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

The (2√3×3)rect. phase of alkylthiolate self-assembled monolayers on Au(111): a symmetry-constrained structural solution

Low-energy electron-diffraction (LEED) patterns of the Au(111)(2√3×3)rect.-butylthiolate surface phase (a structure also seen in longer alkane chain thiolate self-assembled monolayers) show missing diffracted beams characteristic of glide symmetry, but do not show the larger set of missing beams found in surface x-ray diffraction (SXRD). The difference can be attributed to the greatly enhanced role of multiple scattering in LEED, but the combination of symmetry constraints placed on possible structural models by the observed SXRD and LEED beam extinctions greatly reduces the number of possible structural models. Only three such models are identified, one of which is clearly incompatible with other published experimental data. The relative merits of the remaining models, both involving Au adatom-thiolate moieties, are discussed in the light of the results of previous experimental studies

The local adsorption site of methylthiolate on Au(1 1 1): Bridge or atop?

Measurements of the local adsorption geometry of the S head-group atom in the Au(1 1 1)(√3 × √3)R30°–CH3S surface have been made using normal incidence X-ray standing waves (NIXSW) and S 1s scanned-energy mode photoelectron diffraction on the same surface preparations. The results confirm that the local adsorption site is atop an Au atom in a bulk-continuation site with a S–Au bondlength of 2.42 ± 0.02 Å, and that there can be no significant fraction of coadsorbed bridging species as recently proposed in a combined molecular dynamics/experimental study by Mazzarello et al. [R. Mazzarello, A. Cossaro, A. Verdini, R. Rousseau, L. Casalis, M.F. Danisman, L. Floreano, S. Scandolo, A. Morgante, G. Scoles, Phys. Rev. Lett. 98 (2007) 016102]. The results do not, however, clearly distinguish the different local reconstruction (adatom) models proposed for this surface

The local adsorption structure of benzene on Si(001)-(2 × 1): a photoelectron diffraction investigation

Scanned-energy mode C 1s photoelectron diffraction has been used to investigate the local adsorption geometry of benzene on Si(001) at saturation coverage and room temperature. The results show that two different local bonding geometries coexist, namely the 'standard butterfly' (SB) and 'tilted bridge' (TB) forms, with a composition of 58 ± 29% of the SB species. Detailed structural parameter values are presented for both species including Si–C bond lengths. On the basis of published measurements of the rate of conversion of the SB to the TB form on this surface, we estimate that the timescale of our experiment is sufficient for achieving equilibrium, and in this case our results indicate that the difference in the Gibbs free energy of adsorption, ΔG(TB)−ΔG(SB), is in the range −0.023 to +0.049 eV. We suggest, however, that the relative concentration of the two species may also be influenced by a combination of steric effects influencing the kinetics, and a sensitivity of the adsorption energies of the adsorbed SB and TB forms to the nature of the surrounding benzene molecules

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

Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.Comment: 30 pages, to appear in J Phys A Math Ge

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

The structure of the Au(111)/methylthiolate interface : new insights from near-edge X-ray absorption spectroscopy and X-ray standing waves

The local structure of the Au(111)([square root of]3×[square root of]3)R30°-methylthiolate surface phase has been investigated by S K-edge near-edge s-ray absorption fine structure (NEXAFS) both experimentally and theoretically and by experimental normal-incidence x-ray standing waves (NIXSW) at both the C and S atomic sites. NEXAFS shows not only excitation into the intramolecular sigma* S–C resonance but also into a sigma* S–Au orbital perpendicular to the surface, clearly identifying the local S headgroup site as atop a Au atom. Simulations show that it is not possible, however, to distinguish between the two possible adatom reconstruction models; a single thiolate species atop a hollow-site Au adatom or a dithiolate moiety comprising two thiolate species bonded to a bridge-bonded Au adatom. Within this dithiolate moiety a second sigma* S–Au orbital that lies near parallel to the surface has a higher energy that overlaps that of the sigma* S–C resonance. The new NIXSW data show the S–C bond to be tilted by 61° relative to the surface normal, with a preferred azimuthal orientation in , corresponding to the intermolecular nearest-neighbor directions. This azimuthal orientation is consistent with the thiolate being atop a hollow-site Au adatom, but not consistent with the originally proposed Au-adatom-dithiolate moiety. However, internal conformational changes within this species could, perhaps, render this model also consistent with the experimental data

Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge