3,977 research outputs found
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 diffractionâexploiting 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 informationâwas 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 (C6H5NâNC6H5) 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 TiâN 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 be a sparse Johnson-Lindenstrauss
transform [KN14] with non-zeroes per column. For a subset of the unit
sphere, given, we study settings for required to
ensure i.e. so that preserves the norm of every
simultaneously and multiplicatively up to . We
introduce a new complexity parameter, which depends on the geometry of , and
show that it suffices to choose and such that this parameter is small.
Our result is a sparse analog of Gordon's theorem, which was concerned with a
dense 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 H<sub>2</sub>O on TiO<sub>2</sub>(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 Ă
, 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 011ÂŻ 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 2â4 layers high are more typical. STM atomic-scale images show the (2Ă2)pg âclockâ reconstruction on the (100) terraces of the (810) surfaces with both C and N, although a second c(2Ă2) structure, most readily reconciled with a ârumplingâ 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 (1Ă1) 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
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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
, 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
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