Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

In this paper we present a survey of the joint program with Fabrice Baudoin originated with the paper \cite{BG1}, and continued with the works \cite{BG2}, \cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont and Isidro Munive.Comment: arXiv admin note: substantial text overlap with arXiv:1101.359

High-ionization mid-infrared lines as black hole mass and bolometric luminosity indicators in active galactic nuclei

We present relations of the black hole mass and the optical luminosity with the velocity dispersion and the luminosity of the [Ne V] and the [O IV] high-ionization lines in the mid-infrared (MIR) for 28 reverberation-mapped active galactic nuclei. We used high-resolution Spitzer Infrared Spectrograph and Infrared Space Observatory Short Wavelength Spectrometer data to fit the profiles of these MIR emission lines that originate from the narrow-line region of the nucleus. We find that the lines are often resolved and that the velocity dispersion of [Ne V] and [O IV] follows a relation similar to that between the black hole mass and the bulge stellar velocity dispersion found for local galaxies. The luminosity of the [Ne V] and the [O IV] lines in these sources is correlated with that of the optical 5100A continuum and with the black hole mass. Our results provide a means to derive black hole properties in various types of active galactic nuclei, including highly obscured systems.Comment: accepted for publication in ApJ

A view of the narrow-line region in the infrared: active galactic nuclei with resolved fine-structure lines in the Spitzer archive

We queried the Spitzer archive for high-resolution observations with the Infrared Spectrograph of optically selected active galactic nuclei (AGN) for the purpose of identifying sources with resolved fine-structure lines that would enable studies of the narrow-line region (NLR) at mid-infrared wavelengths. By combining 298 Spitzer spectra with 6 Infrared Space Observatory spectra, we present kinematic information of the NLR for 81 z<=0.3 AGN. We used the [NeV], [OIV], [NeIII], and [SIV] lines, whose fluxes correlate well with each other, to probe gas photoionized by the AGN. We found that the widths of the lines are, on average, increasing with the ionization potential of the species that emit them. No correlation of the line width with the critical density of the corresponding transition was found. The velocity dispersion of the gas, sigma, is systematically higher than that of the stars, sigma_*, in the AGN host galaxy, and it scales with the mass of the central black hole, M_BH. Further correlations between the line widths and luminosities L, and between L and M_BH, are suggestive of a three dimensional plane connecting log(M_BH) to a linear combination of log(sigma) and log(L). Such a plane can be understood within the context of gas motions that are driven by AGN feedback mechanisms, or virialized gas motions with a power-law dependence of the NLR radius on the AGN luminosity. The M_BH estimates obtained for 35 type 2 AGN from this plane are consistent with those obtained from the M_BH-sigma_* relation.Comment: ApJ, revised to match the print versio

Measurements of CO2, its stable isotopes, O2/N2, and 222Rn at Bern, Switzerland

A one-year time series of atmospheric CO2 measurements from Bern, Switzerland, is presented. O2/N2 and Ar/N2 ratios as well as stable carbon and oxygen isotopes of CO2 and δ29N2, δ34O2 and δ36Ar were measured periodically during a one year period. Additionally, the 222Rn activity was measured during three months in the winter 2004. Using the correlation from short-term fluctuations of CO2 and 222Rn we estimated a mean CO2 flux density between February 2004 and April 2004 in the region of Bern of 95±39 tC km–2month–1. The continuous observations of carbon dioxide and associated tracers shed light on diurnal and seasonal patterns of the carbon cycle in an urban atmosphere. There is considerable variance in nighttime δ13C and δ18O of source CO2 throughout the year, however, with generally lower values in winter compared to summertime. The O2:CO2 oxidation ratio during the nighttime build-up of CO2 varies between –0.96 and –1.69 mol O2/mol CO2. Furthermore, Ar/N2 measurements showed that artifacts like thermal fractionation at the air intake are relevant for high precision measurements of atmospheric O2

On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions

Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains $\nu_n$ of the $n$-th eigenfunction satisfies $n\ge \nu_n$. Here, we provide a new interpretation for the Courant nodal deficiency $d_n = n-\nu_n$ in the case of quantum graphs. It equals the Morse index --- at a critical point --- of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning --- it is the number of unstable directions in the vicinity of the critical point corresponding to the $n$-th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.Comment: 22 pages, 6 figure

In B-CLL, the codon 72 polymorphic variants of p53 are not related to drug resistance and disease prognosis

BACKGROUND: A common sequence polymorphism at codon 72 of the p53 gene encoding either arginine or proline was recently shown to be functionally relevant for apoptosis induction in vitro. In B-type chronic lymphocytic leukemia (B-CLL), p53 gene mutations occur in a subset of patients and are associated with impaired survival and drug resistance. Here, we address the functional relevance of the codon 72 single nucleotide (SNP) polymorphism for cell death sensitivity following exposure to clinically employed cytotoxic drugs and gamma-irradiation. METHODS: 138 B-CLL samples were analysed by SSCP-PCR and sequencing for single nucleotide polymorphism at codon 72 of the p53 gene. The in vitro cytotoxicity assay (DiSC-assay) was performed with 7 drugs (chlorambucil, mafosfamide, fludarabine phosphate, methylprednisolone, doxorubicin, vincristine) or gamma-irradiation. RESULTS: Of the 138 B-CLL samples, 9 samples were homozygous for proline (Pro/Pro), 78 samples homozygous for arginine (Arg/Arg), and 49 samples heterozygous (Arg/Pro). No differences were found for patient survival and cell death triggered by 7 cytotoxic drugs or gamma-irradiation. CONCLUSION: These data indicate that polymorphic variants of p53 codon 72 are not clinically relevant for apoptosis induction or patient survival in B-CLL

The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.Comment: Update: Added section + Correction of typo