Scrutinizing Various Phenomenological Interactions In The Context Of Holographic Ricci Dark Energy Models

In this paper, we examine two types of interacting holographic dark energy model using Pantheon supernova data, BAO BOSS DR12, CMB Planck 2015, fgas (gas mass fraction) and SZ/Xray (Sunyaev-Zeldovich effect and X-ray emission) data from galaxy clusters (GC). In particular, we considered the Holographic Ricci dark energy and Extended holographic Ricci dark energy models. During this analysis we considered seven type of phenomenological interaction terms (three linear and four non-linear) $Q_1=3Hb\rho_{D}$, $Q_2=3Hb\rho_{m}$, $Q_3=3Hb\left(\rho_{D}+\rho_m\right)$, $Q_4=3Hb\left(\rho_{D}+\frac{\rho_{D}^2}{\rho_{D}+\rho_m}\right)$, $Q_5=3Hb\left(\rho_{m}+\frac{\rho_{m}^2}{\rho_{D}+\rho_m}\right)$, $Q_6=3Hb\left(\rho_{D}+\rho_{m}+\frac{\rho_{D}^2}{\rho_{D}+\rho_m}\right)$, $Q_7=3Hb\left(\rho_{D}+\rho_{m}+\frac{\rho_{m}^2}{\rho_{D}+\rho_m}\right)$ respectively. To find the best model we apply Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) and use the $\Lambda$CDM as the referring model for comparison. Using AIC and BIC models selection method we note that the $Q_1$ and $Q_4$ interaction terms are favored by observational data within the context of the holographic Ricci dark energy models. The obtained results also demonstrated that the considered types of holographic Ricci dark energy model are not favored by observational data since the $\Lambda$CDM is considered as the reference model. We also observed that the values of the deceleration parameter and the transition redshift for all models are compatible with the latest observational data and Planck 2015. In addition, we studied the jerk parameter for all models. Using our modified CAMB code, we observed that the interacting models suppress the CMB spectrum at low multi-poles and enhances the acoustic peaks.Comment: 27 pages, 60 figure

Scalable First-Order Methods for Robust MDPs

Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves primal-dual first-order updates with approximate Value Iteration updates. By carefully controlling the tradeoff between the accuracy and cost of Value Iteration updates, we achieve an ergodic convergence rate of $O \left( A^{2} S^{3}\log(S)\log(\epsilon^{-1}) \epsilon^{-1} \right)$ for the best choice of parameters on ellipsoidal and Kullback-Leibler $s$-rectangular uncertainty sets, where $S$ and $A$ is the number of states and actions, respectively. Our dependence on the number of states and actions is significantly better (by a factor of $O(A^{1.5}S^{1.5})$) than that of pure Value Iteration algorithms. In numerical experiments on ellipsoidal uncertainty sets we show that our algorithm is significantly more scalable than state-of-the-art approaches. Our framework is also the first one to solve robust MDPs with $s$-rectangular KL uncertainty sets

Multimediator models for the galactic center gamma ray excess

Tentative evidence for excess GeV-scale gamma rays from the galactic center has been corroborated by several groups, including the Fermi collaboration, on whose data the observation is based. Dark matter annihilation into standard model particles has been shown to give a good fit to the signal for a variety of final state particles, but generic models are inconsistent with constraints from direct detection. Models where the dark matter annihilates to mediators that subsequently decay are less constrained. We perform global fits of such models to recent data, allowing branching fractions to all possible fermionic final states to vary. The best fit models, including constraints from the AMS-02 experiment (and also antiproton ratio), require branching primarily to muons, with a $\sim 10-20\%$ admixture of $b$ quarks, and no other species. This suggests models in which there are two scalar mediators that mix with the Higgs, and have masses consistent with such a decay pattern. The scalar that decays to $\mu^+\mu^-$ must therefore be lighter than $2m_\tau \cong 3.6$ GeV. Such a small mass can cause Sommerfeld enhancement, which is useful to explain why the best-fit annihilation cross section is larger than the value needed for a thermal relic density. For light mediator masses $\sim (0.2-2)$ GeV, it can also naturally lead to elastic DM self-interactions at the right level for addressing discrepancies in small structure formation as predicted by collisionless cold dark matter.Comment: 18 pages, 14 figures; v2: updated CMB constraint and added references; v3 corrected direct detection cross sectio

Pricing firms on the basis of fundamentals

Determining the right or fair price of a stock is one of the oldest problems in finance. Business mergers and acquisitions rely on this information, but only in the last several decades have formal models been developed to address the question. This article focuses on fundamental valuation, a technique that determines the right price by forecasting cash flows from a stock market investment and calculating what that income is worth. ; The author first provides an overview of the literature and an illustration of commonly used fundamental valuation techniques based on relative valuation and the Gordon growth model and then discusses a valuation approach he developed in 2001. His work incorporates the proceeds from share liquidation into the cash flows that are used to value the firm, accounting for the reduction in future growth of cash flows from this liquidation of shares. The author demonstrates these methods by applying them to pricing BellSouth shares, the S&P 500 index, and some new-economy stocks. The discussion also looks at prices and estimated fundamental values during severe market turndowns. ; Pricing BellSouth using sales and sales growth is consistent with its dramatic rise and recent decline in price, the author finds; this method is also appropriate for a small group of high-growth stocks. Fundamental models, however, have more trouble explaining the price movements of the overall market. The author concludes that algorithmic valuation techniques provide, at best, a rough starting point for firm valuation.Asset pricing

An Experimental Test of the Global-Game Selection in Coordination Games with Asymmetric Players

In symmetric binary-choice coordination games, the global-game selection (GGS) has been proven to predict a high proportion of observed choices correctly. In these games, the GGS is identical to the best response to Laplacian beliefs about the fraction of players choosing either action. This paper presents an experiment on asymmetric games in which the GGS differs from the best response to Laplacian beliefs. It shows that the best response to Laplacian beliefs is a better predictor of behavior in these games than the GGS. In the considered games, the GGS provides poor guidance and also fails to give the right qualitative comparative statics predictions. Simple cognitive hierarchy models yield better predictions. The best response to a Laplacian belief about the distribution of other players' actions yields the best prediction. Comparing maximum likelihood estimates for four probabilistic models shows that an estimated global-game equilibrium fits worse than a rather simple level-k or Laplacian-belief model combined with a standard error-response function