919 research outputs found
Lossless fault-tolerant data structures with additive overhead
12th International Symposium, WADS 2011, New York, NY, USA, August 15-17, 2011. ProceedingsWe develop the first dynamic data structures that tolerate δ memory faults, lose no data, and incur only an O(δ ) additive overhead in overall space and time per operation. We obtain such data structures for arrays, linked lists, binary search trees, interval trees, predecessor search, and suffix trees. Like previous data structures, δ must be known in advance, but we show how to restore pristine state in linear time, in parallel with queries, making δ just a bound on the rate of memory faults. Our data structures require Θ(δ) words of safe memory during an operation, which may not be theoretically necessary but seems a practical assumption.Center for Massive Data Algorithmics (MADALGO
Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to
the temperature variations in the cosmic microwave background
radiation; can be observed in all directions around us. A standard
but idealised model of this effect leads to an infinite set of moment-like
equations: the integral of with respect to k ()
is equal to a given constant, , for . Here, P is the
power spectrum of the primordial density variations, is a spherical
Bessel function and y is a positive constant. It is shown how to solve these
equations exactly for ~. The same solution can be recovered, in
principle, if the first ~m equations are discarded. Comparisons with classical
moment problems (where is replaced by ) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late
Millisecond-range electron spin memory in singly-charged InP quantum dots
We report millisecond-range spin memory of resident electrons in an ensemble
of InP quantum dots (QDs) under a small magnetic field of 0.1 T applied along
the optical excitation axis at temperatures up to about 5 K. A pump-probe
photoluminescence (PL) technique is used for optical orientation of electron
spins by the pump pulses and for study of spin relaxation over the long time
scale by measuring the degree of circular polarization of the probe PL as a
function of pump-probe delay. Dependence of spin decay rate on magnetic field
and temperature suggests two-phonon processes as the dominant spin relaxation
mechanism in this QDs at low temperatures.Comment: 3 pages, 4 figures, submitted to Appl. Phys. Let
Spectral properties of the Dirichlet-to-Neumann operator for exterior Helmholtz problem and its applications to scattering theory
We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the
lower half of the complex plane. We find several application of this fact in
scattering by obstacles with impedance boundary conditions. In particular, we
find an upper bound for the gradient of the scattering amplitude and for the
total cross section. We justify numerical approximations by providing bounds on
difference between theoretical and approximated solutions without using any a
priory unknown constants
The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding
Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer
Inverse medium problem for a singular contrast
We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.Peer reviewe
Mathematical practice, crowdsourcing, and social machines
The highest level of mathematics has traditionally been seen as a solitary
endeavour, to produce a proof for review and acceptance by research peers.
Mathematics is now at a remarkable inflexion point, with new technology
radically extending the power and limits of individuals. Crowdsourcing pulls
together diverse experts to solve problems; symbolic computation tackles huge
routine calculations; and computers check proofs too long and complicated for
humans to comprehend.
Mathematical practice is an emerging interdisciplinary field which draws on
philosophy and social science to understand how mathematics is produced. Online
mathematical activity provides a novel and rich source of data for empirical
investigation of mathematical practice - for example the community question
answering system {\it mathoverflow} contains around 40,000 mathematical
conversations, and {\it polymath} collaborations provide transcripts of the
process of discovering proofs. Our preliminary investigations have demonstrated
the importance of "soft" aspects such as analogy and creativity, alongside
deduction and proof, in the production of mathematics, and have given us new
ways to think about the roles of people and machines in creating new
mathematical knowledge. We discuss further investigation of these resources and
what it might reveal.
Crowdsourced mathematical activity is an example of a "social machine", a new
paradigm, identified by Berners-Lee, for viewing a combination of people and
computers as a single problem-solving entity, and the subject of major
international research endeavours. We outline a future research agenda for
mathematics social machines, a combination of people, computers, and
mathematical archives to create and apply mathematics, with the potential to
change the way people do mathematics, and to transform the reach, pace, and
impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent
Computer Mathematics, CICM 2013, July 2013 Bath, U
S-wave Meson-Meson Scattering from Unitarized U(3) Chiral Lagrangians
An investigation of the s-wave channels in meson-meson scattering is
performed within a U(3) chiral unitary approach. Our calculations are based on
a chiral effective Lagrangian which includes the eta' as an explicit degree of
freedom and incorporates important features of the underlying QCD Lagrangian
such as the axial U(1) anomaly. We employ a coupled channel Bethe-Salpeter
equation to generate poles from composed states of two pseudoscalar mesons. Our
results are compared with experimental phase shifts up to 1.5 GeV and effects
of the eta' within this scheme are discussed.Comment: 18 pages, 6 figure
- …