698 research outputs found
Collapsing Superstring Conjecture
In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits 2 11/23-approximation in polynomial time (Mucha, SODA\u2713). While this algorithm and its analysis are technically involved, the 30 years old Greedy Conjecture claims that the trivial and efficient Greedy Algorithm gives a 2-approximation for SCS.
We develop a graph-theoretic framework for studying approximation algorithms for SCS. The framework is reminiscent of the classical 2-approximation for Traveling Salesman: take two copies of an optimal solution, apply a trivial edge-collapsing procedure, and get an approximate solution. In this framework, we observe two surprising properties of SCS solutions, and we conjecture that they hold for all input instances. The first conjecture, that we call Collapsing Superstring conjecture, claims that there is an elementary way to transform any solution repeated twice into the same graph G. This conjecture would give an elementary 2-approximate algorithm for SCS. The second conjecture claims that not only the resulting graph G is the same for all solutions, but that G can be computed by an elementary greedy procedure called Greedy Hierarchical Algorithm.
While the second conjecture clearly implies the first one, perhaps surprisingly we prove their equivalence. We support these equivalent conjectures by giving a proof for the special case where all input strings have length at most 3 (which until recently had been the only case where the Greedy Conjecture was proven). We also tested our conjectures on millions of instances of SCS.
We prove that the standard Greedy Conjecture implies Greedy Hierarchical Conjecture, while the latter is sufficient for an efficient greedy 2-approximate approximation of SCS. Except for its (conjectured) good approximation ratio, the Greedy Hierarchical Algorithm provably finds a 3.5-approximation, and finds exact solutions for the special cases where we know polynomial time (not greedy) exact algorithms: (1) when the input strings form a spectrum of a string (2) when all input strings have length at most 2
Quantitative analysis of directional spontaneous emission spectra from light sources in photonic crystals
We have performed angle-resolved measurements of spontaneous-emission spectra
from laser dyes and quantum dots in opal and inverse opal photonic crystals.
Pronounced directional dependencies of the emission spectra are observed:
angular ranges of strongly reduced emission adjoin with angular ranges of
enhanced emission. It appears that emission from embedded light sources is
affected both by the periodicity and by the structural imperfections of the
crystals: the photons are Bragg diffracted by lattice planes and scattered by
unavoidable structural disorder. Using a model comprising diffuse light
transport and photonic band structure, we quantitatively explain the
directional emission spectra. This provides detailed understanding of the
transport of spontaneously emitted light in real photonic crystals, which is
essential in the interpretation of quantum-optics in photonic band-gap crystals
and for applications wherein directional emission and total emission power are
controlled.Comment: 10 pages, 10 figures, corrected pdf, inserted new referenc
Strongly nonexponential time-resolved fluorescence of quantum-dot ensembles in three-dimensional photonic crystals
We observe experimentally that ensembles of quantum dots in three-dimensional (3D) photonic crystals reveal strongly nonexponential time-resolved emission. These complex emission decay curves are analyzed with a continuous distribution of decay rates. The log-normal distribution describes the decays well for all studied lattice parameters. The distribution width is identified with variations of the radiative emission rates of quantum dots with various positions and dipole orientations in the unit cell. We find a striking sixfold change of the width of the distribution by varying the lattice parameter. This interpretation qualitatively agrees with the calculations of the 3D projected local density of states. We therefore conclude that fluorescence decay of ensembles of quantum dots is highly nonexponential to an extent that is controlled by photonic crystals
Minimum Common String Partition: Exact Algorithms
In the minimum common string partition problem (MCSP), one gets two strings and is asked to find the minimum number of cuts in the first string such that the second string can be obtained by rearranging the resulting pieces. It is a difficult algorithmic problem having applications in computational biology, text processing, and data compression. MCSP has been studied extensively from various algorithmic angles: there are many papers studying approximation, heuristic, and parameterized algorithms. At the same time, almost nothing is known about its exact complexity. In this paper, we present new results in this direction. We improve the known 2? upper bound (where n is the length of input strings) to ?? where ? ? 1.618... is the golden ratio. The algorithm uses Fibonacci numbers to encode subsets as monomials of a certain implicit polynomial and extracts one of its coefficients using the fast Fourier transform. Then, we show that the case of constant size alphabet can be solved in subexponential time 2^{O(nlog log n/log n)} by a hybrid strategy: enumerate all long pieces and use dynamic programming over histograms of short pieces. Finally, we prove almost matching lower bounds assuming the Exponential Time Hypothesis
Size-Dependence of the Wavefunction of Self-Assembled Quantum Dots
The radiative and non-radiative decay rates of InAs quantum dots are measured
by controlling the local density of optical states near an interface. From
time-resolved measurements we extract the oscillator strength and the quantum
efficiency and their dependence on emission energy. From our results and a
theoretical model we determine the striking dependence of the overlap of the
electron and hole wavefunctions on the quantum dot size. We conclude that the
optical quality is best for large quantum dots, which is important in order to
optimally tailor quantum dot emitters for, e.g., quantum electrodynamics
experiments.Comment: 5 pages, 3 figure
Attributable deaths and disability-adjusted life-years caused by infections with antibiotic-resistant bacteria in the EU and the European Economic Area in 2015: a population-level modelling analysis
Background: Infections due to antibiotic-resistant bacteria are threatening modern health care. However, estimating their incidence, complications, and attributable mortality is challenging. We aimed to estimate the burden of infections caused by antibiotic-resistant bacteria of public health concern in countries of the EU and European Economic Area (EEA) in 2015, measured in number of cases, attributable deaths, and disability-adjusted life-years (DALYs).
