Saving phase: Injectivity and stability for phase retrieval

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every signal up to a global phase factor, and how many are needed to do so? Furthermore, which measurement ensembles lend stability? This paper presents several results that address each of these questions. We begin by characterizing injectivity, and we identify that the complement property is indeed a necessary condition in the complex case. We then pose a conjecture that 4M-4 generic measurement vectors are both necessary and sufficient for injectivity in M dimensions, and we prove this conjecture in the special cases where M=2,3. Next, we shift our attention to stability, both in the worst and average cases. Here, we characterize worst-case stability in the real case by introducing a numerical version of the complement property. This new property bears some resemblance to the restricted isometry property of compressed sensing and can be used to derive a sharp lower Lipschitz bound on the intensity measurement mapping. Localized frames are shown to lack this property (suggesting instability), whereas Gaussian random measurements are shown to satisfy this property with high probability. We conclude by presenting results that use a stochastic noise model in both the real and complex cases, and we leverage Cramer-Rao lower bounds to identify stability with stronger versions of the injectivity characterizations.Comment: 22 page

The Phoenix Deep Survey: The 1.4 GHz microJansky catalogue

The initial Phoenix Deep Survey (PDS) observations with the Australia Telescope Compact Array have been supplemented by additional 1.4 GHz observations over the past few years. Here we present details of the construction of a new mosaic image covering an area of 4.56 square degrees, an investigation of the reliability of the source measurements, and the 1.4 GHz source counts for the compiled radio catalogue. The mosaic achieves a 1-sigma rms noise of 12 microJy at its most sensitive, and a homogeneous radio-selected catalogue of over 2000 sources reaching flux densities as faint as 60 microJy has been compiled. The source parameter measurements are found to be consistent with the expected uncertainties from the image noise levels and the Gaussian source fitting procedure. A radio-selected sample avoids the complications of obscuration associated with optically-selected samples, and by utilising complementary PDS observations including multicolour optical, near-infrared and spectroscopic data, this radio catalogue will be used in a detailed investigation of the evolution in star-formation spanning the redshift range 0 < z < 1. The homogeneity of the catalogue ensures a consistent picture of galaxy evolution can be developed over the full cosmologically significant redshift range of interest. The 1.4 GHz mosaic image and the source catalogue are available on the web at http://www.atnf.csiro.au/~ahopkins/phoenix/ or from the authors by request.Comment: 16 pages, 11 figures, 4 tables. Accepted for publication by A

MACHO Mass Determination Based on Space Telescope Observation

We investigate the possibility of lens mass determination for a caustic crossing microlensing event based on a space telescope observation. We demonstrate that the parallax due to the orbital motion of a space telescope causes a periodic fluctuation of the light curve, from which the lens distance can be derived. Since the proper motion of the lens relative to the source is also measurable for a caustic crossing event, one can find a full solution for microlensing properties of the event, including the lens mass. To determine the lens mass with sufficient accuracy, the light curve near the caustic crossing should be observed within uncertainty of $\sim$ 1%. We argue that the Hubble Space Telescope observation of the caustic crossing supplied with ground-based observations of the full light curve will enable us to determine the mass of MACHOs, which is crucial for understanding the nature of MACHOs.Comment: 9 pages + 3 figures, accepted for publication in ApJ Letter

SDSSJ143244.91+301435.3 at VLBI: a compact radio galaxy in a narrow-line Seyfert 1

We present VLBI observations, carried out with the European Very Long Baseline Interferometry Network (EVN), of SDSSJ143244.91+301435.3, a radio-loud narrow-line Seyfert 1 (RLNLS1) characterized by a steep radio spectrum. The source, compact at Very Large Array (VLA) resolution, is resolved on the milliarcsec scale, showing a central region plus two extended structures. The relatively high brightness temperature of all components (5x10^6-1.3x10^8 K) supports the hypothesis that the radio emission is non-thermal and likely produced by a relativistic jet and/or small radio lobes. The observed radio morphology, the lack of a significant core and the presence of a low frequency (230 MHz) spectral turnover are reminiscent of the Compact Steep Spectrum sources (CSS). However, the linear size of the source (~0.5kpc) measured from the EVN map is lower than the value predicted using the turnover/size relation valid for CSS sources (~6kpc). This discrepancy can be explained by an additional component not detected in our observations, accounting for about a quarter of the total source flux density, combined to projection effects. The low core-dominance of the source (CD<0.29) confirms that SDSSJ143244.91+301435.3 is not a blazar, i.e. the relativistic jet is not pointing towards the observer. This supports the idea that SDSSJ143244.91+301435.3 may belong to the "parent population" of flat-spectrum RLNLS1 and favours the hypothesis of a direct link between RLNLS1 and compact, possibly young, radio galaxies.Comment: 8 pages, 3 figures, accepted for publication in MNRA

