The Complexity of Routing with Few Collisions

We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is whether one can connect the terminals by at least $p$ routes (e.g. paths) such that at most $k$ edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if $k$ is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary $k$ and on directed graphs if $k$ is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs

Restricting the Maximum Number of Actions for Decision Support Under Uncertainty

Standard approaches for decision support are computing a maximum expected utility or solving a partially observable Markov decision process. To the best of our knowledge, in both approaches, external restrictions are not accounted for. However, restrictions to actions often exists, for example in the form of limited resources. We demonstrate that restrictions to actions can lead to a combinatorial explosion if performed on a ground level, making ground inference intractable. Therefore, we extend a formalism that solves a lifted maximum expected utility problem to handle restricted actions. To test its relevance, we apply the new formalism to enterprise architecture analysis

Corrections to the SU(3)×SU(3){\bf SU(3)\times SU(3)} Gell-Mann-Oakes-Renner relation and chiral couplings L8rL^r_8 and H2rH^r_2

Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $\psi_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55 \pm 5)$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $\rho$-meson mass.Comment: Revised version with minor correction

Extended Generalized Feistel Networks using Matrix Representation

International audienceWhile Generalized Feistel Networks have been widely studied in the literature as a building block of a block cipher, we propose in this paper a unified vision to easily represent them through a matrix representation. We then propose a new class of such schemes called Extended Generalized Feistel Networks well suited for cryptographic applications. We instantiate those proposals into two particular constructions and we finally analyze their security

Measurement of the Dipion Mass Spectrum in X(3872) -> J/Psi Pi+ Pi- Decays

We measure the dipion mass spectrum in X(3872)--> J/Psi Pi+ Pi- decays using 360 pb-1 of pbar-p collisions at 1.96 TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C-parity (3S1, 1P1, and 3DJ) charmonia decaying to J/Psi Pi+ Pi-, as well as even C-parity states in which the pions are from Rho0 decay. The latter case also encompasses exotic interpretations, such as a D0-D*0Bar molecule. Only the 3S1 and J/Psi Rho hypotheses are compatible with our data. Since 3S1 is untenable on other grounds, decay via J/Psi Rho is favored, which implies C=+1 for the X(3872). Models for different J/Psi-Rho angular momenta L are considered. Flexibility in the models, especially the introduction of Rho-Omega interference, enable good descriptions of our data for both L=0 and 1.Comment: 7 pages, 4 figures -- Submitted to Phys. Rev. Let

Top Quark Mass Measurement from Dilepton Events at CDF II with the Matrix-Element Method

We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from $p\bar{p}$ collisions with $\sqrt s = 1.96$ TeV at the Fermilab Tevatron. The likelihood in top mass is calculated for each event by convoluting the leading order matrix element describing $q\bar{q} \to t\bar{t} \to b\ell\nu_{\ell}\bar{b}\ell'\nu_{\ell'}$ with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb$^{-1}$, we observe 33 candidate events and measure $M_{top} = 165.2 \pm 6.1(\textrm{stat.}) \pm 3.4(\textrm{syst.}) \mathrm{~GeV}/c^2.$ This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.Comment: 21 pages, 14 figure

Search for New Physics in Lepton + Photon + X Events with L=305 pb-1 of ppbar Collisions at roots=1.96 TeV

We present results of a search for anomalous production of events containing a charged lepton (either electron or muon) and a photon, both with high transverse momentum, accompanied by additional signatures, X, including missing transverse energy (MET) and additional leptons and photons. We use the same kinematic selection criteria as in a previous CDF search, but with a substantially larger data set, 305 pb-1, a ppbar collision energy of 1.96 TeV, and the upgraded CDF II detector. We find 42 Lepton+Photon+MET events versus a standard model expectation of 37.3 +- 5.4 events. The level of excess observed in Run I, 16 events with an expectation of 7.6 +- 0.7 events (corresponding to a 2.7 sigma effect), is not supported by the new data. In the signature of Multi-Lepton+Photon+X we observe 31 events versus an expectation of 23.0 +- 2.7 events. In this sample we find no events with an extra photon or MET and so find no events like the one ee+gg+MET event observed in Run I.Comment: 7 pages, 3 figures, 1 table. Accepted to PR