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

Nanometer-scale Tomographic Reconstruction of 3D Electrostatic Potentials in GaAs/AlGaAs Core-Shell Nanowires

We report on the development of Electron Holographic Tomography towards a versatile potential measurement technique, overcoming several limitations, such as a limited tilt range, previously hampering a reproducible and accurate electrostatic potential reconstruction in three dimensions. Most notably, tomographic reconstruction is performed on optimally sampled polar grids taking into account symmetry and other spatial constraints of the nanostructure. Furthermore, holographic tilt series acquisition and alignment have been automated and adapted to three dimensions. We demonstrate 6 nm spatial and 0.2 V signal resolution by reconstructing various, previously hidden, potential details of a GaAs/AlGaAs core-shell nanowire. The improved tomographic reconstruction opens pathways towards the detection of minute potentials in nanostructures and an increase in speed and accuracy in related techniques such as X-ray tomography

Efficiently and Effectively Recognizing Toricity of Steady State Varieties

We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of shifted toric varieties which generalizes the notion of toric varieties. This requires a geometric view on the varieties rather than an algebraic view on the ideals. We present algorithms and computations on 129 models from the BioModels repository testing for group and coset structures over both the complex numbers and the real numbers. Our methods over the complex numbers are based on Gr\"obner basis techniques and binomiality tests. Over the real numbers we use first-order characterizations and employ real quantifier elimination. In combination with suitable prime decompositions and restrictions to subspaces it turns out that almost all models show coset structure. Beyond our practical computations, we give upper bounds on the asymptotic worst-case complexity of the corresponding problems by proposing single exponential algorithms that test complex or real varieties for toricity or shifted toricity. In the positive case, these algorithms produce generating binomials. In addition, we propose an asymptotically fast algorithm for testing membership in a binomial variety over the algebraic closure of the rational numbers

Monomer dynamics of a wormlike chain

We derive the stochastic equations of motion for a tracer that is tightly attached to a semiflexible polymer and confined or agitated by an externally controlled potential. The generalised Langevin equation, the power spectrum, and the mean-square displacement for the tracer dynamics are explicitly constructed from the microscopic equations of motion for a weakly bending wormlike chain by a systematic coarse-graining procedure. Our accurate analytical expressions should provide a convenient starting point for further theoretical developments and for the analysis of various single-molecule experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure

Mid-Infrared Diagnostics of LINERs

We report results from the first mid-infrared spectroscopic study of a comprehensive sample of 33 LINERs, observed with the Spitzer Space Telescope. We compare the properties of two different LINER populations: infrared-faint LINERs, with LINER emission arising mostly in compact nuclear regions, and infrared-luminous LINERs, which often show spatially extended (non-AGN) LINER emission. We show that these two populations can be easily distinguished by their mid-infrared spectra in three different ways: (i) their mid-IR spectral energy distributions (SEDs), (ii) the emission features of polycyclic aromatic hydrocarbons (PAHs), and (iii) various combinations of IR fine-structure line ratios. IR-luminous LINERs show mid-IR SEDs typical of starburst galaxies, while the mid-IR SEDs of IR-faint LINERs are much bluer. PAH flux ratios are significantly different in the two groups. Fine structure emission lines from highly excited gas, such as [O IV], are detected in both populations, suggesting the presence of an additional AGN also in a large fraction of IR-bright LINERs, which contributes little to the combined mid-IR light. The two LINER groups occupy different regions of mid-infrared emission-line excitation diagrams. The positions of the various LINER types in our diagnostic diagrams provide important clues regarding the power source of each LINER type. Most of these mid-infrared diagnostics can be applied at low spectral resolution, making AGN- and starburst-excited LINERs distinguishable also at high redshifts.Comment: 11 pages, including 2 eps figures, accepted for publication in ApJ

Three examples where the specific surface area of snow increased over time

Snow on the ground impacts climate through its high albedo and affects atmospheric composition through its ability to adsorb chemical compounds. The quantification of these effects requires the knowledge of the specific surface area (SSA) of snow and its rate of change. All relevant studies indicate that snow SSA decreases over time. Here, we report for the first time three cases where the SSA of snow increased over time. These are (1) the transformation of a melt-freeze crust into depth hoar, producing an increase in SSA from 3.4 to 8.8m2 kg−1. (2) The mobilization of surface snow by wind, which reduced the size of snow crystals by sublimation and fragmented them. This formed a surface snow layer with a SSA of 61m2 kg−1 from layers whose SSAs were originally 42 and 50m2 kg−1. (3) The sieving of blowing snow by a snow layer, which allowed the smallest crystals to penetrate into open spaces in the snow, leading to an SSA increase from 32 to 61m2 kg−1. We discuss that other mechanisms for SSA increase are possible. Overall, SSA increases are probably not rare. They lead to enhanced uptake of chemical compounds and to increases in snow albedo, and their inclusion in relevant chemical and climate models deserves consideration

Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces

This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on particular fractals and further less regular cases as well. The proof is based on a new chaining argument and it is free of volume growth assumptions

The K→(ππ)I=2K\to(\pi\pi)_{I=2} Decay Amplitude from Lattice QCD

We report on the first realistic \emph{ab initio} calculation of a hadronic weak decay, that of the amplitude $A_2$ for a kaon to decay into two \pi-mesons with isospin 2. We find Re$A_2=(1.436\pm 0.063_{\textrm{stat}}\pm 0.258_{\textrm{syst}})\,10^{-8}\,\textrm{GeV}$ in good agreement with the experimental result and for the hitherto unknown imaginary part we find {Im}$\,A_2=-(6.83 \pm 0.51_{\textrm{stat}} \pm 1.30_{\textrm{syst}})\,10^{-13}\,{\rm GeV}$. Moreover combining our result for Im\,$A_2$ with experimental values of Re\,$A_2$, Re\,$A_0$ and $\epsilon^\prime/\epsilon$, we obtain the following value for the unknown ratio Im\,$A_0$/Re\,$A_0$ within the Standard Model: $\mathrm{Im}\,A_0/\mathrm{Re}\,A_0=-1.63(19)_{\mathrm{stat}}(20)_{\mathrm{syst}}\times10^{-4}$. One consequence of these results is that the contribution from Im\,$A_2$ to the direct CP violation parameter $\epsilon^{\prime}$ (the so-called Electroweak Penguin, EWP, contribution) is Re$(\epsilon^\prime/\epsilon)_{\mathrm{EWP}} = -(6.52 \pm 0.49_{\textrm{stat}} \pm 1.24_{\textrm{syst}}) \times 10^{-4}$. We explain why this calculation of $A_2$ represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP-violation in kaon decays.Comment: 5 pages, 1 figur