Distinguishing f(R) theories from general relativity by gravitational lensing effect

The post-Newtonian formulation of a general class of f(R) theories is set up to 3rd order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. Although the Yukawa potential is canceled in the 2nd order expression of the effective refraction index of light, detailed analysis shows that the difference of the lensing effect between the f(R) gravity and general relativity does appear at the 3rd order when $\sqrt{f''(0)/f'(0)}$ is larger than the distance $d_0$ to the gravitational source. However, the difference between these two kinds of theories will disappear in the axially symmetric spacetime region. Therefore only in very rare case the f(R) theories are distinguishable from general relativity by gravitational lensing effect at the 3rd order post-Newtonian approximation.Comment: 14 page

Lyα\alpha Leaks in the Absorption Spectra of High Redshift QSOs

Spectra of high redshift QSOs show deep Gunn-Peterson absorptions on the blue sides of the \Lya emissions lines. They can be decomposed into components called \Lya leaks, defined to be emissive regions in complementary to otherwise zero-fluxed absorption gaps. Just like \Lya absorption forests at low redshifts, \Lya leaks are both easy to find in observations and containing rich sets of statistical properties that can be used to study the early evolution of the IGM. Among all properties of a leak profile, we investigate its equivalent width in this paper, since it is weakly affected by instrumental resolution and noise. Using 10 Keck QSO spectra at $z\sim6$, we have measured the number density distribution function $n(W,z)$, defined to be the number of leaks per equivalent width $W$ and per redshift $z$, in the redshift range $5.4 - 6.0$. These new observational statistics, in both the differential and cumulative forms, fit well to hydro numerical simulations of uniform ionizing background in the $\Lambda$CDM cosmology. In this model, Ly $\alpha$ leaks are mainly due to low density voids. It supports the early studies that the IGM at $z\simeq6$ would still be in a highly ionized state with neutral hydrogen fraction $\simeq 10^{-4}$. Measurements of $n(W,z)$ at $z>6$ would be effective to probe the reionization of the IGM.Comment: 3 figs, accepted by ApJ

Covariant μˉ{\bar{\mu}}-scheme effective dynamics, mimetic gravity, and non-singular black holes: Applications to spherical symmetric quantum gravity and CGHS model

We propose a new $\bar{\mu}$-scheme Hamiltonian effective dynamics in the spherical symmetric sector of Loop Quantum Gravity (LQG). The effective dynamics is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in 4 dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the non-singular Loop-Quantum-Cosmology (LQC) effective dynamics. From the effective dynamics, we obtain the non-singular black hole solution, which has a killing symmetry in addition to the spherical symmetry and reduces to the Schwarzschild geometry asymptotically near the infinity. The black hole spacetime resolves the classical singularity and approaches asymptotically the Nariai geometry $\mathrm{dS}_2\times S^2$ at the future infinity in the interior of the black hole. The resulting black hole spacetime has the complete future null infinity $\mathscr{I}^+$. Thanks to the general covariance, the effective dynamics can be reformulated in the light-cone gauge. We generalize the covariant $\bar{\mu}$-scheme effective dynamics to the Callan-Giddings-Harvey-Strominger (CGHS) model and apply the light-cone formulation to the CGHS black hole solution with the null-shell collapse. We focus on the effective dynamics projected along the null shell. The result shows that both the 2d scalar curvature and the derivative of dilaton field are finite, in contrast to the divergence in the CGHS model.Comment: 49 pages, 23 figure

Throughput capacity of two-hop relay MANETs under finite buffers

Since the seminal work of Grossglauser and Tse [1], the two-hop relay algorithm and its variants have been attractive for mobile ad hoc networks (MANETs) due to their simplicity and efficiency. However, most literature assumed an infinite buffer size for each node, which is obviously not applicable to a realistic MANET. In this paper, we focus on the exact throughput capacity study of two-hop relay MANETs under the practical finite relay buffer scenario. The arrival process and departure process of the relay queue are fully characterized, and an ergodic Markov chain-based framework is also provided. With this framework, we obtain the limiting distribution of the relay queue and derive the throughput capacity under any relay buffer size. Extensive simulation results are provided to validate our theoretical framework and explore the relationship among the throughput capacity, the relay buffer size and the number of nodes

Understanding big consumer opinion data for market-driven product design

Big consumer data provide new opportunities for business administrators to explore the value to fulfil customer requirements (CRs). Generally, they are presented as purchase records, online behaviour, etc. However, distinctive characteristics of big data, Volume, Variety, Velocity and Value or ‘4Vs’, lead to many conventional methods for customer understanding potentially fail to handle such data. A visible research gap with practical significance is to develop a framework to deal with big consumer data for CRs understanding. Accordingly, a research study is conducted to exploit the value of these data in the perspective of product designers. It starts with the identification of product features and sentiment polarities from big consumer opinion data. A Kalman filter method is then employed to forecast the trends of CRs and a Bayesian method is proposed to compare products. The objective is to help designers to understand the changes of CRs and their competitive advantages. Finally, using opinion data in Amazon.com, a case study is presented to illustrate how the proposed techniques are applied. This research is argued to incorporate an interdisciplinary collaboration between computer science and engineering design. It aims to facilitate designers by exploiting valuable information from big consumer data for market-driven product design

Fermions in Loop Quantum Gravity and Resolution of Doubling Problem

The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity. As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the background geometry given by a coherent state resembling the classical Minkowski spacetime. Moreover, as a critical feature of loop quantum gravity, the superposition over graphs is employed to define the vacuum state. It turns out that the graph superposition leads to the propagator being the average of the propagators of the lattice field theory over various graphs so that all fermion doubler modes are suppressed in the propagator. This resolves the doubling problem in loop quantum gravity. Our result suggests that the superposition nature of quantum geometry should, on the one hand, resolve the tension between fermion and the fundamental discreteness and, on the other hand, relate to the continuum limit of quantum gravity.Comment: 25+9 pages, 2 figure