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

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

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

Adsorption bond length for H₂O on TiO₂(110): A key parameter for theoretical understanding

Scanned-energy mode photoelectron diffraction results show the adsorption site of molecular water on TiO2(110) to be atop under-coordinated surface Ti atoms, confirming the results of total energy calculations and STM imaging. However, the Ti-Owater bond length is 2.21±0.02 Å, much longer than Ti-O bond lengths in strongly chemisorbed species on this surface, but significantly shorter than found in most total energy calculations. The need for theory to describe this weak bond effectively may be a key factor in the controversial problem of understanding this important surface reaction system

A scanning tunnelling microscopy study of C and N adsorption phases on the vicinal Ni(100) surfaces Ni(810) and Ni(911)

The influence of N and C chemisorption on the morphology and local structure of nominal Ni(810) and Ni(911) surfaces, both vicinal to (100) but with [001] and 011¯ step directions, respectively, has been investigated using scanning tunnelling microscopy (STM) and low energy electron diffraction. Ni(911) undergoes substantial step bunching in the presence of both adsorbates, with the (911)/N surface showing (411) facets, whereas for Ni(810), multiple steps 2–4 layers high are more typical. STM atomic-scale images show the (2×2)pg ‘clock’ reconstruction on the (100) terraces of the (810) surfaces with both C and N, although a second c(2×2) structure, most readily reconciled with a ‘rumpling’ reconstruction, is also seen on Ni(810)/N. On Ni(911), the clock reconstruction is not seen on the (100) terraces with either adsorbate, and these images are typified by protrusions on a (1×1) mesh. This absence of clock reconstruction is attributed to the different constraints imposed on the lateral movements of the surface Ni atoms adjacent to the up-step edge of the terraces with a [011] step direction

High-pressure optical combustion probe

An optical access probe was developed to meet the demands of a gas turbine combustor in a Cooperative Research and Development Agreement (CRADA) with the Westinghouse Science and Technology Center. The probe is water-cooled, has no external fittings, and is pressure-sealed with a conventional compression fitting. The probe utilizes a 1.0-mm diameter sapphire rod as a lightpipe for optical access and fiber optic coupling to the spectroscopic experiments. This is coupled with a fused silica optical fiber to the optical experiments employed to study the combustion process. The probe has been tested to 10{sup 6} Pa in a test combustor exhibiting 10{sup 5} Pa instability oscillations. To test its spectral range, the probe investigated OH emissions at 310 nm, C{sub 2} and CH emissions from 400 to 500 nm, Near IR emissions from 800 to 1,800 nm, and temperature measurements using an Accufiber detection system

A Multi-scale Approach for Simulations of Kelvin Probe Force Microscopy with Atomic Resolution

The distance dependence and atomic-scale contrast observed in nominal contact potential difference (CPD) signals recorded by KPFM on surfaces of insulating and semiconducting samples, have stimulated theoretical attempts to explain such effects. We attack this problem in two steps. First, the electrostatics of the macroscopic tip-cantilever-sample system is treated by a finite-difference method on an adjustable nonuniform mesh. Then the resulting electric field under the tip apex is inserted into a series of atomistic wavelet-based density functional theory (DFT) calculations. Results are shown for a realistic neutral but reactive silicon nano-scale tip interacting with a NaCl(001) sample. Bias-dependent forces and resulting atomic displacements are computed to within an unprecedented accuracy. Theoretical expressions for amplitude modulation (AM) and frequency modulation (FM) KPFM signals and for the corresponding local contact potential differences (LCPD) are obtained by combining the macroscopic and atomistic contributions to the electrostatic force component generated at the voltage modulation frequency, and evaluated for several tip oscillation amplitudes A up to 10 nm. Being essentially constant over a few Volts, the slope of atomistic force versus bias is the basic quantity which determines variations of the atomic-scale LCPD contrast. Already above A = 0.1 nm, the LCPD contrasts in both modes exhibit almost the same spatial dependence as the slope. In the AM mode, this contrast is approximately proportional to $A^{-1/2}$, but remains much weaker than the contrast in the FM mode, which drops somewhat faster as A is increased. These trends are a consequence of the macroscopic contributions to the KPFM signal, which are stronger in the AM-mode and especially important if the sample is an insulator even at sub-nanometer separations where atomic-scale contrast appears.Comment: 19 pages, 13 figure

Tension and stiffness of the hard sphere crystal-fluid interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the (001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is denoting the thermal energy and \sigma the hard sphere diameter. We compare our results with existing experimental findings

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