The variational Poisson cohomology

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the two Hamiltonian operators. In the first part of the paper we explain how to introduce various cohomology complexes, including Lie superalgebra and Poisson cohomology complexes, and basic and reduced Lie conformal algebra and Poisson vertex algebra cohomology complexes, by making use of the corresponding universal Lie superalebra or Lie conformal superalgebra. The most relevant are certain subcomplexes of the basic and reduced Poisson vertex algebra cohomology complexes, which we identify (non-canonically) with the generalized de Rham complex and the generalized variational complex. In the second part of the paper we compute the cohomology of the generalized de Rham complex, and, via a detailed study of the long exact sequence, we compute the cohomology of the generalized variational complex for any quasiconstant coefficient Hamiltonian operator with invertible leading coefficient. For the latter we use some differential linear algebra developed in the Appendix.Comment: 130 pages, revised version with minor changes following the referee's suggestion

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

Sustainable Triazine-Based Dehydro-Condensation Agents for Amide Synthesis

Conventional methods employed today for the synthesis of amides often lack of economic and environmental sustainability. Triazine-derived quaternary ammonium salts, e.g., 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholinium chloride (DMTMM(Cl)), emerged as promising dehydro-condensation agents for amide synthesis, although suffering of limited stability and high costs. In the present work, a simple protocol for the synthesis of amides mediated by 2-chloro-4,6-dimethoxy-1,3,5-triazine (CDMT) and a tert-amine has been described and data are compared to DMTMM(Cl) and other CDMT-derived quaternary ammonium salts (DMT-Ams(X), X: Cl- or ClO4-). Different tert-amines (Ams) were tested for the synthesis of various DMT-Ams(Cl), but only DMTMM(Cl) could be isolated and employed for dehydro-condensation reactions, while all CDMT/tert-amine systems tested were efficient as dehydro-condensation agents. Interestingly, in best reaction conditions, CDMT and 1,4-dimethylpiperazine gave N-phenethyl benzamide in 93% yield in 15 min, with up to half the amount of tert-amine consumption. The efficiency of CDMT/tert-amine was further compared to more stable triazine quaternary ammonium salts having a perchlorate counter anion (DMT-Ams(ClO4)). Overall CDMT/tert-amine systems appear to be a viable and more economical alternative to most dehydro-condensation agents employed today

Vertex Operator Superalgebras and Odd Trace Functions

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call `odd trace functions'. We examine the case of the N=1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.Comment: 13 pages, 0 figures. To appear in Conference Proceedings `Advances in Lie Superalgebras

Implications of Halo Inside-out Growth on the X-Ray Properties of Nearby Galaxy Systems within the Preheating Scenario

We present an entirely analytic model for a preheated, polytropic intergalactic medium in hydrostatic equilibrium within a NFW dark halo potential in which the evolution of the halo structure between major merger events proceeds inside-out by accretion. This model is used to explain, within a standard $\Lambda$CDM cosmogony, the observed X-ray properties of nearby relaxed, non-cooling flow groups and clusters of galaxies. We find that our preferred solution to the equilibrium equations produces scaling relations in excellent agreement with observations, while simultaneously accounting for the typical structural characteristics of the distribution of the diffuse baryons. In the class of preheating models, ours stands out because it offers a unified description of the intrahalo medium for galaxy systems with total masses above \sm 2\times 10^{13}\msun, does not produce baryonic configurations with large isentropic cores, and reproduces faithfully the observed behavior of the gas entropy at large radii. All this is achieved with a moderate level of energy injection of about half a keV, which can be easily accommodated within the limits of the total energy released by the most commonly invoked feedback mechanisms, as well as with a polytropic index of 1.2, consistent with both many observational determinations and predictions from high-resolution gas-dynamical simulations of non-cooling flow clusters. More interestingly, our scheme offers a physical motivation for the adoption of this specific value of the polytropic index, as it is the one that best ensures the conservation after halo virialization of the balance between the total specific energies of the gas and dark matter components for the full range of masses investigated.Comment: 18 pages, 11 figures, accepted for publication in the Astrophysical Journa

Reconstruction of Network Evolutionary History from Extant Network Topology and Duplication History

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.Comment: 15 pages, 5 figures, submitted to ISBRA 201

Estimating spring terminus submarine melt rates at a greenlandic tidewater glacier using satellite imagery

