219 research outputs found
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
Fracture of a biopolymer gel as a viscoplastic disentanglement process
We present an extensive experimental study of mode-I, steady, slow crack
dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic
stiffness to gel composition and history we confirm and extend the model for
fracture of physical hydrogels which we proposed in a previous paper (Nature
Materials, doi:10.1038/nmat1666 (2006)), which attributes decohesion to the
viscoplastic pull-out of the network-constituting chains. So, we propose that,
in contrast with chemically cross-linked ones, reversible gels fracture without
chain scission
Scattering in flatland: Efficient representations via wave atoms
This paper presents a numerical compression strategy for the boundary
integral equation of acoustic scattering in two dimensions. These equations
have oscillatory kernels that we represent in a basis of wave atoms, and
compress by thresholding the small coefficients to zero. This phenomenon was
perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context
of local Fourier bases \cite{BCG}. Their results have since then been extended
in various ways. The purpose of this paper is to bridge a theoretical gap and
prove that a well-chosen fixed expansion, the nonstandard wave atom form,
provides a compression of the acoustic single and double layer potentials with
wave number as -by- matrices with
nonnegligible entries, with a constant that depends on the relative
accuracy \eps in an acceptable way. The argument assumes smooth, separated,
and not necessarily convex scatterers in two dimensions. The essential features
of wave atoms that enable to write this result as a theorem is a sharp
time-frequency localization that wavelet packets do not obey, and a parabolic
scaling wavelength (essential diameter). Numerical experiments
support the estimate and show that this wave atom representation may be of
interest for applications where the same scattering problem needs to be solved
for many boundary conditions, for example, the computation of radar cross
sections.Comment: 39 page
Translating the terrestrial mitigation hierarchy to marine megafauna bycatch
In terrestrial and coastal systems, the mitigation hierarchy is widely and
increasingly used to guide actions to ensure that no net loss of biodiversity
ensues from development. We develop a conceptual model which applies
this approach to the mitigation of marine megafauna bycatch in fisheries,
going from defining an overarching goal with an associated quantitative
target, through avoidance, minimisation, remediation to offsetting. We
demonstrate the framework's utility as a tool for structuring thinking and
exposing uncertainties. We draw comparisons between debates ongoing in
terrestrial situations and in bycatch mitigation, to show how insights from
each could inform the other; these are the hierarchical nature of
mitigation, out-of-kind offsets, research as an offset, incentivising
implementation of mitigation measures, societal limits and uncertainty. We
explore how economic incentives could be used throughout the hierarchy to improve the achievement of bycatch goals. We conclude by highlighting the
importance of clear agreed goals, of thinking beyond single species and
individual jurisdictions to account for complex interactions and policy
leakage, of taking uncertainty explicitly into account, and of thinking
creatively about approaches to bycatch mitigation in order to improve
outcomes for conservation and fishers. We suggest that the framework set
out here could be helpful in supporting efforts to improve by catch
mitigation efforts, and highlight the need for a full empirical application to
substantiate this
Proximity effect at superconducting Sn-Bi2Se3 interface
We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions
down to 250 mK and in different magnetic fields. A number of conductance
anomalies were observed below the superconducting transition temperature of Sn,
including a small gap different from that of Sn, and a zero-bias conductance
peak growing up at lower temperatures. We discussed the possible origins of the
smaller gap and the zero-bias conductance peak. These phenomena support that a
proximity-effect-induced chiral superconducting phase is formed at the
interface between the superconducting Sn and the strong spin-orbit coupling
material Bi2Se3.Comment: 7 pages, 8 figure
Single Electrons from Heavy Flavor Decays in p+p Collisions at sqrt(s) = 200 GeV
The invariant differential cross section for inclusive electron production in
p+p collisions at sqrt(s) = 200 GeV has been measured by the PHENIX experiment
at the Relativistic Heavy Ion Collider over the transverse momentum range $0.4
<= p_T <= 5.0 GeV/c at midrapidity (eta <= 0.35). The contribution to the
inclusive electron spectrum from semileptonic decays of hadrons carrying heavy
flavor, i.e. charm quarks or, at high p_T, bottom quarks, is determined via
three independent methods. The resulting electron spectrum from heavy flavor
decays is compared to recent leading and next-to-leading order perturbative QCD
calculations. The total cross section of charm quark-antiquark pair production
is determined as sigma_(c c^bar) = 0.92 +/- 0.15 (stat.) +- 0.54 (sys.) mb.Comment: 329 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett.
Plain text data tables for the points plotted in figures for this and
previous PHENIX publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
Nuclear Modification of Electron Spectra and Implications for Heavy Quark Energy Loss in Au+Au Collisions at sqrt(s_NN)=200 GeV
The PHENIX experiment has measured mid-rapidity transverse momentum spectra
(0.4 < p_T < 5.0 GeV/c) of electrons as a function of centrality in Au+Au
collisions at sqrt(s_NN)=200 GeV. Contributions from photon conversions and
from light hadron decays, mainly Dalitz decays of pi^0 and eta mesons, were
removed. The resulting non-photonic electron spectra are primarily due to the
semi-leptonic decays of hadrons carrying heavy quarks. Nuclear modification
factors were determined by comparison to non-photonic electrons in p+p
collisions. A significant suppression of electrons at high p_T is observed in
central Au+Au collisions, indicating substantial energy loss of heavy quarks.Comment: 330 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett.
Plain text data tables for the points plotted in figures for this and
previous PHENIX publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
Inclusive cross section and double helicity asymmetry for \pi^0 production in p+p collisions at sqrt(s)=200 GeV: Implications for the polarized gluon distribution in the proton
The PHENIX experiment presents results from the RHIC 2005 run with polarized
proton collisions at sqrt(s)=200 GeV, for inclusive \pi^0 production at
mid-rapidity. Unpolarized cross section results are given for transverse
momenta p_T=0.5 to 20 GeV/c, extending the range of published data to both
lower and higher p_T. The cross section is described well for p_T < 1 GeV/c by
an exponential in p_T, and, for p_T > 2 GeV/c, by perturbative QCD. Double
helicity asymmetries A_LL are presented based on a factor of five improvement
in uncertainties as compared to previously published results, due to both an
improved beam polarization of 50%, and to higher integrated luminosity. These
measurements are sensitive to the gluon polarization in the proton, and exclude
maximal values for the gluon polarization.Comment: 375 authors, 7 pages, 3 figures. Submitted to Phys. Rev. D, Rapid
Communications. Plain text data tables for the points plotted in figures for
this and previous PHENIX publications are (or will be) publicly available at
http://www.phenix.bnl.gov/papers.htm
System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes in Cu+Cu and Au+Au Collisions at sqrt(s_NN) = 200 and 62.4 GeV
We present azimuthal angle correlations of intermediate transverse momentum
(1-4 GeV/c) hadrons from {dijets} in Cu+Cu and Au+Au collisions at sqrt(s_NN) =
62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is
broadened, non-Gaussian, and peaked away from \Delta\phi=\pi in central and
semi-central collisions in all the systems. The broadening and peak location
are found to depend upon the number of participants in the collision, but not
on the collision energy or beam nuclei. These results are consistent with sound
or shock wave models, but pose challenges to Cherenkov gluon radiation models.Comment: 464 authors from 60 institutions, 6 pages, 3 figures, 2 tables.
Submitted to Physical Review Letters. Plain text data tables for the points
plotted in figures for this and previous PHENIX publications are (or will be)
publicly available at http://www.phenix.bnl.gov/papers.htm
- …