Methods: We estimated the incidence of infections with 16 antibiotic resistance–bacterium combinations from European Antimicrobial Resistance Surveillance Network (EARS-Net) 2015 data that was country-corrected for population coverage. We multiplied the number of bloodstream infections (BSIs) by a conversion factor derived from the European Centre for Disease Prevention and Control point prevalence survey of health-care-associated infections in European acute care hospitals in 2011–12 to estimate the number of non-BSIs. We developed disease outcome models for five types of infection on the basis of systematic reviews of the literature.
Findings: From EARS-Net data collected between Jan 1, 2015, and Dec 31, 2015, we estimated 671 689 (95% uncertainty interval [UI] 583 148–763 966) infections with antibiotic-resistant bacteria, of which 63·5% (426 277 of 671 689) were associated with health care. These infections accounted for an estimated 33 110 (28 480–38 430) attributable deaths and 874 541 (768 837–989 068) DALYs. The burden for the EU and EEA was highest in infants (aged <1 year) and people aged 65 years or older, had increased since 2007, and was highest in Italy and Greece.
Interpretation: Our results present the health burden of five types of infection with antibiotic-resistant bacteria expressed, for the first time, in DALYs. The estimated burden of infections with antibiotic-resistant bacteria in the EU and EEA is substantial compared with that of other infectious diseases, and has increased since 2007. Our burden estimates provide useful information for public health decision-makers prioritising interventions for infectious diseases
Charge separation relative to the reaction plane in Pb-Pb collisions at TeV
Measurements of charge dependent azimuthal correlations with the ALICE
detector at the LHC are reported for Pb-Pb collisions at TeV. Two- and three-particle charge-dependent azimuthal correlations in
the pseudo-rapidity range are presented as a function of the
collision centrality, particle separation in pseudo-rapidity, and transverse
momentum. A clear signal compatible with a charge-dependent separation relative
to the reaction plane is observed, which shows little or no collision energy
dependence when compared to measurements at RHIC energies. This provides a new
insight for understanding the nature of the charge dependent azimuthal
correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published
version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286
A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE
In this small note we are concerned with the solution of Forward-Backward
Stochastic Differential Equations (FBSDE) with drivers that grow quadratically
in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem
is a comparison result that allows comparing componentwise the signs of the
control processes of two different qgFBSDE. As a byproduct one obtains
conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio
Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at , 2.76 and 7 TeV
Measurements of the sphericity of primary charged particles in minimum bias
proton--proton collisions at , 2.76 and 7 TeV with the ALICE
detector at the LHC are presented. The observable is linearized to be collinear
safe and is measured in the plane perpendicular to the beam direction using
primary charged tracks with GeV/c in . The
mean sphericity as a function of the charged particle multiplicity at
mid-rapidity () is reported for events with different
scales ("soft" and "hard") defined by the transverse momentum of the leading
particle. In addition, the mean charged particle transverse momentum versus
multiplicity is presented for the different event classes, and the sphericity
distributions in bins of multiplicity are presented. The data are compared with
calculations of standard Monte Carlo event generators. The transverse
sphericity is found to grow with multiplicity at all collision energies, with a
steeper rise at low , whereas the event generators show the
opposite tendency. The combined study of the sphericity and the mean with multiplicity indicates that most of the tested event generators
produce events with higher multiplicity by generating more back-to-back jets
resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with
tune PERUGIA-2011 exhibits a noticeable improvement in describing the data,
compared to the other tested generators.Comment: 21 pages, 9 captioned figures, 3 tables, authors from page 16,
published version, figures from
http://aliceinfo.cern.ch/ArtSubmission/node/308
Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at TeV
The elliptic, , triangular, , and quadrangular, , azimuthal
anisotropic flow coefficients are measured for unidentified charged particles,
pions and (anti-)protons in Pb-Pb collisions at TeV
with the ALICE detector at the Large Hadron Collider. Results obtained with the
event plane and four-particle cumulant methods are reported for the
pseudo-rapidity range at different collision centralities and as a
function of transverse momentum, , out to GeV/.
The observed non-zero elliptic and triangular flow depends only weakly on
transverse momentum for GeV/. The small dependence
of the difference between elliptic flow results obtained from the event plane
and four-particle cumulant methods suggests a common origin of flow
fluctuations up to GeV/. The magnitude of the (anti-)proton
elliptic and triangular flow is larger than that of pions out to at least
GeV/ indicating that the particle type dependence persists out
to high .Comment: 16 pages, 5 captioned figures, authors from page 11, published
version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186
- …