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 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

The adsorption structure of furan on Pd(1 1 1)

The structure of molecular furan, C4H4O, on Pd(1 1 1) has been investigated by O K-edge near-edge X-ray absorption fine structure (NEXAFS) and C 1s scanned-energy mode photoelectron diffraction (PhD). NEXAFS shows the molecule to be adsorbed with the molecular plane close to parallel to the surface, a conclusion confirmed by the PhD analysis. Chemical-state specific C 1s PhD data were obtained for the two inequivalent C atoms in the furan, the α-C atoms adjacent to the O atom, and the β-C atoms bonded only to C atoms, but only the PhD modulations for the α-C emitters were of sufficiently large amplitude for detailed evaluation using multiple scattering calculations. This analysis shows the α-C atoms to be located approximately 0.6 Å off-atop surface Pd atoms with an associated C–Pd bondlength of 2.13 ± 0.03 Å. Two alternative local geometries consistent with the data place the O atom in off-atop or near-hollow locations, and for each of these local structures there are two equally-possible registries relative to the fcc and hcp hollow sites. The results are in good agreement with earlier density functional theory calculations which indicate that the fcc and hcp registries are equally probable, but the PhD results fail to distinguish the two distinct local bonding geometries

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

A structural study of a C3H3 species coadsorbed with CO on Pd(1 1 1)

The combination of chemical-state-specific C 1s scanned-energy mode photoelectron diffraction (PhD) and O K-edge near-edge X-ray absorption fine structure (NEXAFS) has been used to determine the local adsorption geometry of the coadsorbed C3H3 and CO species formed on Pd(1 1 1) by dissociation of molecular furan. CO is found to adopt the same geometry as in the Pd(1 1 1)c(4 × 2)-CO phase, occupying the two inequivalent three-fold coordinated hollow sites with the C–O axis perpendicular to the surface. C3H3 is found to lie with its molecular plane almost parallel to the surface, most probably with the two ‘outer’ C atoms in equivalent off-atop sites, although the PhD analysis formally fails to distinguish between two distinct local adsorption sites

Toward a unified theory of sparse dimensionality reduction in Euclidean space

Let $\Phi\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column. For a subset $T$ of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $$\mathop{\mathbb{E}}_\Phi \sup_{x\in T} \left|\|\Phi x\|_2^2 - 1 \right| < \varepsilon ,$$ i.e. so that $\Phi$ preserves the norm of every $x\in T$ simultaneously and multiplicatively up to $1+\varepsilon$. We introduce a new complexity parameter, which depends on the geometry of $T$, and show that it suffices to choose $s$ and $m$ such that this parameter is small. Our result is a sparse analog of Gordon's theorem, which was concerned with a dense $\Phi$ having i.i.d. Gaussian entries. We qualitatively unify several results related to the Johnson-Lindenstrauss lemma, subspace embeddings, and Fourier-based restricted isometries. Our work also implies new results in using the sparse Johnson-Lindenstrauss transform in numerical linear algebra, classical and model-based compressed sensing, manifold learning, and constrained least squares problems such as the Lasso

Identifying the Azobenzene/Aniline reaction intermediate on TiO2-(110) : a DFT Study

Density functional theory (DFT) calculations, both with and without dispersion corrections, have been performed to investigate the nature of the common surface reaction intermediate that has been shown to exist on TiO2(110) as a result of exposure to either azobenzene (C6H5N═NC6H5) or aniline (C6H5NH2). Our results confirm the results of a previous DFT study that dissociation of azobenzene into two adsorbed phenyl imide (C6H5N) fragments, as was originally proposed, is not energetically favorable. We also find that deprotonation of aniline to produce this surface species is even more strongly energetically disfavored. A range of alternative surface species has been considered, and while dissociation of azobenzene to form surface C6H4NH species is energetically favored, the same surface species cannot form from adsorbed aniline. On the contrary, adsorbed aniline is much the most stable surface species. Comparisons with experimental determinations of the local adsorption site, the Ti–N bond length, the molecular orientation, and the associated C 1s and N 1s photoelectron core level shifts are all consistent with the DFT results for adsorbed aniline and are inconsistent with other adsorbed species considered. Possible mechanisms for the hydrogenation of azobenzene required to produce this surface species are discussed

Oscillatory Electron-Phonon Coupling in Ultra-Thin Silver Films on V(100)

The temperature dependence of peak widths in high resolution angle-resolved photoelectron spectroscopy from quantum well states in ultra thin Ag films on V(100) has been used to determine the electron-phonon coupling constant, lambda, for films of thickness 1-8 layers. A strong oscillatory variation in coupling strength is observed as a function of film thickness, peaking at a 2 layer film for which lambda~1. A simple theory incorporating interaction of the photo-hole with the thermal vibrations of the potential step at the adlayer-vacuum interface is shown to reproduce the main features of these results.Comment: 6 pages, 3 figure