The quadratic isoperimetric inequality for mapping tori of free group automorphisms II: The general case

If F is a finitely generated free group and \phi is an automorphism of F then the mapping torus of \phi admits a quadratic isoperimetric inequality. This is the third and final paper in a series proving this theorem. The first two were math.GR/0211459 and math.GR/0507589.Comment: 73 page

Modelling the Pan-Spectral Energy Distributions of Starburst & Active Galaxies

We present results of a self-consistent model of the spectral energy distribution (SED) of starburst galaxies. Two parameters control the IR SED, the mean pressure in the ISM and the destruction timescale of molecular clouds. Adding a simplified AGN spectrum provides mixing lines on IRAS color : color diagrams. This reproduces the observed colors of both AGNs and starbursts.Comment: Poster Paper for IAU 222: The Interplay among Black Holes, Stars and ISM in Galactic Nucle

Bringing Salary Transparency to the World: Computing Robust Compensation Insights via LinkedIn Salary

The recently launched LinkedIn Salary product has been designed with the goal of providing compensation insights to the world's professionals and thereby helping them optimize their earning potential. We describe the overall design and architecture of the statistical modeling system underlying this product. We focus on the unique data mining challenges while designing and implementing the system, and describe the modeling components such as Bayesian hierarchical smoothing that help to compute and present robust compensation insights to users. We report on extensive evaluation with nearly one year of de-identified compensation data collected from over one million LinkedIn users, thereby demonstrating the efficacy of the statistical models. We also highlight the lessons learned through the deployment of our system at LinkedIn.Comment: Conference information: ACM International Conference on Information and Knowledge Management (CIKM 2017

A New Approach to Better Low-Cost MEMS IMU Performance Using Sensor Arrays

Over the past decade and a half, the combination of low-cost, lightweight micro-electro-mechanical sensors (MEMS) technology and multisensor integration has enabled inertial sensors to be deployed over a much wider range of navigation applications [1]. Examples include pedestrian dead-reckoning using step detection technology [2, 3], aiding of GNSS signal tracking during jamming [4, 5], and simultaneous localisation and mapping (SLAM) using radio signals [6]. However, for best performance, a MEMS inertial measurement unit (IMU) must be calibrated in the laboratory prior to use, which increases the cost by more than $1000 per unit. In this paper, we examine and present a range of techniques which use an array of inexpensive MEMS sensors to improve the performance of a MEMS IMU without requiring a full calibration prior to use. As the cost of calibration of a high-performance MEMS IMU far outweighs the cost of the hardware, there is considerable scope to improve the performance by adding additional sensors, before the cost of the IMU reaches that of a laboratory calibrated equivalent. Combining MEMS IMUs in an array has been studied before. However, the most common approach was simply to take an average of the input of several identical sensors [7]. If the sensor errors were independent, this could be expected to improve performance by a factor of root-n where, n is the number of IMUs combined. In this paper more sophisticated techniques are investigated that use knowledge of the sensor characteristics to obtain better performance. Three different properties of MEMS sensors may potentially be exploited: 1) The common-mode errors of different sensors of the same design; 2) The different characteristics of in-plane and out-of-plane sensors; and 3) The complementary properties of MEMS sensors with different dynamic ranges. In [8], it is shown that different individual sensors of the same design exhibit similar bias variation with temperature and that improved accuracy may be obtained by differencing the outputs of two gyroscopes mounted with their sensitive axes in opposing directions. Here, this approach will be independently verified and the performance benefits assessed with a range of different MEMS accelerometers and gyros, including Bosch BMA180 accelerometers, Analogue Devices ADXL345 accelerometers, ST Microtronics L3G4200D gyroscopes. Preliminary indications are that there is considerable common bias variation with temperature for the in-plane sensors of L3G4200D gyroscopes, and some common mode behaviour for the low-cost accelerometers. The second idea presented is exploiting the differences between the in-plane and out-of-plane axis outputs of single-chip inertial sensor triads, to improve the performance of an array-based IMU. Early experiment s point to considerable differences between the two which could markedly affect navigation performance. Both accelerometer and gyro triads can exhibit smaller errors from the in-plane sensors than from the out-of-plane sensors. Therefore, experiments were conducted using mutually-perpendicular arrays of accelerometer and gyro triads to determine whether better performance could be obtained using only the in-plane sensors. The third idea is to combine the outputs of MEMS sensors with different dynamic ranges to exploit the lower noise exhibited by some lower-dynamic-range sensors compared to their higher-dynamic-range counterparts. The sensor outputs are thus weighted according to the platform dynamics. That is, predominantly using the high-precision sensor when dynamics are low and using the full-range sensor when the dynamics are high. Several versions of this weighted signal combination will be presented and compared. Early indications are that there can be a significant benefit in this approach for some sensor designs, but not others. Finally, this paper will also examine the efficacy of a once-only static calibration on purchase, performed by the user instead of the supplier, for improving navigation performance. It is essential for a user-performed calibration that the physical movements required of the sensor are very simple and easily understood and completed, even if the underlying method is complex. To this end data, recorded on different days from an array of MEMS sensors within a precisely manufactured rapid prototyped ‘calibration cube’, will be analysed. These measurements are taken at precisely orthogonal angles of the cubes six faces, and allow the scale factor errors, biases and axes alignments of the accelerometers to be determined. The computed calibration corrections over several days will be compared to enable the efficacy of the one-time calibration technique to be assessed. The development of a full calibration routine will be the subject of future research. In summary, this paper will present several new methods for utilising the output of an array of low-cost sensors to improve the performance of a MEMS IMU, and also expands on methods proposed in existing research. As uncalibrated MEMS IMUs are of low performance there is a great potential for new applications if the performance can be improved closer to the level of those which are factory calibrated. / References [1] Groves, P. D., Principles of GNSS, inertial, and multi-sensor integrated navigation systems, Second Edition, Artech House, 2013. [2] Gustafson, D., J. Dowdle, and K. Flueckiger, “A Deeply Integrated Adaptive GPS-Based Navigator with Extended Range Code Tracking,” Proc. IEEE PLANS 2000. [3] Groves, P. D., C. J. Mather and A. A. Macaulay, “Demonstration of Non-Coherent Deep INS/GPS Integration for Optimized Signal to Noise Performance,” Proc. ION GNSS 2007. [4] Ma, Y., W. Soehren, W. Hawkinson, and J. Syrstad, "An Enhanced Prototype Personal Inertial Navigation System," Proc. ION GNSS 2012. [5] Groves, P. D., et al., “Inertial Navigation Versus Pedestrian Dead Reckoning: Optimizing the Integration,” Proc. ION GNSS 2007. [6] Faragher, R. M., C. Sarno, and M. Newman, “Opportunistic Radio SLAM for Indoor Navigation using Smartphone Sensors,” Proc. IEEE/ION PLANS 2012. [7] Bancroft, J. B., and G. Lachapelle, “Data fusion algorithms for multiple inertial measurement units,” Sensors, Vol. 11, No. 7, 2011, pp. 6771-6798. [8] Yuksel, Y., N. El-Sheimy, N., and A. Noureldin, “Error modelling and characterization of environmental effects for low cost inertial MEMS units,” Proc. IEEE/ION PLANS 2010