Microlens Parallaxes with SIRTF

The Space Infrared Telescope Facility (SIRTF) will drift away from the Earth at about 0.1 AU/yr. Microlensing events will therefore have different characteristics as seen from the satellite and the Earth. From the difference, it is possible in principle to measure v-tilde, the transverse velocity of the lens projected onto the observer plane. Since v-tilde has very different values for different populations (disk, halo, Large Magellanic Cloud), such measurements could help identify the location, and hence the nature, of the lenses. I show that the method previously developed by Gould for measuring such satellite parallaxes fails completely in the case of SIRTF: it is overwhelmed by degeneracies which arise from fact that the Earth and satellite observations are in different band passes. I develop a new method which allows for observations in different band passes and yet removes all degeneracies. The method combines a purely ground-based measurement of the "parallax asymmetry" with a measurement of the delay between the time the event peaks at the Earth and satellite. In effect, the parallax asymmetry determines the component of v-tilde in the Earth-Sun direction, while the delay time measures the component of v-tilde in the direction of the Earth's orbit.Comment: 21 pages plus 3 figure

A smartphone-based multi-sensor wireless platform for cycling performance monitoring

In recent years there has been a significant evolution regarding applications for mobile devices that provide location-based services. The mobile devices available on the market already provide a set of integrated sensors and it is also possible to acquire data from external sensors. This chapter presents the development and results concerning a mobile sensing platform applied to cycling which performs data collection using both sensors integrated in the smartphone and multiple wireless sensor nodes, which are used to acquire relevant performance parameters. The data collected by the developed mobile app is stored in a local database and also uploaded to a remote database, where it can be accessed later using the mobile app or a web browser. This mobile app allows users to share data with friends, join or create events, locate friends, consult graphs and access past routes in a map. Based on these functionalities, this system aims to provide detailed feedback regarding the user performance and enhance the enjoyment of the cyclists.This work has been supported by FCT (Fundação para a Ciência e Tecnologia) in the scope of the project: UID/EEA/04436/2013.info:eu-repo/semantics/publishedVersio

Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.Comment: 4 pages, 2 figures. Submitted to ApJ Letter

Programa para a estimativa do custo e produção de energia eléctrica para uma residência

Este trabalho apresenta um programa de computador que permite determinar o custo e a produção de energia proporcionada por abastecimento pela empresa fornecedora de energia eléctrica e por instalações fotovoltaicas, eólicas e híbridas (fotovoltaicas e eólicas), em função da localização da instalação em território lusitano. Este programa leva em consideração a economia efectuada e o prazo de amortização do investimento. O programa foi realizado com a utilização das seguintes linguagens de programação: HTML, JavaScript e PHP. Pretende-se disponibilizar o uso deste programa através da Internet, para que a sua utilização possa ser alargada ao máximo número de pessoas possível.Fundação para a Ciência e a Tecnologia (FCT), financiadora com fundos FEDER e OE do Projecto POCTI/ESE/48242/2002

Rail power conditioner based on indirect AC/DC/AC modular multilevel converter using a three-phase V/V power transformer

This paper presents a rail power conditioner (RPC) system based on an indirect AC/DC/AC modular multilevel converter (MMC) where a V/V power transformer is used to feed the main catenary line and the locomotives. The proposed control strategy for this system has been introduced to guarantee a good compensating performance of negative sequence currents (NSCs) and harmonics on the public grid side. This control strategy has also the ability to achieve balanced and equal voltage between the MMC’s submodules (SMs) capacitors. Simulation results for this RPC based on an indirect MMC are presented in this paper to show the main advantages of using this topology. The results show how the proposed system is able to compensate NSCs and harmonics on the public grid side when the V/V power transformer feeds two unequal load sections.Fundação para a Ciência e Tecnologia (FCT)info:eu-repo/semantics/publishedVersio

Complete Parallax and Proper Motion Solutions For Halo Binary-Lens Microlensing Events

A major problem in the interpretation of microlensing events is that the only measured quantity, the Einstein time scale t_E, is a degenerate combination of the three quantities one would like to know, the mass, distance, and speed of the lens. This degeneracy can be partly broken by measuring either a "parallax" or a "proper motion" and completely broken by measuring both. Proper motions can easily be measured for caustic-crossing binary-lens events. Here we examine the possibility (first discussed by Hardy & Walker) that one could also measure a parallax for some of these events by comparing the light curves of the caustic crossing as seen from two observatories on Earth. We derive analytic expressions for the signal-to-noise ratio of the parallax measurement in terms of the characteristics of the source and the geometry of the event. For Galactic halo binary lenses seen toward the LMC, the light curve is delayed from one continent to another by a seemingly minuscule 15 seconds (compared to t_E ~ 40 days). However, this is sufficient to cause a difference in magnification of order 10%. To actually extract complete parallax information (as opposed to merely detecting the effect) requires observations from three non-collinear observatories. Parallaxes cannot be measured for binary lenses in the LMC but they can be measured for Galactic halo binary lenses seen toward M31. Robust measurements are possible for disk binary lenses seen toward the Galactic bulge, but are difficult for bulge binary lenses.Comment: Revised to take account of important work by Hardy & Walker (1995