From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials

We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov–Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans’ theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of the use of this method with both force-free and non-force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the force-free Harris sheet (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for beta=0.05

Nunalleq, Stories from the Village of Our Ancestors:Co-designing a multivocal educational resource based on an archaeological excavation

This work was funded by the UK-based Arts and Humanities Research Council through grants (AH/K006029/1) and (AH/R014523/1), a University of Aberdeen IKEC Award with additional support for travel and subsistence from the University of Dundee, DJCAD Research Committee RS2 project funding. Thank you to the many people who contributed their support, knowledge, feedback, voices and faces throughout the project, this list includes members of the local community, colleagues, specialists, students, and volunteers. If we have missed out any names we apologize but know that your help was appreciated. Jimmy Anaver, John Anderson, Alice Bailey, Kieran Baxter, Pauline Beebe, Ellinor Berggren, Dawn Biddison, Joshua Branstetter, Brendan Body, Lise Bos, Michael Broderick, Sarah Brown, Crystal Carter, Joseph Carter, Lucy Carter, Sally Carter, Ben Charles, Mary Church, Willard Church, Daniele Clementi, Annie Cleveland, Emily Cleveland, Joshua Cleveland, Aron Crowell, Neil Curtis, Angie Demma, Annie Don, Julia Farley, Veronique Forbes, Patti Fredericks, Tricia Gillam, Sean Gleason, Sven Haakanson, Cheryl Heitman, Grace Hill, Diana Hunter, Joel Isaak, Warren Jones, Stephan Jones, Ana Jorge, Solveig Junglas, Melia Knecht, Rick Knecht, Erika Larsen, Paul Ledger, Jonathan Lim Soon, Amber Lincoln, Steve Luke, Francis Lukezic, Eva Malvich, Pauline Matthews, Roy Mark, Edouard Masson-MacLean, Julie Masson-MacLean, Mhairi Maxwell, Chuna Mcintyre, Drew Michael, Amanda Mina, Anna Mossolova, Carl Nicolai Jr, Chris Niskanen, Molly Odell, Tom Paxton, Lauren Phillips, Lucy Qin, Charlie Roberts, Chris Rowe, Rufus Rowe,Chris Rowland, John Rundall, Melissa Shaginoff, Monica Shah, Anna Sloan, Darryl Small Jr, John Smith, Mike Smith, Joey Sparaga, Hannah Strehlau, Dora Strunk, Larissa Strunk, Lonny Strunk, Larry Strunk, Robbie Strunk, Sandra Toloczko, Richard Vanderhoek, the Qanirtuuq Incorporated Board, the Quinhagak Dance Group and the staff at Kuinerrarmiut Elitnaurviat. We also extend our thanks to three anonymous reviewers for their valuable comments on our paper.Peer reviewedPublisher PD

Risk, precaution and science: towards a more constructive policy debate. Talking point on the precautionary principle

Few issues in contemporary risk policy are as momentous or contentious as the precautionary principle. Since it first emerged in German environmental policy, it has been championed by environmentalists and consumer protection groups, and resisted by the industries they oppose (Raffensperger & Tickner, 1999). Various versions of the principle now proliferate across different national and international jurisdictions and policy areas (Fisher, 2002). From a guiding theme in European Commission (EC) environmental policy, it has become a general principle of EC law (CEC, 2000; Vos & Wendler, 2006). Its influence has extended from the regulation of environmental, technological and health risks to the wider governance of science, innovation and trade (O'Riordan & Cameron, 1994)

Ordinary Percolation with Discontinuous Transitions

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a nontrivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here, we provide a simple example of this transition in form of a small-world network consisting of a one-dimensional lattice combined with a hierarchy of long-range bonds that reveals many features of the transition in a mathematically rigorous manner.Comment: RevTex, 5 pages, 4 eps-figs, and Mathematica Notebook as Supplement included. Final version, with several corrections and improvements. For related work, see http://www.physics.emory.edu/faculty/boettcher

The structure of typical clusters in large sparse random configurations

The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution of concentrations of particles in a medium where particles coalesce pairwise as time passes and each particle can only perform a given number of aggregations. Under appropriate assumptions, the concentrations of particles converge as time tends to infinity to some measure which bears a striking resemblance with the distribution of the total population of a Galton-Watson process started from two ancestors. Roughly speaking, the configuration model is a stochastic construction which aims at producing a typical graph on a set of vertices with pre-described degrees. Specifically, one attaches to each vertex a certain number of stubs, and then join pairwise the stubs uniformly at random to create edges between vertices. In this work, we use the configuration model as the stochastic counterpart of Smoluchowski's coagulation equations with limited aggregations. We establish a hydrodynamical type limit theorem for the empirical measure of the shapes of clusters in the configuration model when the number of vertices tends to $\infty$. The limit is given in terms of the distribution of a Galton-Watson process started with two ancestors

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given in full forma

Alterations in the transcriptome and antibiotic susceptibility of Staphylococcus aureus grown in the presence of diclofenac

