2,717 research outputs found
Almost-Euclidean subspaces of via tensor products: a simple approach to randomness reduction
It has been known since 1970's that the N-dimensional -space contains
nearly Euclidean subspaces whose dimension is . However, proofs of
existence of such subspaces were probabilistic, hence non-constructive, which
made the results not-quite-suitable for subsequently discovered applications to
high-dimensional nearest neighbor search, error-correcting codes over the
reals, compressive sensing and other computational problems. In this paper we
present a "low-tech" scheme which, for any , allows to exhibit nearly
Euclidean -dimensional subspaces of while using only
random bits. Our results extend and complement (particularly) recent work
by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1)
simplicity (we use only tensor products) and (2) yielding "almost Euclidean"
subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor
change
Amenability of algebras of approximable operators
We give a necessary and sufficient condition for amenability of the Banach
algebra of approximable operators on a Banach space. We further investigate the
relationship between amenability of this algebra and factorization of
operators, strengthening known results and developing new techniques to
determine whether or not a given Banach space carries an amenable algebra of
approximable operators. Using these techniques, we are able to show, among
other things, the non-amenability of the algebra of approximable operators on
Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic
Hastings' additivity counterexample via Dvoretzky's theorem
The goal of this note is to show that Hastings' counterexample to the
additivity of minimal output von Neumann entropy can be readily deduced from a
sharp version of Dvoretzky's theorem on almost spherical sections of convex
bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the
paper essentially self-containe
Nonlinear spectral calculus and super-expanders
Nonlinear spectral gaps with respect to uniformly convex normed spaces are
shown to satisfy a spectral calculus inequality that establishes their decay
along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to
behave sub-multiplicatively under zigzag products. These results yield a
combinatorial construction of super-expanders, i.e., a sequence of 3-regular
graphs that does not admit a coarse embedding into any uniformly convex normed
space.Comment: Typos fixed based on referee comments. Some of the results of this
paper were announced in arXiv:0910.2041. The corresponding parts of
arXiv:0910.2041 are subsumed by the current pape
Impact of solid-electrolyte interphase reformation on capacity loss in silicon-based lithium-ion batteries
High-density silicon composite anodes show large volume changes upon charging/discharging triggering the reformation of the solid electrolyte interface (SEI), an interface initially formed at the silicon surface. The question remains how the reformation process and accompanied material evolution, in particular for industrial up-scalable cells, impacts cell performance. Here, we develop a correlated workflow incorporating X-ray microscopy, field-emission scanning electron microscopy tomography, elemental imaging and deep learning-based microstructure quantification suitable to witness the structural and chemical progression of the silicon and SEI reformation upon cycling. The nanometer-sized SEI layer evolves into a micron-sized silicon electrolyte composite structure at prolonged cycles. Experimental-informed electrochemical modelling endorses an underutilisation of the active material due to the silicon electrolyte composite growth affecting the capacity. A chemo-mechanical model is used to analyse the stability of the SEI/silicon reaction front and to investigate the effects of material properties on the stability that can affect the capacity loss
Multijet production in neutral current deep inelastic scattering at HERA and determination of α_{s}
Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 5 GeV and –1 < η_{LAB}^{jet} < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant α_{s} (M_{z}), determined from the ratio of the trijet to dijet cross sections, is α_{s} (M_{z}) = 0.1179 ± 0.0013 (stat.)_{-0.0046}^{+0.0028}(exp.)_{-0.0046}^{+0.0028}(th.)
Jet production in charged current deep inelastic e⁺p scatteringat HERA
The production rates and substructure of jets have been studied in charged current deep inelastic e⁺p scattering for Q² > 200 GeV² with the ZEUS detector at HERA using an integrated luminosity of 110.5 pb⁻¹. Inclusive jet cross sections are presented for jets with transverse energies E_{T}^{jet} > 5 GeV. Measurements of the mean subjet multiplicity, 〈n_{sbj}〉, of the inclusive jet sample are presented. Predictions based on parton-shower Monte Carlo models and next-to-leading-order QCD calculations are compared to the measurements. The value of α_{s} (M_{z}), determined from 〈n_{sbj}〉 at y_{cut} = 10⁻² for jets with 25 < E_{T}^{jet} < 119 GeV, is α_{s} (M_{z}) = 0.1202 ± 0.0052 (stat.)_{-0.0019}^{+0.0060} (syst.)_{-0.0053}^{+0.0065} (th.). The mean subjet multiplicity as a function of Q² is found to be consistent with that measured in NC DIS
Covering convex bodies by cylinders and lattice points by flats
In connection with an unsolved problem of Bang (1951) we give a lower bound
for the sum of the base volumes of cylinders covering a d-dimensional convex
body in terms of the relevant basic measures of the given convex body. As an
application we establish lower bounds on the number of k-dimensional flats
(i.e. translates of k-dimensional linear subspaces) needed to cover all the
integer points of a given convex body in d-dimensional Euclidean space for
0<k<d
Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj
Nuclear shadowing is observed in the per-nucleon cross-sections of positive
muons on carbon, calcium and lead as compared to deuterium. The data were taken
by Fermilab experiment E665 using inelastically scattered muons of mean
incident momentum 470 GeV/c. Cross-section ratios are presented in the
kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are
consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj
decreases, the size of the shadowing effect, as well as its A dependence, are
found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.
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