Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus

The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a torus. In the case of the four-graviton amplitude, each of these modular functions is a multiple sum associated with a Feynman diagram for a free massless scalar field on the torus. The lines in each diagram join pairs of vertex insertion points and the number of lines defines its weight $w$, which corresponds to its order in the low energy expansion. Previous results concerning the low energy expansion of the genus-one four-graviton amplitude led to a number of conjectured relations between modular functions of a given $w$, but different numbers of loops $\le w-1$. In this paper we shall prove the simplest of these conjectured relations, namely the one that arises at weight $w=4$ and expresses the three-loop modular function $D_4$ in terms of modular functions with one and two loops. As a byproduct, we prove three intriguing new holomorphic modular identities.Comment: 38 pages, 9 figures, in version 2: Appendix D added and corrections made in section

Modular Graph Functions

In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices. These functions depend on a coordinate, $\zeta$, on the elliptic curve and reduce to modular graph functions when $\zeta$ is set equal to $1$. We demonstrate that these single-valued elliptic multiple polylogarithms are linear combinations of multiple polylogarithms, and that modular graph functions are sums of single-valued elliptic multiple polylogarithms evaluated at the identity of the elliptic curve, in both cases with rational coefficients. This insight suggests the many interrelations between modular graph functions (a few of which were established in earlier papers) may be obtained as a consequence of identities involving multiple polylogarithms, and explains an earlier observation that the coefficients of the Laurent polynomial at the cusp are given by rational numbers times single-valued multiple zeta values.Comment: 42 pages, significant clarifications added in section 5, minor typos corrected, and references added in version

Accurate molecular imaging of small animals taking into account animal models, handling, anaesthesia, quality control and imaging system performance

Small-animal imaging has become an important technique for the development of new radiotracers, drugs and therapies. Many laboratories have now a combination of different small-animal imaging systems, which are being used by biologists, pharmacists, medical doctors and physicists. The aim of this paper is to give an overview of the important factors in the design of a small animal, nuclear medicine and imaging experiment. Different experts summarize one specific aspect important for a good design of a small-animal experiment

Effective homology and periods of complex projective hypersurfaces

We provide an algorithm to compute an effective description of the homology of complex projective hypersurfaces relying on Picard-Lefschetz theory. Next, we use this description to compute high-precision numerical approximations of the periods of the hypersurface. This is an improvement over existing algorithms as this new method allows for the computation of periods of smooth quartic surfaces in an hour on a laptop, which could not be attained with previous methods. The general theory presented in this paper can be generalised to varieties other than just hypersurfaces, such as elliptic fibrations as showcased on an example coming from Feynman graphs. Our algorithm comes with a SageMath implementation.Comment: 35 page

Crystal structures of the Bacillus licheniformis BS3 class A beta-lactamase and of the acyl-enzyme adduct formed with cefoxitin

The Bacillus licheniformis BS3 beta-lactamase catalyzes the hydrolysis of the beta-lactam ring of penicillins, cephalosporins, and related compounds. The production of beta-lactamases is the most common and thoroughly studied cause of antibiotic resistance. Although they escape the hydrolytic activity of the prototypical Staphylococcus aureus beta-lactamase, many cephems are good substrates for a large number of beta-lactamases. However, the introduction of a 7alpha-methoxy substituent, as in cefoxitin, extends their antibacterial spectrum to many cephalosporin-resistant Gram-negative bacteria. The 7alphamethoxy group selectively reduces the hydrolytic action of many beta-lactamases without having a significant effect on the affinity for the target enzymes, the membrane penicillin-binding proteins. We report here the crystallographic structures of the BS3 enzyme and its acyl-enzyme adduct with cefoxitin at 1.7 Angstrom resolution. The comparison of the two structures reveals a covalent acyl-enzyme adduct with perturbed active site geometry, involving a different conformation of the Omega-loop that bears the essential catalytic Glu166 residue. This deformation is induced by the cefoxitin side chain whose position is constrained by the presence of the alpha-methoxy group. The hydrolytic water molecule is also removed from the active site by the 7beta-carbonyl of the acyl intermediate. In light of the interactions and steric hindrances in the active site of the structure of the BS3-cefoxitin acyl-enzyme adduct, the crucial role of the conserved Asn132 residue is confirmed and a better understanding of the kinetic results emerges

EuReCa ONE—27 Nations, ONE Europe, ONE Registry A prospective one month analysis of out-of-hospital cardiac arrest outcomes in 27 countries in Europe

AbstractIntroductionThe aim of the EuReCa ONE study was to determine the incidence, process, and outcome for out of hospital cardiac arrest (OHCA) throughout Europe.MethodsThis was an international, prospective, multi-centre one-month study. Patients who suffered an OHCA during October 2014 who were attended and/or treated by an Emergency Medical Service (EMS) were eligible for inclusion in the study. Data were extracted from national, regional or local registries.ResultsData on 10,682 confirmed OHCAs from 248 regions in 27 countries, covering an estimated population of 174 million. In 7146 (66%) cases, CPR was started by a bystander or by the EMS. The incidence of CPR attempts ranged from 19.0 to 104.0 per 100,000 population per year. 1735 had ROSC on arrival at hospital (25.2%), Overall, 662/6414 (10.3%) in all cases with CPR attempted survived for at least 30 days or to hospital discharge.ConclusionThe results of EuReCa ONE highlight that OHCA is still a major public health problem accounting for a substantial number of deaths in Europe.EuReCa ONE very clearly demonstrates marked differences in the processes for data collection and reported outcomes following OHCA all over Europe. Using these data and analyses, different countries, regions, systems, and concepts can benchmark themselves and may learn from each other to further improve survival following one of our major health care events

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016

U.S. foreign policy in the Caucasus and Central Asia : pipeline politics and the national interest

This thesis examines the post-Cold War foreign policy of the United States in the Caucasus and Central Asia from a theoretical and practical view. It investigates how U.S. policies towards specific countries in the region have affected the region as a whole. Specifically, three case studies are used to explore the geopolitical implications of pipeline politics in Kazakstan, Azerbaljan, and Turkmenistan. This study concludes with specific options and recommendations for U.S. foreign policy makers to enhance and enlarge U.S. influence in the Caucasus and Central Asiahttp://archive.org/details/usforeignpolicyi00vanhLieutenant Commander, United States NavyApproved for public release; distribution is unlimited

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Effective homology and periods of complex projective hypersurfaces

35 pagesWe provide an algorithm to compute an effective description of the homology of complex projective hypersurfaces relying on Picard-Lefschetz theory. Next, we use this description to compute high-precision numerical approximations of the periods of the hypersurface. This is an improvement over existing algorithms as this new method allows for the computation of periods of smooth quartic surfaces in an hour on a laptop, which could not be attained with previous methods. The general theory presented in this paper can be generalised to varieties other than just hypersurfaces, such as elliptic fibrations as showcased on an example coming from Feynman graphs. Our algorithm comes with a SageMath implementation