Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds

Photoelectron diffraction: from phenomenological demonstration to practical tool

The potential of photoelectron diffraction—exploiting the coherent interference of directly-emitted and elastically scattered components of the photoelectron wavefield emitted from a core level of a surface atom to obtain structural information—was first appreciated in the 1970s. The first demonstrations of the effect were published towards the end of that decade, but the method has now entered the mainstream armoury of surface structure determination. This short review has two objectives: First, to outline the way that the idea emerged and the way this evolved in my own collaboration with Neville Smith and his colleagues at Bell Labs in the early years: Second, to provide some insight into the current state-of-the art in application of (scanned-energy mode) photoelectron diffraction to address two key issue in quantitative surface structure determination, namely, complexity and precision. In this regard a particularly powerful aspect of photoelectron diffraction is its elemental and chemical-state specificity

The Keck Aperture Masking Experiment: spectro-interferometry of 3 Mira Variables from 1.1 to 3.8 microns

We present results from a spectro-interferometric study of the Miras o Cet, R Leo and W Hya obtained with the Keck Aperture Masking Experiment from 1998 Sep to 2002 Jul. The spectrally dispersed visibility data permit fitting with circularly symmetric brightness profiles such as a simple uniform disk. The stellar angular diameter obtained over up to ~ 450 spectral channels spaning the region 1.1-3.8 microns is presented. Use of a simple uniform disk brightness model facilitates comparison between epochs and with existing data and theoretical models. Strong size variations with wavelength were recorded for all stars, probing zones of H2O, CO, OH, and dust formation. Comparison with contemporaneous spectra extracted from our data show a strong anti-correlation between the observed angular diameter and flux. These variations consolidate the notion of a complex stellar atmosphere consisting of molecular shells with time-dependent densities and temperatures. Our findings are compared with existing data and pulsation models. The models were found to reproduce the functional form of the wavelength vs. angular diameter curve well, although some departures are noted in the 2.8-3.5 micron range.Comment: 10 pages, 10 figures Accepted to Ap

Optimal Principal Component Analysis in Distributed and Streaming Models

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to output an $m \times k$ orthonormal matrix $U$ for which $$|| A - U U^T A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2,$$ where $A_k \in R^{m \times n}$ is the best rank-$k$ approximation to $A$. This paper provides improved algorithms for distributed PCA and streaming PCA.Comment: STOC2016 full versio

The Pulsation of Chi Cygni Imaged by Optical Interferometry; a Novel Technique to Derive Distance and Mass of Mira Stars

We present infrared interferometric imaging of the S-type Mira star Chi Cygni. The object was observed at four different epochs in 2005-2006 with the IOTA optical interferometer (H band). Images show up to 40% variation in the stellar diameter, as well as significant changes in the limb darkening and stellar inhomogeneities. Model fitting gave precise time-dependent values of the stellar diameter, and reveals presence and displacement of a warm molecular layer. The star radius, corrected for limb darkening, has a mean value of 12.1 mas and shows a 5.1mas amplitude pulsation. Minimum diameter was observed at phase 0.94+/-0.01. Maximum temperature was observed several days later at phase 1.02+/-0.02. We also show that combining the angular acceleration of the molecular layer with CO (Delta v = 3) radial velocity measurements yields a 5.9+/-1.5 mas parallax. The constant acceleration of the CO molecules -- during 80% of the pulsation cycle -- lead us to argument for a free-falling layer. The acceleration is compatible with a gravitational field produced by a 2.1(+1.5/-0.7) solar mass star. This last value is in agreement with fundamental mode pulsator models. We foresee increased development of techniques consisting in combining radial velocity with interferometric angular measurements, ultimately allowing total mapping of the speed, density, and position of the diverse species in pulsation driven atmospheres.Comment: 36 pages, accepted in Ap

CU Comae: a new field double-mode RR Lyrae, the most metal poor discovered to date

We report the discovery of a new double-mode RR Lyrae variable (RRd) in the field of our Galaxy: CU Comae. CU Comae is the sixth such RRd identified to date and is the most metal-poor RRd ever detected. Based on BVI CCD photometry spanning eleven years of observations, we find that CU Comae has periods P0=0.5441641 +/-0.0000049d and P1=0.4057605 +/-0.0000018d. The amplitude of the primary (first-overtone) period of CU Comae is about twice the amplitude of the secondary (fundamental) period. The combination of the fundamental period of pulsation P0 and the period ratio of P1/P0=0.7457 places the variable on the metal-poor side of the Petersen diagram, in the region occupied by M68 and M15 RRd's. A mass of 0.83 solar masses is estimated for CU Comae using an updated theoretical calibration of the Petersen diagram. High resolution spectroscopy (R=30,000) covering the full pulsation cycle of CU Comae was obtained with the 2.7 m telescope of the Mc Donald Observatory, and has been used to build up the radial velocity curve of the variable. Abundance analysis done on the four spectra taken near minimum light (phase: 0.54 -- 0.71) confirms the metal poor nature of CU Comae, for which we derive [Fe/H]=-2.38 +/-0.20. This value places this new RRd at the extreme metal-poor edge of the metallicity distribution of the RR Lyrae variables in our Galaxy.Comment: 21 pages including 8 Tables, Latex, 11 Figures. Accepted for publication in The Astronomical Journal, October 2000 issu

Two-body Pion Absorption on 3He^3He at Threshold

It is shown that a satisfactory explanation of the ratio of the rates of the reactions $^3He(\pi^-,nn)$ and $^3He(\pi^-,np)$ for stopped pions is obtained once the effect of the short range two-nucleon components of the axial charge operator for the nuclear system is taken into account. By employing realistic models for the nucleon-nucleon interaction in the construction of these components of the axial charge operator, the predicted ratios agree with the empirical value to within 10-20\%.Comment: 19, UHPHYDOR-94-

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence

Statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the kinetic energy spectrum have been calculated in the leading order in Mach number expansion. Furthermore, in this approximation the validity of the Kolmogorov hypothesis on the independence of dissipation length of velocity correlation functions in the inertial range has been proved.Comment: REVTEX file with EPS figure