On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A in R^{m x n} and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: * A proof that linf/l1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. * A new lower bound for the number of linear measurements required to solve l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude. * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover |x|_2 +/- eps|x|_1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of l1/l1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems

Magnetoresistance of metallic perovskite oxide LaNiO3−δ_{3-\delta}

We report a study of the magnetoresistance (MR) of the metallic perovskite oxide LaNiO$_{3-\delta}$ as a function of the oxygen stoichiometry $\delta$ ($\delta \leq$ 0.14), magnetic field (H $\leq 6T$) and temperature (1.5K $\leq$ T $\leq$ 25K). We find a strong dependence of the nature of MR on the oxygen stoichiometry. The MR at low temperatures change from positive to negative as the sample becomes more oxygen deficient (i.e, $\delta$ increases). Some of the samples which are more resistive, show a resistivity minima at $T_{min}$ $\approx$ 20K. We find that in these samples the MR is positive at T > $T_{min}$ and negative for T < $T_{min}$. We conclude that in the absence of strong magnetic interaction, the negative MR in these oxides can arise from weak localisation effects.Comment: 10 pages in REVTeX format, 4 eps fig

Magnetic and electron transport properties of the rare-earth cobaltates, La0.7-xLnxCa0.3CoO3 (Ln = Pr, Nd, Gd and Dy) : A case of phase separation

Magnetic and electrical properties of four series of rare earth cobaltates of the formula La0.7-xLnxCa0.3CoO3 with Ln = Pr, Nd, Gd and Dy have been investigated. Compositions close to x = 0.0 contain large ferromagnetic clusters or domains, and show Brillouin-like behaviour of the field-cooled DC magnetization data with fairly high ferromagnetic Tc values, besides low electrical resistivities with near-zero temperature coefficients. The zero-field-cooled data generally show a non-monotonic behaviour with a peak at a temperatures slightly lower than Tc. The near x = 0.0 compositions show a prominent peak corresponding to the Tc in the AC-susceptibility data. The ferromagnetic Tc varies linearly with x or the average radius of the A-site cations, (rA). With increase in x or decrease in (rA), the magnetization value at any given temperature decreases markedly and the AC-susceptibility measurements show a prominent transition arising from small magnetic clusters with some characteristics of a spin-glass. Electrical resistivity increases with increase in x, showed a significant increase around a critical value of x or (rA), at which composition the small clusters also begin to dominate. These properties can be understood in terms of a phase separation scenario wherein large magnetic clusters give way to smaller ones with increase in x, with both types of clusters being present in certain compositions. The changes in magnetic and electrical properties occur parallely since the large ferromagnetic clusters are hole-rich and the small clusters are hole-poor. Variable-range hopping seems to occur at low temperatures in these cobaltates.Comment: 23 pages including figure

Physical interpretation of the correlation between multi-angle spectral data and canopy height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally

An HST/COS legacy survey of high-velocity ultraviolet absorption in the Milky Way's circumgalactic medium and the Local Group

To characterize the absorption properties of this circumgalactic medium (CGM) and its relation to the LG we present the so-far largest survey of metal absorption in Galactic high-velocity clouds (HVCs) using archival ultraviolet (UV) spectra of extragalactic background sources. The UV data are obtained with the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (HST) and are supplemented by 21 cm radio observations of neutral hydrogen. Along 270 sightlines we measure metal absorption in the lines of SiII, SiIII, CII, and CIV and associated HI 21 cm emission in HVCs in the velocity range |v_LSR|=100-500 km s^-1. With this unprecedented large HVC sample we were able to improve the statistics on HVC covering fractions, ionization conditions, small-scale structure, CGM mass, and inflow rate. For the first time, we determine robustly the angular two point correlation function of the high-velocity absorbers, systematically analyze antipodal sightlines on the celestial sphere, and compare the absorption characteristics with that of Damped Lyman alpha absorbers (DLAs) and constrained cosmological simulations of the LG. Our study demonstrates that the Milky Way CGM contains sufficient gaseous material to maintain the Galactic star-formation rate at its current level. We show that the CGM is composed of discrete gaseous structures that exhibit a large-scale kinematics together with small-scale variations in physical conditions. The Magellanic Stream clearly dominates both the cross section and mass flow of high-velocity gas in the Milky Way's CGM. The possible presence of high-velocity LG gas underlines the important role of the local cosmological environment in the large-scale gas-circulation processes in and around the Milky Way (abridged).Comment: 37 pages, 25 figures, 8 tables, accepted for publication in A&

