In this review, the physiological rationale for atrioventricular and interventricular delay optimization of cardiac resynchronization therapy is discussed including the influence of exercise and long-term cardiac resynchronization therapy. The broad spectrum of both invasive and non-invasive optimization methods is reviewed with critical appraisal of the literature. Although the spectrum of both invasive and non-invasive optimization methods is broad, no single method can be recommend for standard practice as large-scale studies using hard endpoints are lacking. Current efforts mainly investigate optimization during resting conditions; however, there is a need to develop automated algorithms to implement dynamic optimization in order to adapt to physiological alterations during exercise and after anatomical remodeling

Structural determinants of microtubule minus end preference in CAMSAP CKK domains

CAMSAP/Patronins regulate microtubule minus-end dynamics. Their end specificity is mediated by their CKK domains, which we proposed recognise specific tubulin conformations found at minus ends. To critically test this idea, we compared the human CAMSAP1 CKK domain (HsCKK) with a CKK domain from Naegleria gruberi (NgCKK), which lacks minus-end specificity. Here we report near-atomic cryo-electron microscopy structures of HsCKK- and NgCKK-microtubule complexes, which show that these CKK domains share the same protein fold, bind at the intradimer interprotofilament tubulin junction, but exhibit different footprints on microtubules. NMR experiments show that both HsCKK and NgCKK are remarkably rigid. However, whereas NgCKK binding does not alter the microtubule architecture, HsCKK remodels its microtubule interaction site and changes the underlying polymer structure because the tubulin lattice conformation is not optimal for its binding. Thus, in contrast to many MAPs, the HsCKK domain can differentiate subtly specific tubulin conformations to enable microtubule minus-end recognition

2016 ESC Guidelines for the diagnosis and treatment of acute and chronic heart failure: The Task Force for the diagnosis and treatment of acute and chronic heart failure of the European Society of Cardiology (ESC). Developed with the special contribution of the Heart Failure Association (HFA) of the ESC

2016 ESC on Acute and Chronic H

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion