A decomposition approach for undiscounted two-person zero-sum stochastic games

Abstract. Two-person zero-sum stochastic games are considered under the long-run average expected payo¨criterion. State and action spaces are assumed ®nite. By making use of the concept of maximal communicating classes, the following decomposition algorithm is introduced for solving twoperson zero-sum stochastic games: First, the state space is decomposed into maximal communicating classes. Then, these classes are organized in an hierarchical order where each level may contain more than one maximal communicating class. Best stationary strategies for the states in a maximal communicating class at a level are determined by using the best stationary strategies of the states in the previous levels that are accessible from that class. At the initial level, a restricted game is de®ned for each closed maximal communicating class and these restricted games are solved independently. It is shown that the proposed decomposition algorithm is exact in the sense that the solution obtained from the decomposition procedure gives the best stationary strategies for the original stochastic game

Measurement of the double-differential inclusive jet cross section in proton-proton collisions at s\sqrt{s} = 5.02 TeV

International audienceThe inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$

Search for pair production of excited top quarks in the lepton + jets final state

A search is performed for the pair production of spin-3/2 excited top quarks, each decaying to a top quark and a gluon. The search uses the data collected with the CMS detector from proton–proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1 . Events are selected by requiring an isolated muon or electron, an imbalance in the transverse momentum, and at least six jets of which exactly two must be compatible with originating from the fragmentation of a bottom quark. No significant excess over the standard model predictions is found. A lower limit of 1.2 TeV is set at 95% confidence level on the mass of the spin-3/2 excited top quark in an extension of the Randall–Sundrum model, assuming a 100% branching fraction of its decay into a top quark and a gluon. These are the best limits to date in a search for excited top quarks and the first at 13 TeV

Measurement of the double-differential inclusive jet cross section in proton-proton collisions at s= \sqrt{s} = 5.02 TeV

The inclusive jet cross section is measured as a function of jet transverse momentum $p_{\mathrm{T}}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s} =$ 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4$\,\text{pb}^{-1}$. The jets are reconstructed with the anti-$k_{\mathrm{T}}$ algorithm using a distance parameter of $R=$ 0.4, within the rapidity interval $|y| <$ 2, and across the kinematic range 0.06 $< p_{\mathrm{T}} <$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$.The inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$

Measurement of the double-differential inclusive jet cross section in proton-proton collisions at s\sqrt{s} = 5.02 TeV

International audienceThe inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$

Search for pair production of excited top quarks in the lepton+jets final state

A search is performed for the pair production of spin-3/2 excited top quarks, each decaying to a top quark and a gluon. The search uses the data collected with the CMS detector from proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Events are selected by requiring an isolated muon or electron, an imbalance in the transverse momentum, and at least six jets of which exactly two must be compatible with originating from the fragmentation of a bottom quark. No significant excess over the standard model predictions is found. A lower limit of 1.2 TeV is set at 95% confidence level on the mass of the spin-3/2 excited top quark in an extension of the Randall-Sundrum model, assuming a 100% branching fraction of its decay into a top quark and a gluon. These are the best limits to date in a search for excited top quarks and the first at 13 TeV

Measurement of the double-differential inclusive jet cross section in proton-proton collisions at s\sqrt{s} = 5.02 TeV

International audienceThe inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$

Measurement of the double-differential inclusive jet cross section in proton-proton collisions at s\sqrt{s} = 5.02 TeV

International audienceThe inclusive jet cross section is measured as a function of jet transverse momentum $p_\mathrm{T}$ and rapidity $y$. The measurement is performed using proton-proton collision data at $\sqrt{s}$ = 5.02 TeV, recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 27.4 pb$^{-1}$. The jets are reconstructed with the anti-$k_\mathrm{T}$ algorithm using a distance parameter of $R$ = 0.4, within the rapidity interval $\lvert y\rvert$$\lt$ 2, and across the kinematic range 0.06 $\lt$$p_\mathrm{T}$$\lt$ 1 TeV. The jet cross section is unfolded from detector to particle level using the determined jet response and resolution. The results are compared to predictions of perturbative quantum chromodynamics, calculated at both next-to-leading order and next-to-next-to-leading order. The predictions are corrected for nonperturbative effects, and presented for a variety of parton distribution functions and choices of the renormalization/factorization scales and the strong coupling $\alpha_\mathrm{S}$