Systematics in the electron transport and magnetic properties of LnBO<SUB>3</SUB> perovskites

Systematics in the electrical and magnetic properties of transition metal perovskites LnBO3 (Ln=rare-earth ion, B=3d transition metal) with the variation of Ln and B ions are reviewed. The electrical resistivity and activation energy of LnBO3 compounds increase with the decreasing size of the Ln3+ ion for a given B ion. The low-spin to high-spin transition temperature of Co3+ ion in LnCoO3 similarly increases with the decrease in size of Ln3+ while the magnetic ordering temperatures in LnVO3, LnFeO3, LnCrO3 and LnSrCo2O6 decreases with decreasing size of the rare-earth ion. These results may be understood in terms of the increasing acidity of the rare earth ion with decreasing size and the competition between the Ln3+ and the B3+ ions for covalency with the oxygen ions. The effect of this competition on the metal oxygen covalency and crystal field parameter is discussed in relation to the results obtained and Goodenough's phase diagram. The possibility of d-f exchange interaction in La1-xLnx NiO3 is also discussed in the light of ESR results

Absorption of Electro-magnetic Waves in a Magnetized Medium

In continuation to our earlier work, in which the structure of the vacuum polarisation tensor in a medium was analysed in presence of a background electro-magnetic field, we discuss the absorptive part of the vacuum polarization tensor. Using the real time formalism of finite temperature field theory we calculate the absorptive part of 1-loop vacuum polarisation tensor in the weak field limit ($eB < m^2$). Estimates of the absorption probability are also made for different physical conditions of the background medium.Comment: 9 Pages. One figure. LaTe

Taylor Polynomial Estimator for Estimating Frequency Moments

We present a randomized algorithm for estimating the $p$th moment $F_p$ of the frequency vector of a data stream in the general update (turnstile) model to within a multiplicative factor of $1 \pm \epsilon$, for $p > 2$, with high constant confidence. For $0 < \epsilon \le 1$, the algorithm uses space $O( n^{1-2/p} \epsilon^{-2} + n^{1-2/p} \epsilon^{-4/p} \log (n))$ words. This improves over the current bound of $O(n^{1-2/p} \epsilon^{-2-4/p} \log (n))$ words by Andoni et. al. in \cite{ako:arxiv10}. Our space upper bound matches the lower bound of Li and Woodruff \cite{liwood:random13} for $\epsilon = (\log (n))^{-\Omega(1)}$ and the lower bound of Andoni et. al. \cite{anpw:icalp13} for $\epsilon = \Omega(1)$.Comment: Supercedes arXiv:1104.4552. Extended Abstract of this paper to appear in Proceedings of ICALP 201

Smart-phone based spatio-temporal sensing for annotated transit map generation

City transit maps are one of the important resources for public navigation in today's digital world. However, the availability of transit maps for many developing countries is very limited, primarily due to the various socio-economic factors that drive the private operated and partially regulated transport services. Public transports at these cities are marred with many factors such as uncoordinated waiting time at bus stoppages, crowding in the bus, sporadic road conditions etc., which also need to be annotated so that commuters can take informed decision. Interestingly, many of these factors are spatio-temporal in nature. In this paper, we develop CityMap, a system to automatically extract transit routes along with their eccentricities from spatio-temporal crowdsensed data collected via commuters' smart-phones. We apply a learning based methodology coupled with a feature selection mechanism to filter out the necessary information from raw smart-phone sensor data with minimal user engagement and drain of batt