Modeling the Phase-Space Distribution around Massive Halos

The comparison between dynamical mass and lensing mass provides a targeted test for a wide range of modified gravity models. In our previous paper we showed, through numerical simulations, that the measurement of the line-of-sight velocity dispersion around stacked massive clusters whose lensing masses are known allows for stringent constraints on modified gravity on scales of 2 - 15 Mpc/h. In this work we develop a semi-analytical approach based on the halo model to describe the phase-space distribution and the line-of-sight velocity dispersion for different tracers. The model distinguishes contributions from the halo pairwise velocity and the virial velocity within halos. We also discuss observational complications, in particular the contribution from Hubble flow, and show how our model can incorporate these complications. We then incorporate the effects of modified gravity (specifically, f(R) and braneworld models), and show that the model predictions are in excellent agreement with modified gravity simulations. More broadly, the phase-space distribution provides a sensitive test of our understanding of hierarchical structure formation when confronted with observations via this model.Comment: 27 pages, 18 figures. To be submitte

Optimizing weak lensing mass estimates for cluster profile uncertainty

Weak lensing measurements of cluster masses are necessary for calibrating mass-observable relations (MORs) to investigate the growth of structure and the properties of dark energy. However, the measured cluster shear signal varies at fixed mass M_200m due to inherent ellipticity of background galaxies, intervening structures along the line of sight, and variations in the cluster structure due to scatter in concentrations, asphericity and substructure. We use N-body simulated halos to derive and evaluate a weak lensing circular aperture mass measurement M_ap that minimizes the mass estimate variance <(M_ap - M_200m)^2> in the presence of all these forms of variability. Depending on halo mass and observational conditions, the resulting mass estimator improves on M_ap filters optimized for circular NFW-profile clusters in the presence of uncorrelated large scale structure (LSS) about as much as the latter improve on an estimator that only minimizes the influence of shape noise. Optimizing for uncorrelated LSS while ignoring the variation of internal cluster structure puts too much weight on the profile near the cores of halos, and under some circumstances can even be worse than not accounting for LSS at all. We briefly discuss the impact of variability in cluster structure and correlated structures on the design and performance of weak lensing surveys intended to calibrate cluster MORs.Comment: 11 pages, 5 figures; accepted by MNRA

An Econometric Analysis of Loan Loss Provisioning Behaviour in Indian Commercial Banks

Given the raising concern on provisioning in the banking industry, this study aims at evaluating the loan loss provisioning behaviour among Indian commercial banks during the years 2007-2016. The study has been carried out in two stages. In the first stage, the cost efficiency of Indian banks is analysed. The second stage analyse the relationship among the four main hypotheses (namely capital management, business cycle, income smoothing and cost efficiency) and loan loss provisions (LLPs). Results of this study indicate that income smoothing and capital management behaviour through LLPs was not prevalent among Indian commercial banks during the period under review. In addition, no significant relationship is found between cost efficiency and LLPs in this study, which shows little evidence on bad management by Indian commercial banks. However, (i) counter-cyclicality; and (ii) a significant and positive relationship between bank size and LLPs are found from analysing the available data

The non-linear redshift space probability distribution function in models with local primordial non-Gaussianity

We use the ellipsoidal collapse approximation to investigate the non-linear redshift space evolution of the density field with primordial non-Gaussianity of the local fnl-type. We utilize the joint distribution of eigenvalues of the initial non-Gaussian shear field and evaluate the evolved redshift space probability distribution function (PDF). It is shown that, similar to the real space analysis, the underdense tail of the non-linear redshift space PDF differs significantly from that for Gaussian initial conditions. We also derive the lowest order correction of the Kaiser's formula in the presence of a non-zero fn

The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian fnl model. This is possible because, to at least second order in fnl, distributions at fixed overdensity are unchanged from the case fnl= 0. We use this generalization to estimate the effect of fnl≠ 0 on the abundance of virialized haloes. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity) or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on fnl. While a positive fnl produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianit

Cross-disciplinary collaboration through WuZhiQiao Project to foster cultural exchange and community engagement

In 2013, students of the Technological and Higher Education Institute of Hong Kong (THEi), with the support of WuZhiQiao (WZQ) Charitable Foundation, formed a core team of 11 students to organize and participate in social service projects to help the underprivileged in the Chinese mainland. WuZhiQiao (WZQ) projects, the first cross-region social service engagement by THEi students, bring together students from Hong Kong and the Mainland. WZQ Charitable Foundation aims to help the Chinese traditional village in building Pedestrian Bridge and organizing community projects. Since there are Chinese villages facing flooding during rainy seasons, the local villagers will be trapped inside the village without the chance to go outside or wade outside the village. There are hundreds of such villages and they highly need our help. Each project mainly involves two or three institutes from Hong Kong and the Mainland, and they organize the whole volunteer project including planning, investigation, design, promotion and operation. Through involvement in different states or provinces, WZQ projects provide good chance of communication and interaction between Hong Kong teams and the Mainland teams and advocate intercultural social services. The projects can foster the cultural exchange between Hong Kong and the Mainland. Moreover, the majority of WZQ project members are coming from the fields of engineering, architecture and health care. We can practice our learning from lectures through the project implementation. Different parties are involved in the engineering projects including clients, consultants, contractors, surveyors, engineers and workers. Engineering students can gain good understanding of the holistic picture of a real-life engineering project. We visited the location village for investigation to learn more about the local culture, geometry and the people’s needs and discussed with the Mainland Team through online chatting tools in order to propose the optimal pedestrian building design and other community projects. Having spent over six months in planning and preparation, THEi students will implement a bridge-building and community project in Chongqing in January 2015. Through engagement in this service-learning project, not only the undergraduates of THEi can benefit through personal development but the life quality of the disadvantaged can also be improved

Halo abundances and counts-in-cells: The excursion set approach with correlated steps

The Excursion Set approach has been used to make predictions for a number of interesting quantities in studies of nonlinear hierarchical clustering. These include the halo mass function, halo merger rates, halo formation times and masses, halo clustering, analogous quantities for voids, and the distribution of dark matter counts in randomly placed cells. The approach assumes that all these quantities can be mapped to problems involving the first crossing distribution of a suitably chosen barrier by random walks. Most analytic expressions for these distributions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. As a result, the problem is to estimate first crossing distribution by random walks having correlated rather than uncorrelated steps. In 1990, Peacock & Heavens presented a simple approximation for the first crossing distribution of a single barrier of constant height by walks with correlated steps. We show that their approximation can be thought of as a correction to the distribution associated with what we call smooth completely correlated walks. We then use this insight to extend their approach to treat moving barriers, as well as walks that are constrained to pass through a certain point before crossing the barrier. For the latter, we show that a simple rescaling, inspired by bivariate Gaussian statistics, of the unconditional first crossing distribution, accurately describes the conditional distribution, independently of the choice of analytical prescription for the former. In all cases, comparison with Monte-Carlo solutions of the problem shows reasonably good agreement. (Abridged)Comment: 14 pages, 9 figures; v2 -- revised version with explicit demonstration that the original conclusions hold for LCDM, expanded discussion on stochasticity of barrier. Accepted in MNRA