<p>Abstract</p> <p>Background</p> <p>Diclofenac is a non-steroidal anti-inflammatory drug (NSAID) which has been shown to increase the susceptibility of various bacteria to antimicrobials and demonstrated to have broad antimicrobial activity. This study describes transcriptome alterations in <it>S. aureus </it>strain COL grown with diclofenac and characterizes the effects of this NSAID on antibiotic susceptibility in laboratory, clinical and diclofenac reduced-susceptibility (Dc^RS) <it>S. aureus </it>strains.</p> <p>Methods</p> <p>Transcriptional alterations in response to growth with diclofenac were measured using <it>S. aureus </it>gene expression microarrays and quantitative real-time PCR. Antimicrobial susceptibility was determined by agar diffusion MICs and gradient plate analysis. Ciprofloxacin accumulation was measured by fluorescence spectrophotometry.</p> <p>Results</p> <p>Growth of <it>S. aureus </it>strain COL with 80 μg/ml (0.2 × MIC) of diclofenac resulted in the significant alteration by ≥2-fold of 458 genes. These represented genes encoding proteins for transport and binding, protein and DNA synthesis, and the cell envelope. Notable alterations included the strong down-regulation of antimicrobial efflux pumps including <it>mepRAB </it>and a putative <it>emrAB/qacA</it>-family pump. Diclofenac up-regulated <it>sigB </it>(σ^B), encoding an alternative sigma factor which has been shown to be important for antimicrobial resistance. <it>Staphylococcus aureus </it>microarray metadatabase (SAMMD) analysis further revealed that 46% of genes differentially-expressed with diclofenac are also σ^B-regulated. Diclofenac altered <it>S. aureus </it>susceptibility to multiple antibiotics in a strain-dependent manner. Susceptibility increased for ciprofloxacin, ofloxacin and norfloxacin, decreased for oxacillin and vancomycin, and did not change for tetracycline or chloramphenicol. Mutation to Dc^RSdid not affect susceptibility to the above antibiotics. Reduced ciprofloxacin MICs with diclofenac in strain BB255, were not associated with increased drug accumulation.</p> <p>Conclusions</p> <p>The results of this study suggest that diclofenac influences antibiotic susceptibility in <it>S. aureus</it>, in part, by altering the expression of regulatory and structural genes associated with cell wall biosynthesis/turnover and transport.</p

Anti-angiogenic effect of high doses of ascorbic acid

Pharmaceutical doses of ascorbic acid (AA, vitamin C, or its salts) have been reported to exert anticancer activity in vitro and in vivo. One proposed mechanism involves direct cytotoxicity mediated by accumulation of ascorbic acid radicals and hydrogen peroxide in the extracellular environment of tumor cells. However, therapeutic effects have been reported at concentrations insufficient to induce direct tumor cell death. We hypothesized that AA may exert anti-angiogenic effects. To test this, we expanded endothelial progenitor cells (EPCs) from peripheral blood and assessed, whether or not high dose AA would inhibit EPC ability to migrate, change energy metabolism, and tube formation ability. We also evaluated the effects of high dose AA on angiogenic activities of HUVECs (human umbilical vein endothelial cells) and HUAECs (human umbilical arterial endothelial cells). According to our data, concentrations of AA higher than 100 mg/dl suppressed capillary-like tube formation on Matrigel for all cells tested and the effect was more pronounced for progenitor cells in comparison with mature cells. Co-culture of differentiated endothelial cells with progenitor cells showed that there was incorporation of EPCs in vessels formed by HUVECs and HUAECs. Cell migration was assessed using an in vitro wound healing model. The results of these experiments showed an inverse correlation between AA concentrations relative to both cell migration and gap filling capacity. Suppression of NO (nitric oxide) generation appeared to be one of the mechanisms by which AA mediated angiostatic effects. This study supports further investigation into non-cytotoxic antitumor activities of AA

Alterations In the Transciptome and Antibiotic Susceptibility of \u3ci\u3eStaphylococcus aureus\u3c/i\u3e Grown In the Presence of Diclofenac

Background Diclofenac is a non-steroidal anti-inflammatory drug (NSAID) which has been shown to increase the susceptibility of various bacteria to antimicrobials and demonstrated to have broad antimicrobial activity. This study describes transcriptome alterations in S. aureus strain COL grown with diclofenac and characterizes the effects of this NSAID on antibiotic susceptibility in laboratory, clinical and diclofenac reduced-susceptibility (DcRS) S. aureus strains. Methods Transcriptional alterations in response to growth with diclofenac were measured using S. aureus gene expression microarrays and quantitative real-time PCR. Antimicrobial susceptibility was determined by agar diffusion MICs and gradient plate analysis. Ciprofloxacin accumulation was measured by fluorescence spectrophotometry. Results Growth of S. aureus strain COL with 80 μg/ml (0.2 × MIC) of diclofenac resulted in the significant alteration by ≥2-fold of 458 genes. These represented genes encoding proteins for transport and binding, protein and DNA synthesis, and the cell envelope. Notable alterations included the strong down-regulation of antimicrobial efflux pumps including mepRAB and a putative emrAB/qacA-family pump. Diclofenac up-regulated sigB (σB), encoding an alternative sigma factor which has been shown to be important for antimicrobial resistance. Staphylococcus aureus microarray metadatabase (SAMMD) analysis further revealed that 46% of genes differentially-expressed with diclofenac are also σB-regulated. Diclofenac altered S. aureus susceptibility to multiple antibiotics in a strain-dependent manner. Susceptibility increased for ciprofloxacin, ofloxacin and norfloxacin, decreased for oxacillin and vancomycin, and did not change for tetracycline or chloramphenicol. Mutation to DcRS did not affect susceptibility to the above antibiotics. Reduced ciprofloxacin MICs with diclofenac in strain BB255, were not associated with increased drug accumulation. Conclusions The results of this study suggest that diclofenac influences antibiotic susceptibility in S. aureus, in part, by altering the expression of regulatory and structural genes associated with cell wall biosynthesis/turnover and transport