A Comparison of Simple Mass Estimators for Galaxy Clusters

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass m_p \simeq 10^{10} \Msun, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

Lagrangian Perturbation Theory : Exact One-Loop Power Spectrum in General Dark Energy Models

Recently, we find that the correction for the EdS assumption on the one-loop matter power spectrum for general dark energy models using the standard perturbation theory is not negligible \cite{LPB}. Thus, we investigate the same problem by obtaining the exact displacement vector and kernels up to the third order for the general dark energy models in the Lagrangian perturbation theory (LPT). Using these exact solutions, we investigate the present one-loop matter power spectrum in the $\Lambda$CDM model with $\Omega_{m0} = 0.25 (0.3)$ to obtain about 0.2 (0.18) \% error correction compared to that obtained from the EdS assumption for $k = 0.1 \rm{h\, Mpc}^{-1}$ mode. If we consider the total matter power spectrum, the correction is only 0.05 (0.03) \% for the same mode. It means that EdS assumption is a good approximation for $\Lambda$CDM model in LPT theory. However, one can use this method for general models where EdS assumption is improper.Comment: 7 pages, 3 figure

Theoretical correction to the neutral B0B^0 meson asymmetry

Certain types of asymmetries in neutral meson physics have not been treated properly, ignoring the difference of normalization factors with an assumption of the equality of total decay width. Since the corrected asymmetries in $B^0$ meson are different from known asymmetries by a shift in the first order of CP- and CPT-violation parameters, experimental data should be analyzed with the consideration of this effect as in $K^0$ meson physics.Comment: 7 page

A single buyer-single supplier bargaining problem with asymmetric information : theoretical approach and software implementation

This paper is focused on the coordination of order and production policy between buyers and suppliers in supply chains. When a buyer and a supplier of an item work independently, the buyer will place orders based on his economic order quantity (EOQ). However, the buyer s EOQ may not lead to an optimal policy for the supplier. It can be shown that a cooperative batching policy can reduce total cost significantly. Should the buyer have the more powerful position to enforce his EOQ on the supplier, then no incentive exists for him to deviate from his EOQ in order to choose a cooperative batching policy. To provide an incentive to order in quantities suitable to the supplier, the supplier could offer a side payment. One critical assumption made throughout in the literature dealing with incentive schemes to influence buyer s ordering policy is that the supplier has complete information regarding buyer s cost structure. However, this assumption is far from realistic. As a consequence, the buyer has no incentive to report truthfully on his cost structure. Moreover there is an incentive to overstate the total relevant cost in order to obtain as high a side payment as possible. This paper provides a bargaining model with asymmetric information about the buyer s cost structure assuming that the buyer has the bargaining power to enforce his EOQ on the supplier in case of a break-down in negotiations. An algorithm for the determination of an optimal set of contracts which are specifically designed for different cost structures of the buyer, assumed by the supplier, will be presented. This algorithm was implemented in a software application, that supports the supplier in determining the optimal set of contracts

Fast and Robust Rank Aggregation against Model Misspecification

In rank aggregation, preferences from different users are summarized into a total order under the homogeneous data assumption. Thus, model misspecification arises and rank aggregation methods take some noise models into account. However, they all rely on certain noise model assumptions and cannot handle agnostic noises in the real world. In this paper, we propose CoarsenRank, which rectifies the underlying data distribution directly and aligns it to the homogeneous data assumption without involving any noise model. To this end, we define a neighborhood of the data distribution over which Bayesian inference of CoarsenRank is performed, and therefore the resultant posterior enjoys robustness against model misspecification. Further, we derive a tractable closed-form solution for CoarsenRank making it computationally efficient. Experiments on real-world datasets show that CoarsenRank is fast and robust, achieving consistent improvement over baseline methods

The cyclical volatility of labor markets under frictional financial markets

This paper shows in an economy with search on credit and labor markets that a financial multiplier raises the elasticity of labor market tightness to productivity shocks, and that this multiplier is an increasing function of total financial costs in the economy. Under a credit market Hosios-Pissarides rule, total search costs in the credit market are minimized, and so is the financial multiplier. Relaxing that condition leads to larger multipliers which can match or even overshoot the elasticity of market tightness in the data. The reason is similar to that of Hagedorn and Manovskii (2008) small labor surplus assumption: we identify the configurations of parameters leading to small "bank" surplus or a small "firm surplus" in the credit market, conducive of an amplification of productivity shocks. Furthermore, when wages are endogenous, it is possible to partially relax the small labor surplus assumption in order to match the data.