scholarly journals The nodal count {0,1,2,3,…} implies the graph is a tree

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120504 ◽  
Author(s):  
Ram Band
Keyword(s):  
Metric Graphs ◽  
Oscillation Theorem ◽  
Nodal Count ◽  
Metric Graph ◽  
Converse Theorems ◽  
Link Type ◽  
Tree Graphs ◽  
Metric Tree ◽  
Magnetic Stability ◽  
Almost All

Sturm's oscillation theorem states that the n th eigenfunction of a Sturm–Liouville operator on the interval has n −1 zeros (nodes) (Sturm 1836 J. Math. Pures Appl. 1 , 106–186; 373–444). This result was generalized for all metric tree graphs (Pokornyĭ et al. 1996 Mat. Zametki 60 , 468–470 ( doi:10.1007/BF02320380 ); Schapotschnikow 2006 Waves Random Complex Media 16 , 167–178 ( doi:10.1080/1745530600702535 )) and an analogous theorem was proved for discrete tree graphs (Berkolaiko 2007 Commun. Math. Phys. 278 , 803–819 ( doi:10.1007/S00220-007-0391-3 ); Dhar & Ramaswamy 1985 Phys. Rev. Lett. 54 , 1346–1349 ( doi:10.1103/PhysRevLett.54.1346 ); Fiedler 1975 Czechoslovak Math. J. 25 , 607–618). We prove the converse theorems for both discrete and metric graphs. Namely if for all n , the n th eigenfunction of the graph has n −1 zeros, then the graph is a tree. Our proofs use a recently obtained connection between the graph's nodal count and the magnetic stability of its eigenvalues (Berkolaiko 2013 Anal. PDE 6 , 1213–1233 ( doi:10.2140/apde.2013.6.1213 ); Berkolaiko & Weyand 2014 Phil. Trans. R. Soc. A 372 , 20120522 ( doi:10.1098/rsta.2012.0522 ); Colin de Verdière 2013 Anal. PDE 6 , 1235–1242 ( doi:10.2140/apde.2013.6.1235 )). In the course of the proof, we show that it is not possible for all (or even almost all, in the metric case) the eigenvalues to exhibit a diamagnetic behaviour. In addition, we develop a notion of ‘discretized’ versions of a metric graph and prove that their nodal counts are related to those of the metric graph.

In vitro effectiveness of biapenem against IMP-producing Enterobacteriaceae

2021 ◽  
Vol 70 (10) ◽  
Author(s):  
Kazuyoshi Gotoh ◽  
Makoto Miyoshi ◽  
I Putu Bayu Mayura ◽  
Koji Iio ◽  
Osamu Matsushita ◽  
...  
Keyword(s):  
Therapeutic Option ◽  
Small Data ◽  
Limited Data ◽  
Data Set ◽  
Content Type ◽  
Link Type ◽  
Almost All ◽  
New Treatments ◽  
Time Kill

The options available for treating infections with carbapenemase-producing Enterobacteriaceae (CPE) are limited; with the increasing threat of these infections, new treatments are urgently needed. Biapenem (BIPM) is a carbapenem, and limited data confirming its in vitro killing effect against CPE are available. In this study, we examined the minimum inhibitory concentrations (MICs) and minimum bactericidal concentrations (MBCs) of BIPM for 14 IMP-1-producing Enterobacteriaceae strains isolated from the Okayama region in Japan. The MICs against almost all the isolates were lower than 0.5 µg ml−1, indicating susceptibility to BIPM, while approximately half of the isolates were confirmed to be bacteriostatic to BIPM. However, initial killing to a 99.9 % reduction was observed in seven out of eight strains in a time–kill assay. Despite the small data set, we concluded that the in vitro efficacy of BIPM suggests that the drug could be a new therapeutic option against infection with IMP-producing CPE.

New workflow for classification of genetic variants’ pathogenicity applied to hereditary recurrent fevers by the International Study Group for Systemic Autoinflammatory Diseases (INSAID)

2018 ◽  
Vol 55 (8) ◽  
pp. 530-537 ◽  
Author(s):  
Marielle E Van Gijn ◽  
Isabella Ceccherini ◽  
Yael Shinar ◽  
Ellen C Carbo ◽  
Mariska Slofstra ◽  
...  
Keyword(s):  
Clinical Significance ◽  
Clinical Symptoms ◽  
Inflammatory Diseases ◽  
International Study ◽  
Biological Drugs ◽  
Link Type ◽  
Expert Opinions ◽  
Mutational Hotspots ◽  
Almost All

