Pruning Algorithms for Pretropisms of Newton Polytopes

Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton polytopes. We prefer exact arithmetic not only because of the exact input and the degrees of the output, but because of the often unpredictable growth of the coordinates in the face normals, even for polytopes in generic position. We provide experimental results with our preliminary implementation in Sage that compare favorably with the pruning method that relies only on cone intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning, accepted for presentation at Computer Algebra in Scientific Computing, CASC 201

Computing Tropical Varieties

The tropical variety of a $d$-dimensional prime ideal in a polynomial ring with complex coefficients is a pure $d$-dimensional polyhedral fan. This fan is shown to be connected in codimension one. We present algorithmic tools for computing the tropical variety, and we discuss our implementation of these tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have a finite tropical basis, and a sharp lower bound is given for the size of a tropical basis for an ideal of linear forms.Comment: 22 pages, 2 figure

Curie: Constraining Solar System Bombardment Using In Situ Radiometric Dating

The Curie mission would constrain the existence of the putative cataclysm by determining the age of samples directly sourced from the impact melt sheet of a major pre-Imbrium lunar basin. The measurements would also enable further understanding of lunar evolution by characterizing new lunar lithologies far from the Apollo and Luna landing sites, including the very low-Ti basalts in Mare Crisium and potential olivine rich lithologies in the margins of both Mare Nectaris and Mars Crisium. Equipped with a mass spectrometer and a LIBS, Curie would also be well-placed to survey volatile components of the lunar regolith, including surface-bound hydrogen

Local helioseismology of sunspot regions: comparison of ring-diagram and time-distance results

Local helioseismology provides unique information about the subsurface structure and dynamics of sunspots and active regions. However, because of complexity of sunspot regions local helioseismology diagnostics require careful analysis of systematic uncertainties and physical interpretation of the inversion results. We present new results of comparison of the ring-diagram analysis and time-distance helioseismology for active region NOAA 9787, for which a previous comparison showed significant differences in the subsurface sound-speed structure, and discuss systematic uncertainties of the measurements and inversions. Our results show that both the ring-diagram and time-distance techniques give qualitatively similar results, revealing a characteristic two-layer seismic sound-speed structure consistent with the results for other active regions. However, a quantitative comparison of the inversion results is not straightforward. It must take into account differences in the sensitivity, spatial resolution and the averaging kernels. In particular, because of the acoustic power suppression, the contribution of the sunspot seismic structure to the ring-diagram signal can be substantially reduced. We show that taking into account this effect reduces the difference in the depth of transition between the negative and positive sound-speed variations inferred by these methods. Further detailed analysis of the sensitivity, resolution and averaging properties of the local helioseismology methods is necessary for consolidation of the inversion results. It seems to be important that both methods indicate that the seismic structure of sunspots is rather deep and extends to at least 20 Mm below the surface, putting constraints on theoretical models of sunspots.Comment: 10 pages, 10 figures, submitted to Journal of Physics: Conference Series (JPCS) GONG 2010 - SoHO 24 "A new era of seismology of the Sun and solar-like stars", June 27 - July 2, 2010 Aix-en-Provence, Franc

The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO)

The Helioseismic and Magnetic Imager (HMI) instrument and investigation as a part of the NASA Solar Dynamics Observatory (SDO) is designed to study convection-zone dynamics and the solar dynamo, the origin and evolution of sunspots, active regions, and complexes of activity, the sources and drivers of solar magnetic activity and disturbances, links between the internal processes and dynamics of the corona and heliosphere, and precursors of solar disturbances for space-weather forecasts. A brief overview of the instrument, investigation objectives, and standard data products is presented

VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager

In this paper we describe in detail the implementation and main properties of a new inversion code for the polarized radiative transfer equation (VFISV: Very Fast inversion of the Stokes vector). VFISV will routinely analyze pipeline data from the Helioseismic and Magnetic Imager (HMI) on-board of the Solar Dynamics Observatory (SDO). It will provide full-disk maps (4096$\times$4096 pixels) of the magnetic field vector on the Solar Photosphere every 10 minutes. For this reason VFISV is optimized to achieve an inversion speed that will allow it to invert 16 million pixels every 10 minutes with a modest number (approx. 50) of CPUs. Here we focus on describing a number of important details, simplifications and tweaks that have allowed us to significantly speed up the inversion process. We also give details on tests performed with data from the spectropolarimeter on-board of the Hinode spacecraft.Comment: 23 pages, 9 figures (2 color). Submitted for publication to Solar Physic

Progression of Lung Disease in Preschool Patients with Cystic Fibrosis

RATIONALE: Implementation of intervention strategies to prevent lung damage in early cystic fibrosis (CF) requires objective outcome measures that capture and track lung disease. OBJECTIVES: To define the utility of the Lung Clearance Index (LCI), measured by multiple breath washout, as a means to track disease progression in preschool children with CF. METHODS: Children with CF between the ages of 2.5 and 6 years with a confirmed diagnosis of CF and age-matched healthy control subjects were enrolled at three North American CF centers. Multiple breath washout tests were performed at baseline, 1, 3, 6, and 12 months to mimic time points chosen in clinical care and interventional trials; spirometry was also conducted. A generalized linear mixed-effects model was used to distinguish LCI changes associated with normal growth and development (i.e., healthy children) from the progression of CF lung disease. MEASUREMENTS AND MAIN RESULTS: Data were collected on 156 participants with 800 LCI measurements. Although both LCI and spirometry discriminated health from disease, only the LCI identified significant deterioration of lung function in CF over time. The LCI worsened during cough episodes and pulmonary exacerbations, whereas similar symptoms in healthy children were not associated with increased LCI values. CONCLUSIONS: LCI is a useful marker to track early disease progression and may serve as a tool to guide therapies in young patients with CF

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Helioseismology of Sunspots: A Case Study of NOAA Region 9787

Various methods of helioseismology are used to study the subsurface properties of the sunspot in NOAA Active Region 9787. This sunspot was chosen because it is axisymmetric, shows little evolution during 20-28 January 2002, and was observed continuously by the MDI/SOHO instrument. (...) Wave travel times and mode frequencies are affected by the sunspot. In most cases, wave packets that propagate through the sunspot have reduced travel times. At short travel distances, however, the sign of the travel-time shifts appears to depend sensitively on how the data are processed and, in particular, on filtering in frequency-wavenumber space. We carry out two linear inversions for wave speed: one using travel-times and phase-speed filters and the other one using mode frequencies from ring analysis. These two inversions give subsurface wave-speed profiles with opposite signs and different amplitudes. (...) From this study of AR9787, we conclude that we are currently unable to provide a unified description of the subsurface structure and dynamics of the sunspot.Comment: 28 pages, 18 figure