Minimization via duality

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object

Graphical models for interactive POMDPs: representations and solutions

We develop new graphical representations for the problem of sequential decision making in partially observable multiagent environments, as formalized by interactive partially observable Markov decision processes (I-POMDPs). The graphical models called interactive inf uence diagrams (I-IDs) and their dynamic counterparts, interactive dynamic inf uence diagrams (I-DIDs), seek to explicitly model the structure that is often present in real-world problems by decomposing the situation into chance and decision variables, and the dependencies between the variables. I-DIDs generalize DIDs, which may be viewed as graphical representations of POMDPs, to multiagent settings in the same way that IPOMDPs generalize POMDPs. I-DIDs may be used to compute the policy of an agent given its belief as the agent acts and observes in a setting that is populated by other interacting agents. Using several examples, we show how I-IDs and I-DIDs may be applied and demonstrate their usefulness. We also show how the models may be solved using the standard algorithms that are applicable to DIDs. Solving I-DIDs exactly involves knowing the solutions of possible models of the other agents. The space of models grows exponentially with the number of time steps. We present a method of solving I-DIDs approximately by limiting the number of other agents’ candidate models at each time step to a constant. We do this by clustering models that are likely to be behaviorally equivalent and selecting a representative set from the clusters. We discuss the error bound of the approximation technique and demonstrate its empirical performance

A deep cut ellipsoid algorithm for convex programming

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported

A survey of solution techniques for the partially observed Markov decision process

We survey several computational procedures for the partially observed Markov decision process (POMDP) that have been developed since the Monahan survey was published in 1982. The POMDP generalizes the standard, completely observed Markov decision process by permitting the possibility that state observations may be noise-corrupted and/or costly. Several computational procedures presented are convergence accelerating variants of, or approximations to, the Smallwood-Sondik algorithm. Finite-memory suboptimal design results are reported, and new research directions involving heuristic search are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44198/1/10479_2005_Article_BF02204836.pd

Search for the doubly heavy baryon Ξbc+\it{\Xi}_{bc}^{+} decaying to J/ψΞc+J/\it{\psi} \it{\Xi}_{c}^{+}

A first search for the $\it{\Xi}_{bc}^{+}\to J/\it{\psi}\it{\Xi}_{c}^{+}$ decay is performed by the LHCb experiment with a data sample of proton-proton collisions, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$ recorded at centre-of-mass energies of 7, 8, and $13\mathrm{\,Te\kern -0.1em V}$. Two peaking structures are seen with a local (global) significance of $4.3\,(2.8)$ and $4.1\,(2.4)$ standard deviations at masses of $6571\,\mathrm{Me\kern -0.1em V\!/}c^2$ and $6694\,\mathrm{Me\kern -0.1em V\!/}c^2$, respectively. Upper limits are set on the $\it{\Xi}_{bc}^{+}$ baryon production cross-section times the branching fraction relative to that of the $B_{c}^{+}\to J/\it{\psi} D_{s}^{+}$ decay at centre-of-mass energies of 8 and $13\mathrm{\,Te\kern -0.1em V}$, in the $\it{\Xi}_{bc}^{+}$ and in the $B_{c}^{+}$ rapidity and transverse-momentum ranges from 2.0 to 4.5 and 0 to $20\,\mathrm{Ge\kern -0.1em V\!/}c$, respectively. Upper limits are presented as a function of the $\it{\Xi}_{bc}^{+}$ mass and lifetime.Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-005.html (LHCb public pages

Study of the lineshape of the chi(c1) (3872) state

A study of the lineshape of the chi(c1) (3872) state is made using a data sample corresponding to an integrated luminosity of 3 fb(-1) collected in pp collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate chi(c1)(3872) and psi(2S) mesons from b-hadron decays are selected in the J/psi pi(+)pi(-) decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the chi(c1 )(3872) and psi(2S) states, Delta m, and the width of the chi(c1 )(3872) state, Gamma(Bw), are determined to be (Delta m=185.598 +/- 0.067 +/- 0.068 Mev,)(Gamma BW=1.39 +/- 0.24 +/- 0.10 Mev,) where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be (mode=3871.69+0.00+0.05 MeV.)(FWHM=0.22-0.04+0.13+0.07+0.11-0.06-0.13 MeV, ) An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasibound D-0(D) over bar*(0) state but a quasivirtual state is still allowed at the level of 2 standard deviations

Measurement of the CKM angle γγ in B±→DK±B^\pm\to D K^\pm and B±→Dπ±B^\pm \to D π^\pm decays with D→KS0h+h−D \to K_\mathrm S^0 h^+ h^-

A measurement of $CP$-violating observables is performed using the decays $B^\pm\to D K^\pm$ and $B^\pm\to D \pi^\pm$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K_{\mathrm S}\pi^+\pi^-$ and $K_{\mathrm S}K^+K^-$ (commonly denoted $K_{\mathrm S} h^+h^-$). The decays are analysed in bins of the $D$-decay phase space, leading to a measurement that is independent of the modelling of the $D$-decay amplitude. The observables are interpreted in terms of the CKM angle $\gamma$. Using a data sample corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$ collected in proton-proton collisions at centre-of-mass energies of $7$, $8$, and $13\,\text{TeV}$ with the LHCb experiment, $\gamma$ is measured to be $\left(68.7^{+5.2}_{-5.1}\right)^\circ$. The hadronic parameters $r_B^{DK}$, $r_B^{D\pi}$, $\delta_B^{DK}$, and $\delta_B^{D\pi}$, which are the ratios and strong-phase differences of the suppressed and favoured $B^\pm$ decays, are also reported

Study of the doubly charmed tetraquark T+cc

Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an exotic narrow state in the D0D0π+ mass spectrum just below the D*+D0 mass threshold produced in proton-proton collisions collected with the LHCb detector at the Large Hadron Collider. The state is consistent with the ground isoscalar T+cc tetraquark with a quark content of ccu⎯⎯⎯d⎯⎯⎯ and spin-parity quantum numbers JP = 1+. Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D*+ mesons is consistent with the observed D0π+ mass distribution. To analyse the mass of the resonance and its coupling to the D*D system, a dedicated model is developed under the assumption of an isoscalar axial-vector T+cc state decaying to the D*D channel. Using this model, resonance parameters including the pole position, scattering length, effective range and compositeness are determined to reveal important information about the nature of the T+cc state. In addition, an unexpected dependence of the production rate on track multiplicity is observed