BackgroundHereditary recurrent fevers (HRFs) are rare inflammatory diseases sharing similar clinical symptoms and effectively treated with anti-inflammatory biological drugs. Accurate diagnosis of HRF relies heavily on genetic testing.ObjectivesThis study aimed to obtain an experts’ consensus on the clinical significance of gene variants in four well-known HRF genes: MEFV, TNFRSF1A, NLRP3 and MVK.MethodsWe configured a MOLGENIS web platform to share and analyse pathogenicity classifications of the variants and to manage a consensus-based classification process. Four experts in HRF genetics submitted independent classifications of 858 variants. Classifications were driven to consensus by recruiting four more expert opinions and by targeting discordant classifications in five iterative rounds.ResultsConsensus classification was reached for 804/858 variants (94%). None of the unsolved variants (6%) remained with opposite classifications (eg, pathogenic vs benign). New mutational hotspots were found in all genes. We noted a lower pathogenic variant load and a higher fraction of variants with unknown or unsolved clinical significance in the MEFV gene.ConclusionApplying a consensus-driven process on the pathogenicity assessment of experts yielded rapid classification of almost all variants of four HRF genes. The high-throughput database will profoundly assist clinicians and geneticists in the diagnosis of HRFs. The configured MOLGENIS platform and consensus evolution protocol are usable for assembly of other variant pathogenicity databases. The MOLGENIS software is available for reuse at http://github.com/molgenis/molgenis; the specific HRF configuration is available at http://molgenis.org/said/. The HRF pathogenicity classifications will be published on the INFEVERS database at https://fmf.igh.cnrs.fr/ISSAID/infevers/.

scholarly journals Monte Carlo sampling processes and incentive compatible allocations in large economies

2020 ◽  
Author(s):  
Peter J. Hammond ◽  
Lei Qiao ◽  
Yeneng Sun
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Incentive Compatibility ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Econ Theory ◽  
Monte Carlo Sampling ◽  
Link Type ◽  
Stochastic Framework ◽  
Almost All

Abstract Monte Carlo simulation is used in Hammond and Sun (Econ Theory 36:303–325, 2008. 10.1007/s00199-007-0279-7) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This leads to a necessary and sufficient condition for the classical law of large numbers to hold in a general Hilbert space. Applying this analysis to large economies with asymmetric information shows that the conflict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, following some similar results in McLean and Postlewaite (Econometrica 70:2421–2453, 2002) and Sun and Yannelis (J Econ Theory 134:175–194, 2007. 10.1016/j.jet.2006.03.001).

scholarly journals EMBEDDING OF METRIC GRAPHS ON HYPERBOLIC SURFACES

2019 ◽  
Vol 99 (03) ◽  
pp. 508-520
Author(s):  
BIDYUT SANKI
Keyword(s):  
Euler Characteristic ◽  
Isometric Embedding ◽  
Hyperbolic Surface ◽  
Hyperbolic Surfaces ◽  
Metric Graphs ◽  
Metric Graph ◽  
Complementary Region

An embedding of a metric graph $(G,d)$ on a closed hyperbolic surface is essential if each complementary region has a negative Euler characteristic. We show, by construction, that given any metric graph, its metric can be rescaled so that it admits an essential and isometric embedding on a closed hyperbolic surface. The essential genus $g_{e}(G)$ of $(G,d)$ is the lowest genus of a surface on which such an embedding is possible. We establish a formula to compute $g_{e}(G)$ and show that, for every integer $g\geq g_{e}(G)$ , there is an embedding of $(G,d)$ (possibly after a rescaling of $d$ ) on a surface of genus $g$ . Next, we study minimal embeddings where each complementary region has Euler characteristic $-1$ . The maximum essential genus $g_{e}^{\max }(G)$ of $(G,d)$ is the largest genus of a surface on which the graph is minimally embedded. We describe a method for an essential embedding of $(G,d)$ , where $g_{e}(G)$ and $g_{e}^{\max }(G)$ are realised.

scholarly journals A metric graph satisfying w41=1$w_4^1 = 1$ that cannot be lifted to a curve satisfying dim⁡ (W41)=1$\dim \;(W_4^1 ) = 1$

2016 ◽  
Vol 14 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marc Coppens
Keyword(s):  
Linear Systems ◽  
Harmonic Morphism ◽  
Metric Graphs ◽  
Clifford Index ◽  
Special Linear ◽  
Metric Graph ◽  
Index 2

AbstractFor all integers g ≥ 6 we prove the existence of a metric graph G with $w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

scholarly journals CharKey: An electronic identification key for wood charcoals of French Guiana

IAWA Journal ◽  
2019 ◽  
Vol 40 (1) ◽  
pp. 75-S20 ◽  
Author(s):  
Stéphanie C. Bodin ◽  
Rita Scheel-Ybert ◽  
Jacques Beauchêne ◽  
Jean-François Molino ◽  
Laurent Bremond
Keyword(s):  
French Guiana ◽  
Wood Anatomy ◽  
Identification Key ◽  
Anatomical Features ◽  
Link Type ◽  
Taxonomic Description ◽  
Computer Aided ◽  
Microscopic Features ◽  
Tropical Woods ◽  
Almost All