Dust in dwarf galaxies: The case of NGC 4214

We have carried out a detailed modelling of the dust heating and emission in the nearby, starbursting dwarf galaxy NGC 4214. Due to its proximity and the great wealth of data from the UV to the millimeter range (from GALEX, HST, {\it Spitzer}, Herschel, Planck and IRAM) it is possible to separately model the emission from HII regions and their associated photodissociation regions (PDRs) and the emission from diffuse dust. Furthermore, most model parameters can be directly determined from the data leaving very few free parameters. We can fit both the emission from HII+PDR regions and the diffuse emission in NGC 4214 with these models with "normal" dust properties and realistic parameters.Comment: 4pages, 3 figures. To appear in 'The Spectral Energy Distribution of Galaxies' Proceedings IAU Symposium No 284, 201

Charged Particles on Surfaces: Coexistence of Dilute Phases and Periodic Structures on Membranes

We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the coexistence between a patterned solid phase and a charge-dilute phase. The patterns in the solid phase arise from competition between short-range immiscibility and long-range electrostatic attractions between the charged species. The coexistence between phases leads to observations of stable patterned domains immersed in a neutral matrix background.Comment: 5 pages, 3 figure

Fermionic Zero Modes on Domain Walls

We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.Comment: 6 pages, 3 figures, matches version published in PR

K 3-22: a D-type symbiotic star

A goal of the IPHAS survey is to determine the frequency and nature of emission-line sources in the Galactic plane. According to our selection criteria, K 3-22 is a candidate symbiotic star, but it was previously classified as a planetary nebula. To determine its nature, we acquired a low-resolution optical spectrum of K 3-22. Our analysis of our spectroscopy demonstrates that K 3-22 is indeed a D-type symbiotic star, because of its high excitation nebular spectrum and the simultaneous presence of Raman-scattered O VI emission at 6825 and 7082 angstrom, which is detected primarily in symbiotic stars.Comment: 3 pages, 1 figure. Accepted for publication on Astronomy and Astrophysic

The Physical Conditions in Starbursts Derived from Bayesian Fitting of Mid-IR SEDS: 30 Doradus as a Template

To understand and interpret the observed Spectral Energy Distributions (SEDs) of starbursts, theoretical or semi-empirical SED models are necessary. Yet, while they are well-founded in theory, independent verification and calibration of these models, including the exploration of possible degeneracies between their parameters, are rarely made. As a consequence, a robust fitting method that leads to unique and reproducible results has been lacking. Here we introduce a novel approach based on Bayesian analysis to fit the Spitzer-IRS spectra of starbursts using the SED models proposed by Groves et al. (2008). We demonstrate its capabilities and verify the agreement between the derived best fit parameters and actual physical conditions by modelling the nearby, well-studied, giant HII region 30 Dor in the LMC. The derived physical parameters, such as cluster mass, cluster age, ISM pressure and covering fraction of photodissociation regions, are representative of the 30 Dor region. The inclusion of the emission lines in the modelling is crucial to break degeneracies. We investigate the limitations and uncertainties by modelling sub-regions, which are dominated by single components, within 30 Dor. A remarkable result for 30 Doradus in particular is a considerable contribution to its mid-infrared spectrum from hot ({\simeq} 300K) dust. The demonstrated success of our approach will allow us to derive the physical conditions in more distant, spatially unresolved starbursts.Comment: 17 pages, 10 figures. Accepted por publication in the Astrophysical Journa