Polynomial algorithms for partitioning a tree into single-center subtrees to minimize flat service costs

This paper deals with the following graph partitioning problem. Consider a connected graph with n nodes, p of which are centers, while the remaining ones are units. For each unit-center pair there is a fixed service cost and the goal is to find a partition into connected components such that each component contains only one center and the total service cost is minimum. This problem is known to be NP-hard on general graphs, and here we show that it remains such even if the service cost is monotone and the graph is bipartite. However, in this paper we derive some polynomial time algorithms for trees. For this class of graphs we provide several reformulations of the problem as integer linear programs proving the integrality of the corresponding polyhedra. As a consequence, the tree partitioning problem can be solved in polynomial time either by linear programming or by suitable convex nondifferentiable optimization algorithms. Moreover, we develop a dynamic programming algorithm, whose recursion is based on sequences of minimum weight closure problems, which solves the problem on trees in O(np) time

Gradient catastrophe and flutter in vortex filament dynamics

Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes motion of filament with slow varying curvature and torsion. Geometrically this catastrophe manifests as a rapid oscillation of a filament curve in a point that resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painlev\'e-I equation.Comment: 11 pages, 3 figures, typos corrected, references adde

Measurement of transverse momentum relative to dijet systems in PbPb and pp collisions at sqrt(s_NN) = 2.76 TeV

An analysis of dijet events in PbPb and pp collisions is performed to explore the properties of energy loss by partons traveling in a quark-gluon plasma. Data are collected at a nucleon-nucleon center-of-mass energy of 2.76 TeV at the LHC. The distribution of transverse momentum (p T) surrounding dijet systems is measured by selecting charged particles in different ranges of p T and at different angular cones of pseudorapidity and azimuth. The measurement is performed as a function of centrality of the PbPb collisions, the p T asymmetry of the jets in the dijet pair, and the distance parameter R used in the anti-k T jet clustering algorithm. In events with unbalanced dijets, PbPb collisions show an enhanced multiplicity in the hemisphere of the subleading jet, with the p T imbalance compensated by an excess of low-p T particles at large angles from the jet axes

Search for supersymmetry in electroweak production with photons and large missing transverse energy in pp collisions at sqrt(s) = 8 TeV

Results are reported from a search for supersymmetry with gauge-mediated supersymmetry breaking in electroweak production. Final states with photons and large missing transverse energy ( View the MathML sourceETmiss) were examined. The data sample was collected in pp collisions at View the MathML sources=8TeV with the CMS detector at the LHC and corresponds to 7.4View the MathML sourcefb−1. The analysis focuses on scenarios in which the lightest neutralino has bino- or wino-like components, resulting in decays to photons and gravitinos, where the gravitinos escape undetected. The data were obtained using a specially designed trigger with dedicated low thresholds, providing good sensitivity to signatures with photons, View the MathML sourceETmiss, and low hadronic energy. No excess of events over the standard model expectation is observed. The results are interpreted using the model of general gauge mediation. With the wino mass fixed at 10View the MathML sourceGeV above that of the bino, wino masses below 710View the MathML sourceGeV are excluded at 95% confidence level. Constraints are also set in the context of two simplified models, for which the analysis sets the lowest cross section limits on the electroweak production of supersymmetric particles

Stability of vortices in rotating taps: a 3d analysis

We study the stability of vortex-lines in trapped dilute gases subject to rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a 3d condensate in spherically and cilyndrically symmetric stationary traps, from small to very large nonlinearities. In the stationary case it is found that the vortex states with unit and $m=2$ charge are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1$ vortex-line, and that the multicharged vortices are never a local minimum of the energy functional, which implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value, $\Omega > \Omega_2$.Comment: 10 pages, 7 figures in EPS forma

Observation of top quark pairs produced in association with a vector boson in pp collisions at sqrt(s) = 8 TeV

Measurements of the cross sections for top quark pairs produced in association with a W or Z boson are presented, using 8TeV pp collision data corresponding to an integrated luminosity of 19.5 fb1, collected by the CMS experiment at the LHC. Final states are selected in which the associated W boson decays to a charged lepton and a neutrino or the Z boson decays to two charged leptons. Signal events are identied by matching reconstructed objects in the detector to specic nal state particles from ttW or ttZ decays. The ttW cross section is measured to be 382+117 102 fb with a signicance of 4.8 standard deviations from the background-only hypothesis. The ttZ cross section is measured to be 242+65 55 fb with a signicance of 6.4 standard deviations from the background-only hypothesis. These measurements are used to set bounds on ve anomalous dimension-six operators that would aect the ttW and ttZ cross sections