ABSTRACT Tropical tree floras are highly diverse and many genera and species share similar anatomical patterns, making the identification of tropical wood charcoal very difficult. Appropriate tools to characterize charcoal anatomy are thus needed to facilitate and improve identification in such species-rich areas. This paper presents the first computer-aided identification key designed for charcoals from French Guiana, based on the wood anatomy of 507 species belonging to 274 genera and 71 families, which covers respectively 28%, 67% and 86% of the tree species, genera and families currently listed in this part of Amazonia. Species of the same genus are recorded together except those described under a synonym genus in Détienne et al. (1982) that were kept separately. As a result, the key contains 289 ‘items’ and mostly aims to identify charcoals at the genus level. It records 26 anatomical features leading to 112 feature states, almost all of which are illustrated by SEM photographs of charcoal. The descriptions were mostly taken from Détienne et al.’s guidebook on tropical woods of French Guiana (1982) and follow the IAWA list of microscopic features for hardwood identification (Wheeler et al. 1989). Some adjustments were made to a few features and those that are unrelated to charcoal identification were excluded. The whole tool, named CharKey, contains the key itself and the associated database including photographs. It can be downloaded on Figshare at https://figshare.com/s/d7d40060b53d2ad60389 (doi: 10.6084/m9.figshare.6396005). CharKey is accessible using the free software Xper2, specifically conceived for taxonomic description and computer aided-identification.

scholarly journals Carbon footprint of fertilizer imports to the East African Bloc and policy recommendations for decarbonization

2020 ◽  
Vol 3 ◽  
pp. 21
Author(s):  
Stella Kabiri
Keyword(s):  
Carbon Footprint ◽  
Calcium Nitrate ◽  
Freight Transportation ◽  
Synthesis Process ◽  
Transport Sector ◽  
East African ◽  
Community Needs ◽  
Link Type ◽  
N Fertilizers ◽  
Almost All

Background: Almost all nitrogenous (N) fertilizers are fixed on an enormous scale using the Haber-Bosch ammonia synthesis process via a reaction of Nitrogen with hydrogen in the presence of a catalyst. This process is a leading global polluter, emitting 830 megatons of CO2 to the atmosphere annually. On the other hand, the global transport sector emits 7.5 gigatons of CO2 yet the fraction of emissions from freight transportation of N fertilizers from exporting countries to the East African (EA) Bloc is not known. This study examined the carbon footprint from freight transportation of N fertilizers. The findings are useful in the regions’ nationally determined contributions (NDCs) as per the Paris Agreement of December 2015 regarding downsizing emissions from the transport sector. Methods: The study area included five EA Community (EAC) countries namely, Kenya, Uganda, Tanzania, Rwanda and Burundi. Statistics of fertilizers were obtained from https://africafertilizer.org/. The carbon footprint calculator (CFC) for fertilizer production (obtained from https://www.fertilizerseurope.com/), certified by the Carbon Trust Standard, was used. Results: Over 93% of fertilizers imported to the EA Bloc are N fertilizers, leaving a carbon footprint of 4.9 megatons CO2-eq. Of these emissions, 1.1 megatons CO2-eq were contributed by imports from Saudi Arabia and 0.8 megatons CO2-eq from China. The ‘dirtiest’ of N fertilizers that accounted for the highest carbon footprint on the EA bloc were urea ammonium nitrate, calcium nitrate, nitrophosphates and ammonium sulphate. Conclusions: Every metric ton of N imported results in a carbon footprint of 4.5 metric tons CO2-eq. The Ammonia production process of exporting countries, freight distance, choice and number of N fertilizers imported are significant determinants of greenhouse gas emissions to East Africa’s NDCs. To reach net-zero emissions the EA community needs to invest in new processes, circular economy and decarbonization pathways.

scholarly journals Leaf Peeling method for the wave equation on metric tree graphs

2020 ◽  
Vol 0 (0) ◽  
pp. 1-15 ◽  
Author(s):  
Sergei Avdonin ◽  
◽  
Yuanyuan Zhao ◽  
◽  
Keyword(s):  
Wave Equation ◽  
Tree Graphs ◽  
Metric Tree

scholarly journals Comment on ‘Are some people suffering as a result of increasing mass exposure of the public to ultrasound in air?’

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160828 ◽  
Author(s):  
T. G. Leighton
Keyword(s):  
Human Factors ◽  
The Public ◽  
Link Type ◽  
Small Set ◽  
Almost All

A number of queries regarding the paper ‘Are some people suffering as a result of increasing mass exposure of the public to ultrasound in air?’ (Leighton 2016 Proc. R. Soc. A 472 , 20150624 ( doi:10.1098/rspa.2015.0624 )) have been sent in from readers, almost all based around some or all of a small set of questions. These can be grouped into issues of engineering, human factors and timeliness. Those issues (represented by the most typical wording used in queries) and my responses are summarized in this comment.

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