Lower bounds for polynomials using geometric programming

We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points

The development of tape recorded discussions and check lists for evaluating progression in grades one through four.

Thesis (Ed.M.)--Boston Universit

The Lerch Zeta Function II. Analytic Continuation

This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables. We that it is well defined as a multivalued function on the manifold M equal to C^3 with the hyperplanes corresponding to integer values of the two variables a and c removed. We show that it becomes single valued on the maximal abelian cover of M. We compute the monodromy functions describing the multivalued nature of this function on M, and determine various of their properties.Comment: 29 pages, 3 figures; v2 notation changes, homotopy action on lef

Tumor bed brachytherapy for locally advanced laryngeal cancer: a feasibility assessment of combination with ferromagnetic hyperthermia

Purpose. To assess the feasibility of adding hyperthermia to an original method of organ-preserving brachytherapy treatment for locally advanced head and neck tumors. Methods and materials. The method involves organ-preserving tumor resection and adjunctive high-dose-rate (HDR) brachytherapy delivered via afterloading catheters. These catheters are embedded in a polymeric implant prepared intraoperatively to fill the resection cavity, allowing precise computer planning of dose distribution in the surrounding at-risk tumor bed tissue. Theoretical and experimental analyzes address the feasibility of heating the tumor bed implant by coupling energy from a 100 kHz magnetic field applied externally into ferromagnetic particles, which are uniformly distributed within the implant. The goal is to combine adjuvant hyperthermia (40 °C–45 °C) to at-risk tissue within 5 mm of the resection cavity for thermal enhancement of radiation and chemotherapy response. Results. A five-year relapse free survival rate of 95.8% was obtained for a select group of 48 male patients with T3N0M0 larynx tumors, when combining organ-preserving surgery with HDR brachytherapy from a tumor bed implant. Anticipating the need for additional treatment in patients with more advanced disease, a theoretical analysis demonstrates the ability to heat at-risk tissue up to 10 mm from the surface of an implant filled with magnetically coupled ferromagnetic balls. Using a laboratory induction heating system, it takes just over 2 min to increase the target tissue temperature by 10 °C using a 19% volume fraction of ferromagnetic spheres in a 2 cm diameter silicone implant. Conclusion. The promising clinical results of a 48 patient pilot study demonstrate the feasibility of a new organ sparing treatment for laryngeal cancer. Anticipating the need for additional therapy, theoretical estimations of potential implant heating are confirmed with laboratory experiments, preparing the way for future implementation of a thermobrachytherapy implant approach for organ-sparing treatment of locally advanced laryngeal cancer

Enhancement of Cavity Cooling of a Micromechanical Mirror Using Parametric Interactions

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. Further if in case of a precooled mirror one can reach millikelvin temperatures starting with about 1 K. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics.Comment: 14 pages, 7 figure

Far-UV Observations of NGC 4151 during the ORFEUS-SPAS II Mission

We observed the Seyfert 1 galaxy NGC 4151 on eleven occasions at 1-2 day intervals using the Berkeley spectrometer during the ORFEUS-SPAS II mission in 1996 November. The mean spectrum covers 912-1220 A at ~0.3 A resolution with a total exposure of 15,658 seconds. The mean flux at 1000 A was 4.7e-13 erg/cm^2/s/A. We identify the neutral hydrogen absorption with a number of components that correspond to the velocity distribution of \ion{H}{1} seen in our own Galaxy as well as features identified in the CIV 1549 absorption profile by Weymann et al. The main component of neutral hydrogen in NGC 4151 has a total column density of log N_HI = 18.7 +/- 1.5 cm^{-2} for a Doppler parameter b=250 +/- 50 km/s, and it covers 84 +/- 6% of the source. This is consistent with previous results obtained with the Hopkins Ultraviolet Telescope. Other intrinsic far-UV absorption features are not resolved, but the CIII* 1176 absorption line has a significantly higher blueshift relative to NGC 4151 than the CIII 977 resonance line. This implies that the highest velocity region of the outflowing gas has the highest density. Variations in the equivalent width of the CIII* 1176 absorption line anticorrelate with continuum variations on timescales of days. For an ionization timescale <1 day, we set an upper limit of 25 pc on the distance of the absorbing gas from the central source. The OVI 1034 and HeII 1085 emission lines also vary on timescales of 1-2 days, but their response to the continuum variations is complex. For some continuum variations they show no response, while for others the response is instantaneous to the limit of our sampling interval.Comment: 4 pages, 2 PostScript figures, uses emulateapj.sty, apjfonts.sty. To appear in the Astrophysical Journal (Letters) special issue for ORFEU