Search for standard model production of four top quarks in the lepton + jets channel in pp collisions at sqrt(s) = 8 TeV

A search is presented for standard model (SM) production of four top quarks (tt\uaftt\uaf) in pp collisions in the lepton + jets channel. The data correspond to an integrated luminosity of 19.6 fb 121 recorded at a centre-of-mass energy of 8 TeV with the CMS detector at the CERN LHC. The expected cross section for SM tt\uaftt\uaf production is \u3c3SMtt\uaftt\uaf 481fb. A combination of kinematic reconstruction and multivariate techniques is used to distinguish between the small signal and large background. The data are consistent with expectations of the SM, and an upper limit of 32 fb is set at a 95% confidence level on the cross section for producing four top quarks in the SM, where a limit of 32 \ub1 17 fb is expected

Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at sqrt(s) = 8 TeV

A search for new physics is performed in multijet events with large missing transverse momentum produced in proton-proton collisions at s√ = 8 TeV using a data sample corresponding to an integrated luminosity of 19.5 fb−1 collected with the CMS detector at the LHC. The data sample is divided into three jet multiplicity categories (3-5, 6-7, and ≥8 jets), and studied further in bins of two variables: the scalar sum of jet transverse momenta and the missing transverse momentum. The observed numbers of events in various categories are consistent with backgrounds expected from standard model processes. Exclusion limits are presented for several simplified supersymmetric models of squark or gluino pair production

Measurement of the W+W- cross section in pp collisions at sqrt(s) = 8 TeV and limits on anomalous gauge couplings

A measurement of the W boson pair production cross section in proton-proton collisions at $\sqrt{s} = 8$ TeV is presented. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 19.4$\,\text {fb}^\text {-1}$. The ${{\mathrm{W} }^{+} }\mathrm{W}^{-}$ candidates are selected from events with two charged leptons, electrons or muons, and large missing transverse energy. The measured ${{\mathrm{W} }^{+} }\mathrm{W}^{-}$ cross section is $60.1\pm 0.9\,\text {(stat)} \pm 3.2\,\text {(exp)} \pm 3.1\,\text {(theo)} \pm 1.6\,\text {(lumi)} \text {\,pb} = 60.1\pm 4.8\text {\,pb}$, consistent with the standard model prediction. The ${{\mathrm{W} }^{+} }\mathrm{W}^{-}$ cross sections are also measured in two different fiducial phase space regions. The normalized differential cross section is measured as a function of kinematic variables of the final-state charged leptons and compared with several perturbative QCD predictions. Limits on anomalous gauge couplings associated with dimension-six operators are also given in the framework of an effective field theory. The corresponding 95 % confidence level intervals are $-5.7< c_{\mathrm {WWW}}/\Lambda ^2 < 5.9\,\mathrm{TeV}^{-2}$, $-11.4< c_{\mathrm {W}}/\Lambda ^2 < 5.4\,\mathrm{TeV}^{-2}$, $-29.2< c_{\mathrm {B}}/\Lambda ^2 < 23.9\,\mathrm{TeV}^{-2}$, in the HISZ basis

Search for baryon number violation in top quark decays

A search for baryon number violation (BNV) in top-quark decays is performed using pp collisions produced by the LHC at View the MathML source. The top-quark decay considered in this search results in one light lepton (muon or electron), two jets, but no neutrino in the final state. Data used for the analysis were collected by the CMS detector and correspond to an integrated luminosity of 19.5 fb 121. The event selection is optimized for top quarks produced in pairs, with one undergoing the BNV decay and the other the standard model hadronic decay to three jets. No significant excess of events over the expected yield from standard model processes is observed. The upper limits at 95% confidence level on the branching fraction of the BNV top-quark decay are calculated to be 0.0016 and 0.0017 for the muon and the electron channels, respectively. Assuming lepton universality, an upper limit of 0.0015 results from the combination of the two channels. These limits are the first that have been obtained on a BNV process involving the top quark