50,944 research outputs found
The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems
Based on the Kupershmidt deformation for any integrable bi-Hamiltonian
systems presented in [4], we propose the generalized Kupershmidt deformation to
construct new systems from integrable bi-Hamiltonian systems, which provides a
nonholonomic perturbation of the bi-Hamiltonian systems. The generalized
Kupershmidt deformation is conjectured to preserve integrability. The
conjecture is verified in a few representative cases: KdV equation, Boussinesq
equation, Jaulent-Miodek equation and Camassa-Holm equation. For these specific
cases, we present a general procedure to convert the generalized Kupershmidt
deformation into the integrable Rosochatius deformation of soliton equation
with self-consistent sources, then to transform it into a -type
bi-Hamiltonian system. By using this generalized Kupershmidt deformation some
new integrable systems are derived. In fact, this generalized Kupershmidt
deformation also provides a new method to construct the integrable Rosochatius
deformation of soliton equation with self-consistent sources.Comment: 21 pages, to appear in Journal of Mathematical Physic
Enhancing network robustness for malicious attacks
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors
proposed a simple measure for network robustness under malicious attacks on
nodes. With a greedy algorithm, they found the optimal structure with respect
to this quantity is an onion structure in which high-degree nodes form a core
surrounded by rings of nodes with decreasing degree. However, in real networks
the failure can also occur in links such as dysfunctional power cables and
blocked airlines. Accordingly, complementary to the node-robustness measurement
(), we propose a link-robustness index (). We show that solely
enhancing cannot guarantee the improvement of . Moreover, the
structure of -optimized network is found to be entirely different from
that of onion network. In order to design robust networks resistant to more
realistic attack condition, we propose a hybrid greedy algorithm which takes
both the and into account. We validate the robustness of our
generated networks against malicious attacks mixed with both nodes and links
failure. Finally, some economical constraints for swapping the links in real
networks are considered and significant improvement in both aspects of
robustness are still achieved.Comment: 6 pages, 6 figure
Threshold Resummed and Approximate NNLO results for W+W- Pair Production at the LHC
The next-to-leading order (NLO) QCD radiative corrections to W+W- production
at hadron colliders are well understood. We combine NLO perturbative QCD
calculations with soft-gluon resummation of threshold logarithms to find a
next-to-next-to leading logarithmic (NNLL) prediction for the total cross
section and the invariant mass distribution at the LHC. We also obtain
approximate next-to-next-to-leading order (NNLO) results for the total W+W-
cross section at the LHC which includes all contributions from the scale
dependent leading singular terms. Our result for the approximate NNLO total
cross section is the most precise theoretical prediction available.
Uncertainties due to scale variation are shown to be small when the threshold
logarithms are included. NNLL threshold resummation increases the W+W-
invariant mass distribution by ~ 3-4% in the peak region for both \sqrt{S}=8
and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections
increase the NLO cross section by 0.5-3% for \sqrt{S}=7, 8, 13, and 14 TeV.Comment: 29 pages, 7 figures, 3 tables. Discussion added to introduction,
references updated, and typos correcte
Conductance oscillation and quantization in monoatomic Al wires
We present first-principles calculations for the transport properties of
monoatomic Al wires sandwiched between Al(100) electrodes. The conductance of
the monoatomic Al wires oscillates with the number of the constituent atoms as
a function of the wire length, either with a period of four-atom for wires with
the typical interatomic spacing or a period of six-atom with the interatomic
spacing of the bulk fcc aluminum, indicating a dependence of the period of
conductance oscillation on the interatomic distance of the monoatomic Al wires
Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing
We propose and demonstrate localized mode coupling as a viable dispersion
engineering technique for phase-matched resonant four-wave mixing (FWM). We
demonstrate a dual-cavity resonant structure that employs coupling-induced
frequency splitting at one of three resonances to compensate for cavity
dispersion, enabling phase-matching. Coupling strength is controlled by thermal
tuning of one cavity enabling active control of the resonant
frequency-matching. In a fabricated silicon microresonator, we show an 8 dB
enhancement of seeded FWM efficiency over the non-compensated state. The
measured four-wave mixing has a peak wavelength conversion efficiency of -37.9
dB across a free spectral range (FSR) of 3.334 THz (27 nm). Enabled by
strong counteraction of dispersion, this FSR is, to our knowledge, the largest
in silicon to demonstrate FWM to date. This form of mode-coupling-based, active
dispersion compensation can be beneficial for many FWM-based devices including
wavelength converters, parametric amplifiers, and widely detuned correlated
photon-pair sources. Apart from compensating intrinsic dispersion, the proposed
mechanism can alternatively be utilized in an otherwise dispersionless
resonator to counteract the detuning effect of self- and cross-phase modulation
on the pump resonance during FWM, thereby addressing a fundamental issue in the
performance of light sources such as broadband optical frequency combs
Why not Merge the International Monetary Fund (IMF) with the International Bank for Reconstruction and Development (World Bank)
Motivation: Cellular Electron CryoTomography (CECT) is an emerging 3D imaging technique that visualizes subcellular organization of single cells at sub-molecular resolution and in near-native state. CECT captures large numbers of macromolecular complexes of highly diverse structures and abundances. However, the structural complexity and imaging limits complicate the systematic de novo structural recovery and recognition of these macromolecular complexes. Efficient and accurate reference-free subtomogram averaging and classification represent the most critical tasks for such analysis. Existing subtomogram alignment based methods are prone to the missing wedge effects and low signal-to-noise ratio (SNR). Moreover, existing maximum-likelihood based methods rely on integration operations, which are in principle computationally infeasible for accurate calculation. Results: Built on existing works, we propose an integrated method, Fast Alignment Maximum Likelihood method (FAML), which uses fast subtomogram alignment to sample sub-optimal rigid transformations. The transformations are then used to approximate integrals for maximum-likelihood update of subtomogram averages through expectation-maximization algorithm. Our tests on simulated and experimental subtomograms showed that, compared to our previously developed fast alignment method (FA), FAML is significantly more robust to noise and missing wedge effects with moderate increases of computation cost. Besides, FAML performs well with significantly fewer input subtomograms when the FA method fails. Therefore, FAML can serve as a key component for improved construction of initial structuralmodels frommacromolecules captured by CECT
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