Oceanic forcing of the Greenland Ice Sheet is believed to promote widespread thinning at tidewater glaciers, with submarine melting proposed as a potential trigger of increased glacier calving, retreat, and subsequent acceleration. The precise mechanism(s) driving glacier instability, however, remain poorly understood, and while increasing evidence points to the importance of submarine melting, estimates of melt rates are uncertain. Here we estimate submarine melt rate by examining freeboard changes in the seasonal ice tongue of Kangiata Nunaata Sermia (KNS) at the head of Kangersuneq Fjord (KF), southwest Greenland. We calculate melt rates for March and May 2013 by differencing along-fjord surface elevation, derived from high-resolution TanDEM-X digital elevation models (DEMs), in combination with ice velocities derived from offset tracking applied to TerraSAR-X imagery. Estimated steady state melt rates reach up to 1.4 ± 0.5m d-1 near the glacier grounding line, with mean values of up to 0.8 ± 0.3 and 0.7 ± 0.3m d-1 for the eastern and western parts of the ice tongue, respectively. Melt rates decrease with distance from the ice front and vary across the fjord. This methodology reveals spatio-temporal variations in submarine melt rates (SMRs) at tidewater glaciers which develop floating termini, and can be used to improve our understanding of ice-ocean interactions and submarine melting in glacial fjords.Publisher PDFPeer reviewe

Benchmarking and viability assessment of optical packet switching for metro networks

Optical packet switching (OPS) has been proposed as a strong candidate for future metro networks. This paper assesses the viability of an OPS-based ring architecture as proposed within the research project DAVID (Data And Voice Integration on DWDM), funded by the European Commission through the Information Society Technologies (IST) framework. Its feasibility is discussed from a physical-layer point of view, and its limitations in size are explored. Through dimensioning studies, we show that the proposed OPS architecture is competitive with respect to alternative metropolitan area network (MAN) approaches, including synchronous digital hierarchy, resilient packet rings (RPR), and star-based Ethernet. Finally, the proposed OPS architectures are discussed from a logical performance point of view, and a high-quality scheduling algorithm to control the packet-switching operations in the rings is explained

Noninvasive Brain Stimulation and Noninvasive Peripheral Stimulation for Neglect Syndrome Following Acquired Brain Injury

OBJECTIVE: Hemispatial neglect is a frequent condition usually following nondominant hemispheric brain injury. It strongly affects rehabilitation strategies and everyday life activities. It is associated with behavioral and cognitive disability with a strong impact on patient's life. METHODS: We reviewed the published literature on the use of noninvasive brain stimulation, including repetitive transcranial magnetic stimulation (rTMS) and transcranial direct current stimulation (tDCS), and of noninvasive peripheral muscle stimulation, as therapeutic strategies for rehabilitation of neglect after acquired brain injury, such as in stroke or in traumatic injuries. The studies were grouped as controlled or uncontrolled studies in each stimulation techniques. RESULTS: Thirty-four studies were identified and 16 on rTMS, 10 on tDCS, and 8 on vibration. All studies were conducted in adult patients who suffered a stroke, except for one that was conducted in a patient suffering traumatic acquired brain injury and another that was conducted in a patient with brain tumor. In spite of significant variability in treatment protocols, patients' features and assessment of neglect, improvement was reported in almost all studies with no side-effects. CONCLUSIONS: Noninvasive brain stimulation and neuromuscular vibration are promising therapeutic neuromodulatory approaches for neglect. Further randomized-controlled studies are needed to corroborate their effectiveness as separate and combined techniques

Greenland ice sheet annual motion insensitive to spatial variations in subglacial hydraulic structure

We present ice velocities observed with global positioning systems and TerraSAR-X/TanDEM-Xin a land-terminating region of the southwest Greenland ice sheet (GrIS) during the melt year 2012–2013, toexamine the spatial pattern of seasonal and annual ice motion. We find that while spatial variability in theconfiguration of the subglacial drainage system controls ice motion at short timescales, this configurationhas negligible impact on the spatial pattern of the proportion of annual motion which occurs duringsummer. While absolute annual velocities vary substantially, the proportional contribution of summermotion to annual motion does not. These observations suggest that in land-terminating margins of the GrIS,subglacial hydrology does not significantly influence spatial variations in net summer speedup.Furthermore, our findings imply that not every feature of the subglacial drainage system needs to beresolved in ice sheet models