Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

The Effects of Diffuse Ionized Gas and Spatial Resolution on Metallicity Gradients: TYPHOON Two-Dimensional Spectrophotometry of M83

We present a systematic study of the diffuse ionized gas (DIG) in M83 and its effects on the measurement of metallicity gradients at varying resolution scales. Using spectrophotometric data cubes of M83 obtained at the 2.5m duPont telescope at Las Campanas Observatory as part of the TYPHOON program, we separate the HII regions from the DIG using the [SII]/H$\alpha$ ratio, HIIphot (HII finding algorithm) and the H$\alpha$ surface brightness. We find that the contribution to the overall H$\alpha$ luminosity is approximately equal for the HII and DIG regions. The data is then rebinned to simulate low-resolution observations at varying resolution scales from 41 pc up to 1005 pc. Metallicity gradients are measured using five different metallicity diagnostics at each resolution. We find that all metallicity diagnostics used are affected by the inclusion of DIG to varying degrees. We discuss the reasons of why the metallicity gradients are significantly affected by DIG using the HII dominance and emission line ratio radial profiles. We find that applying the [SII]/H$\alpha$ cut will provide a closer estimate of the true metallicity gradient up to a resolution of 1005 pc for all metallicity diagnostics used in this study.Comment: 26 pages, 12 figures + Appendix/Supplementary Material, accepted for publication by MNRA

Starburst-AGN mixing: TYPHOON observations of NGC 1365, NGC 1068, and the effect of spatial resolution on the AGN fraction

We demonstrate a robust method of resolving the star-formation and AGN contributions to emission lines using two very well known AGN systems: NGC 1365, and NGC 1068, using the high spatial resolution data from the TYPHOON/PrISM survey. We expand the previous method of calculating the AGN fraction by using theoretical-based model grids rather than empirical points. The high spatial resolution of the TYPHOON/PrISM observations show evidence of both star formation and AGN activity occurring in the nuclei of the two galaxies. We rebin the data to the lower resolutions, typically found in other integral field spectroscopy surveys such as SAMI, MaNGA, and CALIFA. The results show that when rebinned from the native resolution of TYPHOON (< 200 pc/pixel) to 1 kpc/pixel, the effects include a roughly 3 kpc increase in the radius of measured AGN activity, and a factor of 2 to 7 increase in the detection of low surface brightness features such as shocks. All of this information is critical, because information on certain physical processes may be lost at varying resolutions. We make recommendations for analysing data at current IFU survey resolutions.Comment: 30 pages, 28 figures, accepted for publication by MNRA

Vibrational modes in nanocrystalline iron under high pressure

The phonon density of states (DOS) of nanocrystalline 57Fe was measured using nuclear resonant inelastic x-ray scattering (NRIXS) at pressures up to 28 GPa in a diamond anvil cell. The nanocrystalline material exhibited an enhancement in its DOS at low energies by a factor of 2.2. This enhancement persisted throughout the entire pressure range, although it was reduced to about 1.7 after decompression. The low-energy regions of the spectra were fitted to the function AEn, giving values of n close to 2 for both the bulk control sample and the nanocrystalline material, indicative of nearly three-dimensional vibrational dynamics. At higher energies, the van Hove singularities observed in both samples were coincident in energy and remained so at all pressures, indicating that the forces conjugate to the normal coordinates of the nanocrystalline materials are similar to the interatomic potentials of bulk crystals

Flow network controlled shape transformation of a thin membrane through differential fluid storage and surface expansion

The mechanical properties of a thin, planar material, perfused by an embedded flow network, can be changed locally and globally by the fluid transport and storage, resulting in small or large-scale deformation, such as out-of-plane buckling. Fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and swell unevenly, prompting a differential expansion of the surface. In order to computationally study the hydraulically induced differential swelling and buckling of such a membrane, we develop a network model that describes both the membrane shape and fluid movement, coupling mechanics with hydrodynamics. We simulate the time-dependent fluid distribution in the flow network based on a spatially explicit resistor network model with local fluid-storage capacitance. The shape of the surface is modeled by a spring network produced by a tethered mesh discretization, in which local bond rest lengths are adjusted instantaneously according to associated local fluid content in the capacitors in a quasi-static way. We investigate the effects of various designs of the flow network, including overall hydraulic traits (resistance and capacitance) and hierarchical architecture (arrangement of major and minor veins), on the specific dynamics of membrane shape transformation. To quantify these effects, we explore the correlation between local Gaussian curvature and relative stored fluid content in each hierarchy by using linear regression, which reveals that stronger correlations could be induced by less densely connected major veins. This flow-controlled mechanism of shape transformation was inspired by the blooming of flowers through the unfolding of petals. It can potentially offer insights for other reversible motions observed in plants induced by differential turgor and water transport through the xylem vessels, as well as engineering applications

Azimuthal variations of gas-phase oxygen abundance in NGC 2997

13 pages, 17 figures, accepted to A&A Reproduced with permission from Astronomy & Astrophysics. © 2018 ESO.The azimuthal variation of the HII region oxygen abundance in spiral galaxies is a key observable for understanding how quickly oxygen produced by massive stars can be dispersed within the surrounding interstellar medium. Observational constraints on the prevalence and magnitude of such azimuthal variations remain rare in the literature. Here, we report the discovery of pronounced azimuthal variations of HII region oxygen abundance in NGC 2997, a spiral galaxy at approximately 11.3 Mpc. Using 3D spectroscopic data from the TYPHOON Program, we study the HII region oxygen abundance at a physical resolution of 125 pc. Individual HII regions or complexes are identified in the 3D optical data and their strong emission line fluxes measured to constrain their oxygen abundances. We find 0.06 dex azimuthal variations in the oxygen abundance on top of a radial abundance gradient that is comparable to those seen in other star-forming disks. At a given radial distance, the oxygen abundances are highest in the spiral arms and lower in the inter-arm regions, similar to what has been reported in NGC 1365 using similar observations. We discuss whether the azimuthal variations could be recovered when the galaxy is observed at worse physical resolutions and lower signal-to-noise ratios.Peer reviewe

A Symposium on Donor‐Specific Antibodies after Transplantation Introduction

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106818/1/j.1399-3046.2011.01521.x.pd

Lymphocyte Phenotype during Therapy for Acute Graft-versus-Host Disease: A Brief Report from BMT-CTN 0302

AbstractAlthough significant strides have been made in understanding the biology of graft-versus-host disease (GVHD) and its prevention over the last 4 decades, little is known about the different populations of lymphocytes and the changes in response to treatment for this condition. BMT-CTN 0302 was a randomized phase II clinical trial in the Blood and Marrow Transplant Clinical Trials Network that assessed the efficacy of combination therapy with steroids plus pentostatin, mycophenolate mofetil, etanercept, or denileukin diftitox in patients with acute GVHD. Patients enrolled in the study underwent blood analysis by flow cytometry on days 0, 14, and 28 of therapy to enumerate the number of total lymphocytes, T cells, B cells, and lymphocytes expressing activation markers. Baseline total lymphocyte counts and subpopulations were similar in the 4 treatment arms. Responding patients had a smaller decrease in total CD45+ cell count (P = .005) compared with nonresponding patients at day 28. On univariate analysis, those who developed chronic GVHD had significantly higher CD8+ cell counts at day 14 compared with those without it (P = .005). There was no significant association between baseline lymphocyte count and survival. On univariate analysis, among the patients with higher lymphocyte counts at days 14 and 28, there was a trend toward better survival at day 180, although this trend did not reach the predetermined threshold for significance. We found no significant differences in lymphocyte total or subpopulation counts among the 4 treatment arms, and no notable influence on outcomes