Stochastic Bandits with Delay-Dependent Payoffs

Motivated by recommendation problems in music streaming platforms, we propose a nonstationary stochastic bandit model in which the expected reward of an arm depends on the number of rounds that have passed since the arm was last pulled. After proving that finding an optimal policy is NP-hard even when all model parameters are known, we introduce a class of ranking policies provably approximating, to within a constant factor, the expected reward of the optimal policy. We show an algorithm whose regret with respect to the best ranking policy is bounded by Oe 1a kT , where k is the number of arms and T is time. Our algorithm uses only O k ln ln T) switches, which helps when switching between policies is costly. As constructing the class of learning policies requires ordering the arms according to their expectations, we also bound the number of pulls required to do so. Finally, we run experiments to compare our algorithm against UCB on different problem instance

Optical response of a misaligned and suspended Fabry-Perot cavity

The response to a probe laser beam of a suspended, misaligned and detuned optical cavity is examined. A five degree of freedom model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product $\varpi \tau$ of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility.Comment: 14 pages (4 figures) submitted to Phys. Rev.

Rare radiative B decays to orbitally excited K mesons

The exclusive rare radiative B meson decays to orbitally excited axial-vector mesons K_1^*(1270), K_1(1400) and to the tensor meson K_2^*(1430) are investigated in the framework of the relativistic quark model based on the quasipotential approach in quantum field theory. These decays are considered without employing the heavy quark expansion for the s quark. Instead the s quark is treated to be light and the expansion in inverse powers of the large recoil momentum of the final K^{**} meson is used to simplify calculations. It is found that the ratio of the branching fractions of rare radiative B decays to axial vector K^*_1(1270) and K_1(1400) mesons is significantly influenced by relativistic effects. The obtained results for B decays to the tensor meson K_2^*(1430) agree with recent experimental data from CLEO.Comment: 17 pages, revte

Association between the multidimensional prognostic index and mortality during 15 Years of Follow-up in the InCHIANTI Study

Background: Multidimensional Prognostic Index (MPI) is recognized as a prognostic tool in hospitalized patients, but data on the value of MPI in community-dwelling older persons are limited. Using data from a representative cohort of community-dwelling persons, we tested the hypothesis that MPI explains mortality during 15 years of follow-up. Methods: A standardized comprehensive geriatric assessment was used to calculate the MPI and to categorize participants in low-, moderate-, and high-risk classes. The results were reported as hazard ratios (HRs) and the accuracy was evaluated with the area under the curve (AUC), with 95% confidence intervals (CIs) and the C-index. We also reported the median survival time by standard age groups. Results: All 1453 participants (mean age 68.9 years, women = 55.8%) enrolled in the InCHIANTI study at baseline were included. Compared to low-risk group, participants in moderate (HR = 2.10; 95% CI: 1.73-2.55) and high-risk MPI group (HR = 4.94; 95% CI: 3.91-6.24) had significantly higher mortality risk. The C-index of the model containing age, sex, and MPI was 82.1, indicating a very good accuracy of this model in explaining mortality. Additionally, the time-dependent AUC indicated that the accuracy of the model incorporating MPI to age and sex was excellent (>85.0) during the whole follow-up period. Compared to participants in the low-risk MPI group across different age groups, those in moderate- and high-risk groups survived 2.9-7.0 years less and 4.3-8.9 years less, respectively. Conclusions: In community-dwelling individuals, higher MPI values are associated with higher risk of all-cause mortality with a dose-response effect. © 2020 The Author(s) 2020

Exclusive B --> K^* l^+ l^-$ decay in the three Higgs doublet model

We study the differential Branching ratio and CP asymmetry for the exclusive decay B --> K^* l^+ l^- in the three Higgs doublet model with additional global O(2) symmetry in the Higgs sector. We analyse dilepton mass square q^2 dependency of the these quantities. Further, we study the effect of new parameter of the global symmetry in the Higgs sector on the differential branching ratio and CP asymmetry. We see that there exist an enhancement in the branching ratio and a considerable CP violation for the relevant process. In addition to this, we realize that fixing dilepton mass gives information about the sign of the Wilson coefficient C_7^{eff}.Therefore, the future measurements of the CP asymmetry for B\to K^* l^+ l^- decay will give a powerful information about the sign of Wilson coefficient C_{7}^{eff} and new physics beyond the SM.Comment: 19 pages, 6 figure

The CP asymmetry for B--> K^* l^+ l^- decay in the general two Higgs doublet model

We study CP asymmetry for the exclusive decay B --> K^* l^+ l^- in the two Higgs doublet model with three level flavor changing neutral currents (model III). We analyse the dependency of this quantity to the new phase coming from the complex Yukawa couplings in the theory and we find that there exist a considerable CP violation for the relevant process. Further, we see that the sign of the Wilson coefficient C_7^{eff} can be determined by fixing dilepton mass. Therefore, the future measurements of CP asymmetry for B --> K^* l^+ l^- decay will give a powerful information about the sign of Wilson coefficient C_{7}^{eff} and the new physics beyond the SM.Comment: 22 pages, 8 figure

Constraints From b→sγb \to s\gamma on the Left-Right Symmetric Model

Recent results from the CLEO Collaboration on both inclusive and exclusive radiative $B$ decays are used to constrain the parameter space of two versions of the Left-Right Symmetric Model. In the first scenario, when the left- and right-handed Cabibbo-Kobayashi-Maskawa mixing matrices are equal, $V_L=V_R$, the radiative $B$ decay data is shown to lead to strong bounds on the $W_L-W_R$ mixing angle that are quite insensitive to either the top quark or $W_R$ mass. The second scenario examined is that of Gronau and Wakaizumi wherein $b$-quark decays proceed only via right-handed currents and $V_L$ and $V_R$ are quite distinct. For this model, the combined constraints from Tevatron $W_R$ searches, the $B$ lifetime, and radiative $B$ decays lead to a very highly restricted allowed range for the $W_L-W_R$ mixing angle.Comment: 16 pages, 9 figures(not included), LaTex, SLAC-PUB-642