ORFEUS II Far-UV Spectroscopy of AM Herculis

Six high-resolution (\lambda/\Delta\lambda ~ 3000) far-UV (\lambda\lambda = 910-1210 \AA) spectra of the magnetic cataclysmic variable AM Herculis were acquired in 1996 November during the flight of the ORFEUS-SPAS II mission. AM Her was in a high optical state at the time of the observations, and the spectra reveal emission lines of O VI \lambda\lambda 1032, 1038, C III \lambda 977, \lambda 1176, and He II \lambda 1085 superposed on a nearly flat continuum. Continuum flux variations can be described as per Gansicke et al. by a ~ 20 kK white dwarf with a ~ 37 kK hot spot covering a fraction f~0.15 of the surface of the white dwarf, but we caution that the expected Lyman absorption lines are not detected. The O VI emission lines have narrow and broad component structure similar to that of the optical emission lines, with radial velocities consistent with an origin in the irradiated face of the secondary and the accretion funnel, respectively. The density of the narrow- and broad-line regions is n_{nlr} ~ 3\times 10^{10} cm^{-3} and n_{blr} ~ 1\times 10^{12} cm^{-3}, respectively, yet the narrow-line region is optically thick in the O VI line and the broad-line region is optically thin; apparently, the velocity shear in the broad-line region allows the O VI photons to escape, rendering the gas effectively optically thin. Unexplained are the orbital phase variations of the emission-line fluxes.Comment: 15 pages, 6 Postscript figures; LaTeX format, uses aaspp4.sty; table2.tex included separately because it must be printed sideways - see instructions in the file; accepted on April 17, 1998 for publication in The Astrophysical Journa

GHRS and ORFEUS-II Observations of the Highly Ionized Interstellar Medium Toward ESO141-055

We present Goddard High Resolution Spectrograph and ORFEUS-II measurements of Si IV, CIV, N V, and O VI absorption in the interstellar medium of the Galactic disk and halo toward the nucleus of the Seyfert galaxy ESO141-055. The high ionization absorption is strong, with line strengths consistent with the spectral signature expected for hot (log T = 5-6) collisionally ionized gas in either a ``Galactic fountain'' or an inhomogeneous medium containing a mixture of conductive interfaces and turbulent mixing layers. The total O VI column density of log N ~ 15 suggests that the scale height of O VI is large (>3 kpc) in this direction. Comparison of the high ion column densities with measurements for other sight lines indicates that the highly ionized gas distribution is patchy. The amount of O VI perpendicular to the Galactic plane varies by at least a factor of ~4 among the complete halo sight lines thus far studied. In addition to the high ion absorption, lines of low ionization species are also present in the spectra. With the possible exception of Ar I, which may have a lower than expected abundance resulting from partial photoionization of gas along the sight line, the absorption strengths are typical of those expected for the warm, neutral interstellar medium. The sight line intercepts a cold molecular cloud with log N(H2) ~ 19. The cloud has an identifiable counterpart in IRAS 100-micron emission maps of this region of the sky. We detect a Ly-alpha absorber associated with ESO141-055 at z = 0.03492. This study presents an enticing glimpse into the interstellar and intergalactic absorption patterns that will be observed at high spectral resolution by the Far Ultraviolet Spectroscopic Explorer.Comment: 24 pages + 8 figures, uses aaspp4.sty. Accepted for publication in Ap

Local Pheromone Release from Dynamic Polarity Sites Underlies Cell-Cell Pairing during Yeast Mating.

Cell pairing is central for many processes, including immune defense, neuronal connection, hyphal fusion, and sexual reproduction. How does a cell orient toward a partner, especially when faced with multiple choices? Fission yeast Schizosaccharomyces pombe P and M cells, which respectively express P and M factor pheromones [1, 2], pair during the mating process induced by nitrogen starvation. Engagement of pheromone receptors Map3 and Mam2 [3, 4] with their cognate pheromone ligands leads to activation of the Gα protein Gpa1 to signal sexual differentiation [3, 5, 6]. Prior to cell pairing, the Cdc42 GTPase, a central regulator of cell polarization, forms dynamic zones of activity at the cell periphery at distinct locations over time [7]. Here we show that Cdc42-GTP polarization sites contain the M factor transporter Mam1, the general secretion machinery, which underlies P factor secretion, and Gpa1, suggesting that these are sub-cellular zones of pheromone secretion and signaling. Zone lifetimes scale with pheromone concentration. Computational simulations of pair formation through a fluctuating zone show that the combination of local pheromone release and sensing, short pheromone decay length, and pheromone-dependent zone stabilization leads to efficient pair formation. Consistently, pairing efficiency is reduced in the absence of the P factor protease. Similarly, zone stabilization at reduced pheromone levels, which occurs in the absence of the predicted GTPase-activating protein for Ras, leads to reduction in pairing efficiency. We propose that efficient cell pairing relies on fluctuating local signal emission and perception, which become locked into place through stimulation

Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio