Linear Integer Arithmetic Revisited

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanovic and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not terminate, in general. In this paper we extend their CUTSAT algorithm by refined inference rules, a new type of conflicting core, and a dedicated rule application strategy. This leads to our algorithm CUTSAT++, which guarantees termination

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

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

Minimizing magnetic fields for precision experiments

An increasing number of measurements in fundamental and applied physics rely on magnetically shielded environments with sub nano-Tesla residual magnetic fields. State of the art magnetically shielded rooms (MSRs) consist of up to seven layers of high permeability materials in combination with highly conductive shields. Proper magnetic equilibration is crucial to obtain such low magnetic fields with small gradients in any MSR. Here we report on a scheme to magnetically equilibrate MSRs with a 10 times reduced duration of the magnetic equilibration sequence and a significantly lower magnetic field with improved homogeneity. For the search of the neutron's electric dipole moment, our finding corresponds to a linear improvement in the systematic reach and a 40 % improvement of the statistical reach of the measurement. However, this versatile procedure can improve the performance of any MSR for any application.Comment: 5 pages, 4 figure

Effect of Surgical Fusion on Volitional Weight-Shifting in Individuals With Adolescent Idiopathic Scoliosis

Study Design Prospective. Objectives The goals of this study were to (1) evaluate the differences in weightbearing symmetry between individuals with adolescent idiopathic scoliosis (AIS) and typically developing controls; (2) observe the effect of posterior spinal fusion and instrumentation (PSFI) on volitional weight-shifting at 1 and 2 years postoperatively; and (3) evaluate whether lowest instrumented fusion level (ie, lowest instrumented vertebra [LIV]) in PSFI has an effect on volitional weight-shifting. Summary of Background Data Previous studies have conflicting findings with regard to the effect of scoliosis on postural control tasks as well as the effect of surgery. They have also noted an inconsistent effect of PSFI at different LIVs, with more distal LIVs exhibiting greater reductions in postoperative range of motion. Methods The study was designed with an AIS group of 41 patients (8 males and 33 females) with AIS who underwent PSFI, along with a Control Group of 24 age-matched typically developing participants (12 male and 12 female). Both groups performed postural control tasks (static balance and volitional weight-shifting), with the AIS group repeating the tasks at 1 and 2 years postoperatively. Results At baseline, the AIS group showed increased weightbearing asymmetry than the Control Group (p = .01). The AIS group showed improvements in volitional weight-shifting at 2 years over baseline (p \u3c .01). There was no effect of LIV on volitional weight-shifting by the second postoperative year. Conclusions Individuals with AIS have greater weightbearing asymmetry but improved volitional weight-shifting over typically developing controls. PSFI improves volitional weight-shifting beyond preoperative baseline but does not differ significantly by LIV

Spitzer Mid-Infrared Spectroscopy of 70um-Selected Distant Luminous Infrared Galaxies

We present mid-infrared spectroscopy obtained with the Spitzer Space Telescope of a sample of 11 optically faint, infrared luminous galaxies selected from a Spitzer MIPS 70um imaging survey of the NDWFS Bootes field. These are the first Spitzer IRS spectra presented of distant 70um-selected sources. All the galaxies lie at redshifts 0.3<z<1.3 and have very large infrared luminosities of L_IR~ 0.1-17 x 10^12 solar luminosities. Seven of the galaxies exhibit strong emission features attributed to polycyclic aromatic hydrocarbons (PAHs). The average IRS spectrum of these sources is characteristic of classical starburst galaxies, but with much larger infrared luminosities. The PAH luminosities of L(7.7) ~ 0.4 - 7 x 10^11 solar luminosities imply star formation rates of ~ 40 - 720 solar masses per year. Four of the galaxies show deep 9.7um silicate absorption features and no significant PAH emission features (6.2um equivalent widths < 0.03um). The large infrared luminosities and low f70/f24 flux density ratios suggests that these sources have AGN as the dominant origin of their large mid-infrared luminosities, although deeply embedded but luminous starbursts cannot be ruled out. If the absorbed sources are AGN-dominated, a significant fraction of all far-infrared bright, optically faint sources may be dominated by AGN.Comment: 8 Pages, ApJ accepte

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