Global Euler obstruction and polar invariants

For an affine complex algebraic singular space Y, we define a global Euler obstruction Eu(Y) which extends the Euler-Poincare characteristic of a nonsingular Y. Using Lefschetz pencils, we express Eu(Y) as alternating sum of global polar invariants.Comment: 9 pages, 1 figur

On the class of caustics by reflection

Given any light position S in the complex projective plane P^2 and any algebraic curve C of P^2 (with any kind of singularities), we consider the incident lines coming from S (i.e. the lines containing S) and their reflected lines after reflection off the mirror curve C. The caustic by reflection is the Zariski clusure of the envelope of these reflected lines. We introduce the notion of reflected polar curve and express the class of the caustic by reflection in terms of intersection numbers of C with the reflected polar curve, thanks to a fundamental lemma established in [14]. This approach enables us to get an explicit formula for the class of the caustic by reflection in every case in terms of intersection numbers of the initial curve C.Comment: 21 pages, 1 figur

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

South polar dynamics of the Venusian atmosphere from VIRTIS/Venus Express mapping in the thermal range

We report on measurements of Venus cloud velocities from VIRTIS/Venus Express observations of the south polar region of Venus. Cloud tracking has been performed using a method of automated digital correlation. Tracking has been performed on pairs of monochromatic VIRTIS images selected mainly in the 5 μm window, but also at 1.74, 2.3, 3.93 micrometers. Wind measurements from vector retrievals based on automated feature tracking show high variability, indicating the presence of important transient motions. The time-averaged zonal winds indicate different day and night side regimes. On the day side both the zonal wind component (u) and the meridional one (v) are approximately uniform between 84S and 76S, with u ∼ −40 m/s and v ∼ −10 m/s. On the night side the zonal wind decreases poleward, from a maximum at 76S. The meridional wind is smaller than on the day side and appears to change sign from poleward to equatorward at 76S. The cold collar boundary appears to be a transition region not only for the temperature, but for the winds as well. In this region wave motions are also apparent, with amplitudes on the order of 40 m/s for u′ and 10 m/s for v′

XJ-BP: Express Journey Belief Propagation Decoding for Polar Codes

This paper presents a novel propagation (BP) based decoding algorithm for polar codes. The proposed algorithm facilitates belief propagation by utilizing the specific constituent codes that exist in the factor graph, which results in an express journey (XJ) for belief information to propagate in each decoding iteration. In addition, this XJ-BP decoder employs a novel round-trip message passing scheduling method for the increased efficiency. The proposed method simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP decoding by 90.4%; this enables an energy-efficient hardware implementation of BP decoding in practice.Comment: submitted to GLOBECOMM 201

Winds and cloud morphology in the southern polar region of Venus

Spinning on average 60 times faster than the surface, the atmosphere of Venus is superrotational, a state in which the averaged angular momentum is much greater than that corresponding to co-rotation with the solid globe. The rapid mean flow, which is main- tained by momentum transports in the deep atmo- sphere, presents a puzzle to the atmospheric and plan- etary sciences[1]. After previous missions revealed a bright polar feature at the north pole[9, 10], the Venus Express spacecraft discovered a fast-rotating counter- part at the southern polar region[6], which has been identified as a vortex[2]. The southern polar vortex can be observed at 5.0 μm as a bright, highly vari- able structure which is ∼ 15 K warmer than the sur- rounding air[6]. Although the Venus superrotation has been measured by tracking cloud features at UV and infrared wavelengths[7, 4, 8, 5], the winds in the po- lar region remain poorly constrained. Characterizing the zonal and meridional circulation in this region, as well as their variability, is crucial for understanding the mechanisms that maintain superrotation. In partic- ular, mean zonal winds are necessary to understand the nature of the polar vortex, how it is connected with the general circulation of the atmosphere, and to diagnose momentum transports. Winds at 45 and 65 km can be detected from cloud motion monitoring by the VIRTIS-M subsection on- board the Venus Express (VEX) spacecraft. Our ob- jective is to provide direct wind measurements at cloud tops and in the lower cloud level, in order to help in- terpret the VEX observations concerning the meso- spheric wind regime and temperature fields. In par- ticular, we present direct measurements of the zonal and meridional winds at both altitudes. For this work we selected nadir-pointing, high- spatial resolution VIRTIS data cubes obtained from apocenter in order to minimize the geometric distortion of the polar region. On average these contain lat- itudes extending from the pole to 70S. Since the VIR- TIS field of view is rectangular, lower latitudes are also present but cannot be observed over full latitude circles. Cloud tracking has been performed using the method of digital correlation described in a previous article[3]. VEX orbits were selected so as to have in each one at least one pair of images suitable for track- ing, i.e., with a considerable spatial overlap. Tracking has been performed on pairs of monochromatic im- ages at wavelengths of 1.74 μm, 2.3 μm, 3.93 μm and 5 μm. In the data cubes obtained with longer integration times (3s) the long-wavelength range of the spectrum, above 4.3 μm, is saturated. In those cases we se- lected the 3.93 μm radiance map instead of the one at 5 μm. The monochromatic radiance maps are first ex- tracted from data cubes that have undergone the stan- dard VIRTIS calibration procedures. The maps are then projected onto a polar stereographic grid and the wind retrieval procedure is applied. A total of 20 lat- itude bins, separated by 1 degree were used. For the analysis of transient motions the spatial averaging was done in 72 longitude bins at 5 degree intervals. In order to evaluate the variability over the time scale of one orbit, we have computed the orbital aver- ages, i.e., averages of all measurements coming from one given orbit. These orbital averages are only ap- proximations to temporal averages, since they do not cover one full rotation. The differences between same- orbit averages are apparent in both day and night side averages. Some notable features indicating different day and night side regimes are also apparent in the or- bit averages, and the boundary of the cold collar ap- pears to be a transition latitude. Moreover, the vari- ability that can be observed from orbit to orbit and be- tween series of observations from the same orbit indi- cates that departures from this mean flow are large and a persistent feature of the global circulation