Search results for "Functions"
showing 10 items of 1066 documents
Bi-homogeneity and integrability of rational potentials
2020
Abstract In this paper we consider natural Hamiltonian systems with two degrees of freedom for which Hamiltonian function has the form H = 1 2 ( p 1 2 + p 2 2 ) + V ( q 1 , q 2 ) and potential V ( q 1 , q 2 ) is a rational function. Necessary conditions for the integrability of such systems are deduced from integrability of dominate term of the potential which usually is appropriately chosen homogeneous term of V. We show that introducing weights compatible with the canonical structure one can find new dominant terms which can give new necessary conditions for integrability. To deduce them we investigate integrability of a family of bi-homogeneous potentials which depend on two integer para…
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Mutations in KIAA0586 Cause Lethal Ciliopathies Ranging from a Hydrolethalus Phenotype to Short-Rib Polydactyly Syndrome
2015
KIAA0586, the human ortholog of chicken TALPID3, is a centrosomal protein that is essential for primary ciliogenesis. Its disruption in animal models causes defects attributed to abnormal hedgehog signaling; these defects include polydactyly and abnormal dorsoventral patterning of the neural tube. Here, we report homozygous mutations of KIAA0586 in four families affected by lethal ciliopathies ranging from a hydrolethalus phenotype to short-rib polydactyly. We show defective ciliogenesis, as well as abnormal response to SHH-signaling activation in cells derived from affected individuals, consistent with a role of KIAA0586 in primary cilia biogenesis. Whereas centriolar maturation seemed una…
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Indefinite integrals for some orthogonal polynomials obtained using integrating factors
2020
A method has been presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many spec...
Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV
2019
Hessian PDF reweighting, or "profiling", has become a widely used way to study the impact of a new data set on parton distribution functions (PDFs) with Hessian error sets. The available implementations of this method have resorted to a perfectly quadratic approximation of the initial $\chi^2$ function before inclusion of the new data. We demonstrate how one can take into account the first non-quadratic components of the original fit in the reweighting, provided that the necessary information is available. We then apply this method to the CMS measurement of dijet pseudorapidity spectra in proton-proton (pp) and proton-lead (pPb) collisions at 5.02 TeV. The measured pp dijet spectra disagree…
Can we fit nuclear PDFs with the high-x CLAS data?
2020
AbstractNuclear parton distribution functions (nuclear PDFs) are non-perturbative objects that encode the partonic behaviour of bound nucleons. To avoid potential higher-twist contributions, the data probing the high-x end of nuclear PDFs are sometimes left out from the global extractions despite their potential to constrain the fit parameters. In the present work we focus on the kinematic corner covered by the new high-x data measured by the CLAS/JLab collaboration. By using the Hessian re-weighting technique, we are able to quantitatively test the compatibility of these data with globally analyzed nuclear PDFs and explore the expected impact on the valence-quark distributions at high x. W…
Bayesian PDF reweighting meets the Hessian methods
2016
Volume: 273 New data coming from the LHC experiments have a potential to extend the current knowledge of parton distribution functions (PDFs). As a short cut to the cumbersome and time consuming task of performing a new PDF fit, re weighting methods have been proposed. In this talk, we introduce the so-called Hessian re-weighting, valid for PDF fits that carried out a Hessian error analysis, and compare it with the better-known Bayesian methods. We determine the existence of an agreement between the two approaches, and illustrate this using the inclusive jet production at the LHC. Peer reviewed
On the Intrinsic Complexity of Learning
1995
AbstractA new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.
Determination of the Chiral Couplings L10 and C87 from Semileptonic τ Decays
2008
Using recent precise hadronic tau-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energy constants appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L_10^r(M_rho) = -(5.22\pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06\pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89\pm 0.19)10^{-3}GeV^{-2}. In the SU(2) chiral effective theory, the correspon…