A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles

We use convex polyhedral cones to study a large class of multivariate meromorphic germs, namely those with linear poles, which naturally arise in various contexts in mathematics and physics. We express such a germ as a sum of a holomorphic germ and a linear combination of special non-holomorphic germs called polar germs. In analyzing the supporting cones -- cones that reflect the pole structure of the polar germs -- we obtain a geometric criterion for the non-holomorphicity of linear combinations of polar germs. This yields the uniqueness of the above sum when required to be supported on a suitable family of cones and assigns a Laurent expansion to the germ. Laurent expansions provide various decompositions of such germs and thereby a uniformized proof of known results on decompositions of rational fractions. These Laurent expansions also yield new concepts on the space of such germs, all of which are independent of the choice of the specific Laurent expansion. These include a generalization of Jeffrey-Kirwan's residue, a filtered residue and a coproduct in the space of such germs. When applied to exponential sums on rational convex polyhedral cones, the filtered residue yields back exponential integrals.Comment: 30 page

Double shuffle relations and renormalization of multiple zeta values

In this paper we present some of the recent progresses in multiple zeta values (MZVs). We review the double shuffle relations for convergent MZVs and summarize generalizations of the sum formula and the decomposition formula of Euler for MZVs. We then discuss how to apply methods borrowed from renormalization in quantum field theory and from pseudodifferential calculus to partially extend the double shuffle relations to divergent MZVs

Enhancement of the influenza A hemagglutinin (HA)-mediated cell-cell fusion and virus entry by the viral neuraminidase (NA).

International audienceBACKGROUND: The major role of the neuraminidase (NA) protein of influenza A virus is related to its sialidase activity, which disrupts the interaction between the envelope hemagglutinin (HA) protein and the sialic acid receptors expressed at the surface of infected cells. This enzymatic activity is known to promote the release and spread of progeny viral particles following their production by infected cells, but a potential role of NA in earlier steps of the viral life cycle has never been clearly demonstrated. In this study we have examined the impact of NA expression on influenza HA-mediated viral membrane fusion and virion infectivity. METHODOLOGY/PRINCIPAL FINDINGS: The role of NA in the early stages of influenza virus replication was examined using a cell-cell fusion assay that mimics HA-mediated membrane fusion, and a virion infectivity assay using HIV-based pseudoparticles expressing influenza HA and/or NA proteins. In the cell-cell fusion assay, which bypasses the endocytocytosis step that is characteristic of influenza virus entry, we found that in proper HA maturation conditions, NA clearly enhanced fusion in a dose-dependent manner. Similarly, expression of NA at the surface of pseudoparticles significantly enhanced virion infectivity. Further experiments using exogenous soluble NA revealed that the most likely mechanism for enhancement of fusion and infectivity by NA was related to desialylation of virion-expressed HA. CONCLUSION/SIGNIFICANCE: The NA protein of influenza A virus is not only required for virion release and spread but also plays a critical role in virion infectivity and HA-mediated membrane fusion

A Large Double-ring Disk around the Taurus M Dwarf J04124068+2438157

Planet formation imprints signatures on the physical structures of disks. In this paper, we present high-resolution ($\sim$50 mas, 8 au) Atacama Large Millimeter/submillimeter Array (ALMA) observations of 1.3 mm dust continuum and CO line emission toward the disk around the M3.5 star 2MASS J04124068+2438157. The dust disk consists only of two narrow rings at radial distances of 0.47 and 0.78 arcsec ($\sim$70 and 116 au), with Gaussian $\sigma$ widths of 5.6 and 8.5 au, respectively. The width of the outer ring is smaller than the estimated pressure scale height by $\sim25\%$, suggesting dust trapping in a radial pressure bump. The dust disk size, set by the location of the outermost ring, is significantly larger (by $3\sigma$) than other disks with similar millimeter luminosity, which can be explained by an early formation of local pressure bump to stop radial drift of millimeter dust grains. After considering the disk's physical structure and accretion properties, we prefer planet--disk interaction over dead zone or photoevaporation models to explain the observed dust disk morphology. We carry out high-contrast imaging at $L'$ band using Keck/NIRC2 to search for potential young planets, but do not identify any source above $5\sigma$. Within the dust gap between the two rings, we reach a contrast level of $\sim$7 mag, constraining the possible planet below $\sim$2--4 $M_{\rm Jup}$. Analyses of the gap/ring properties suggest a $\sim$Saturn mass planet at $\sim$90 au is likely responsible for the formation of the outer ring, which can be potentially revealed with JWST.Comment: 15 pages, 5 figures. Accepted for publication in Ap